From b9653a0e3e9bc17989143b52980975ca5f10506f Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabrielhrsantos@gmail.com>
Date: Fri, 8 May 2020 09:59:49 -0300
Subject: [PATCH 01/30] fix bug in stepEquilibria maxRow/maxCol

---
 .../explicit/CSGModelCheckerEquilibria.java   | 30 +++++++++++++++++--
 1 file changed, 28 insertions(+), 2 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 10fb3839a..f1de64dbe 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -2035,6 +2035,12 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 			if (!(zeroA && zeroB)) {
 				result = new double[1][2];
 				if(bMaxRow || bMaxCol) {
+					double v1 = Double.NEGATIVE_INFINITY;
+					double v2 = Double.NEGATIVE_INFINITY;
+					double vsum = Double.NEGATIVE_INFINITY; 
+					double tv1 = Double.NEGATIVE_INFINITY;
+					double tv2 = Double.NEGATIVE_INFINITY;
+					double tvsum = Double.NEGATIVE_INFINITY;  
 					if (zeroA) {
 						mIndxs = findMaxIndexes(val2s);
 						mrow = mIndxs[0];
@@ -2051,11 +2057,31 @@ else if (bMaxRow && bMaxCol) {
 					} 
 					else if (bMaxRow) {
 						mrow = maxRow[0];
-						mcol = getMaxIndex(val2s[mrow]);
+						mcol = -1;
+						for (int c = 0; c < ncols; c++) {
+							tv1 = val1s[mrow][c];
+							tv2 = val2s[mrow][c];
+							tvsum = tv1 + tv2;
+							if (Double.compare(tv2, v2) > 0 || (Double.compare(tv2, v2) == 0 && Double.compare(tvsum, vsum) > 0)) {
+					 			mcol = c;
+								v2 = tv2;
+								vsum = tvsum;
+							}       
+						}
 					}
 					else {
+						mrow = -1;
 						mcol = maxCol[0];
-						mrow = getMaxIndex(getCol(val1s, mcol));
+						for (int r = 0; r < nrows; r++) {
+							tv1 = val1s[r][mcol];
+							tv2 = val2s[r][mcol];
+							tvsum = tv1 + tv2;
+							if (Double.compare(tv1, v1) > 0 || (Double.compare(tv1, v1) == 0 && Double.compare(tvsum, vsum) > 0)) {
+								mrow = r;
+								v1 = tv1;
+								vsum = tvsum;
+							}       
+						}
 					}
 					result[0][0] = val1s[mrow][mcol];
 					result[0][1] = val2s[mrow][mcol];

From 011495d907f11755f712524e74fad0a3aa0eb8ba Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabrielhrsantos@gmail.com>
Date: Sat, 23 May 2020 16:51:01 -0300
Subject: [PATCH 02/30] Adds switch for scale factor used when building lps for
 zero-sum model checking.

---
 prism/src/explicit/CSGModelChecker.java |  8 +++++---
 prism/src/prism/PrismSettings.java      | 25 +++++++++++++++++++++++--
 2 files changed, 28 insertions(+), 5 deletions(-)

diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index 9c4d7a848..e3c45f9e9 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -81,6 +81,7 @@
 import prism.PrismLangException;
 import prism.PrismLog;
 import prism.PrismUtils;
+import prism.PrismSettings;
 import strat.CSGStrategy;
 import strat.CSGStrategy.CSGStrategyType;
 import strat.MDStrategyArray;
@@ -106,6 +107,7 @@ public class CSGModelChecker extends ProbModelChecker {
 	protected double[] avgNumActions;
 	
 	protected double minEntry; 
+	protected double scaleFactor = getSettings().getDouble(PrismSettings.PRISM_ZS_LP_SCALE_FACTOR);
 	
 	protected int numCoalitions;
 	protected int numPlayers;
@@ -561,14 +563,14 @@ public void buildLPLpsolve(LpSolve lp, ArrayList<ArrayList<Double>> mgame, boole
 		// Builds each column considering the n + 1 constraints as a matrix
 		for (int j = 0; j < ncols; j++) {
 			vari[k] = 1;
-			row[k] = 1.0;
+			row[k] = scaleFactor;
 			for(int i = 0; i < nrows; i++) {
 				k++;
 				vari[k] = k+1;
 				if (min)
-					row[k] = -1.0 * mgame.get(j).get(i); 
+					row[k] = -1.0 * scaleFactor * mgame.get(j).get(i); 
 				else
-					row[k] = -1.0 * mgame.get(i).get(j); 
+					row[k] = -1.0 * scaleFactor * mgame.get(i).get(j); 
 			}
 			if (min)
 				lp.addConstraintex(nrows+1, row, vari, LpSolve.GE, 0.0);
diff --git a/prism/src/prism/PrismSettings.java b/prism/src/prism/PrismSettings.java
index 94d361924..764923a60 100644
--- a/prism/src/prism/PrismSettings.java
+++ b/prism/src/prism/PrismSettings.java
@@ -124,6 +124,9 @@ public class PrismSettings implements Observer
 	public static final	String PRISM_PARETO_EPSILON					= "prism.paretoEpsilon";
 	public static final	String PRISM_EXPORT_PARETO_FILENAME			= "prism.exportParetoFileName";
 
+	// csg and equilibria
+	public static final String PRISM_ZS_LP_SCALE_FACTOR			= "prism.lpscalefactor";
+
     // multi-objective synthesis for games
 	public static final     String PRISM_MULTI_GAUSS_SEIDEL					= "prism.multiGaussSeidel";
         // iteration control
@@ -348,7 +351,9 @@ public class PrismSettings implements Observer
 																			"Value iteration starts computing points rounded to the maximum reward in each dimension divided by the baseline accuracy, and this accuracy is increased by the increase factor after every iteration." },
 			{ DOUBLE_TYPE,		PRISM_MULTI_INCREASE_FACTOR,					"Increase factor for conjunctive query value iteration",			"4.0.3",			new Double(1.01),															"0,",																						
 																			"Accuracy of conjunctive query value iteration is increased by the increase factor after every iteration." },
-
+			// CSG ZERO-SUM LP SCALE FACTOR
+			{ DOUBLE_TYPE,		PRISM_ZS_LP_SCALE_FACTOR, 					"Scale factor for LPs",			"4.5", 				new Double(1.0), 			"1,",
+																			"Scale factor used when building linear programs for solving matrix games"},
 
 			// OUTPUT OPTIONS:
 			{ BOOLEAN_TYPE,		PRISM_VERBOSE,							"Verbose output",						"2.1",		new Boolean(false),															"",																							
@@ -1142,6 +1147,20 @@ else if (sw.equals("power") || sw.equals("pow") || sw.equals("pwr")) {
 			set(PRISM_MDP_SOLN_METHOD, "Linear programming");
 			set(PRISM_MDP_MULTI_SOLN_METHOD, "Linear programming");
 		}
+		else if (sw.equals("lpscalefactor")) {// Scale factor for LPs (zero-sum)
+			if (i < args.length - 1) {
+				try {
+					d = Double.parseDouble(args[++i]);
+					if (Double.compare(d, 1.0) < 0)
+						throw new NumberFormatException("");
+					set(PRISM_ZS_LP_SCALE_FACTOR, d);
+				} catch (NumberFormatException e) {
+					throw new PrismException("Invalid value for -" + sw + " switch");
+				}
+			} else {
+				throw new PrismException("No value specified for -" + sw + " switch");
+			}
+		}
 
 		// Interval iterations
 		else if (sw.equals("intervaliter") ||
@@ -2021,7 +2040,6 @@ public static void printHelp(PrismLog mainLog)
 		mainLog.println("-ltl2dasyntax <x> .............. Specify output format for -ltl2datool switch (lbt, spin, spot, rabinizer)");
 		mainLog.println("-exportiterations .............. Export vectors for iteration algorithms to file");
 		mainLog.println("-pmaxquotient .................. For Pmax computations in MDPs, compute in the MEC quotient");
-		
 		mainLog.println();
 		mainLog.println("MULTI-OBJECTIVE MODEL CHECKING:");
 		mainLog.println("-linprog (or -lp) .............. Use linear programming for multi-objective model checking");
@@ -2043,6 +2061,9 @@ public static void printHelp(PrismLog mainLog)
 		mainLog.println("-baselineaccuracy <n> .......... Baseline accuracy for CQs.");
 		mainLog.println("-increasefactor <x> ............ Factor by which accuracy is increased every iteration for CQs.");
 		mainLog.println();
+		mainLog.println("CSG EQUILIBRIA COMPUTATION");
+		mainLog.println("-lpscalefactor <n> ............. Scale factor used when building linear programs for solving matrix games [default: 1.0]");
+		mainLog.println();
 		mainLog.println("OUTPUT OPTIONS:");
 		mainLog.println("-verbose (or -v) ............... Verbose mode: print out state lists and probability vectors");
 		mainLog.println("-extraddinfo ................... Display extra info about some (MT)BDDs");

From fd00c2fcba69ea438bf1dc244fe096622d815b9a Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabrielhrs@users.noreply.github.com>
Date: Wed, 28 Oct 2020 23:29:35 +0000
Subject: [PATCH 03/30] Fix bug with equilibria (unique row/column)

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index f1de64dbe..64493f98d 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1950,13 +1950,14 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 				bMaxRow = allEqual(maxRow);
 				if (bMaxRow) {
 					int maxr = maxRow[0];
+					/*
 					if (maxr != 0) {	
 						for (int r = 0; r < nrows; r++) { // is this actually needed?
 							if (r != maxr) 
 								uRow = uRow && !Arrays.equals(val1s[r], val1s[maxRow[0]]);
 						}	 
 					}
-					else {
+					else {*/
 						for (int r = 0; r < nrows; r++) { 
 							if (r != maxr) {
 								for (int c = 0; c < ncols; c++) {
@@ -1965,7 +1966,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 								}
 							}
 						} 
-					}
+					//}
 				}
 				bMaxRow = bMaxRow && uRow; // maximal and unique
 				
@@ -1992,6 +1993,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 				bMaxCol = allEqual(maxCol);
 				if(bMaxCol) {
 					int maxc = maxCol[0];
+					/*
 					if (maxc != 0) {
 						for (int c = 0; c < ncols; c++) { // is this actually needed?
 							if (c != maxc) {
@@ -1999,7 +2001,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 							}
 						}
 					}
-					else {
+					else {*/
 						for (int c = 0; c < ncols; c++) { // is this actually needed?
 							if (c != maxc) {
 								for (int r = 0; r < nrows; r++) {
@@ -2008,7 +2010,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 								}
 							}
 						} 
-					}
+					//}
 				}
 				bMaxCol = bMaxCol && uCol; // maximal and unique
 				

From da4146c44e032cc3c97a7193fbfb776cd1c02809 Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabrielhrsantos@gmail.com>
Date: Wed, 24 Mar 2021 16:59:19 +0000
Subject: [PATCH 04/30] small fixes (including next operator)

---
 prism/src/explicit/CSGLabeledPolytopesZ3.java |  2 +-
 .../explicit/CSGLabeledPolytopesZ3Push.java   |  2 +-
 prism/src/explicit/CSGModelChecker.java       |  8 ++--
 .../explicit/CSGModelCheckerEquilibria.java   | 38 ++++++++++++++++---
 prism/src/explicit/ProbModelChecker.java      |  4 +-
 5 files changed, 40 insertions(+), 14 deletions(-)

diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3.java b/prism/src/explicit/CSGLabeledPolytopesZ3.java
index 673488473..ddfe8d9d1 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3.java
@@ -561,7 +561,7 @@ public double getDoubleValue(Model model, Expr expr) {
 		}
 		else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 			v2 = (AlgebraicNum) model.getConstInterp(expr);
-			v1 = v2.toUpper(9);
+			v1 = v2.toUpper(12);
 			return (Double) (v1.getBigIntNumerator().doubleValue() / v1.getBigIntDenominator().doubleValue());
 		}
 		else
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3Push.java b/prism/src/explicit/CSGLabeledPolytopesZ3Push.java
index e5335c194..76722f62e 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3Push.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3Push.java
@@ -323,7 +323,7 @@ public double getDoubleValue(Model model, Expr expr) {
 		}
 		else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 			v2 = (AlgebraicNum) model.getConstInterp(expr);
-			v1 = v2.toUpper(9);
+			v1 = v2.toUpper(12);
 			return (Double) (v1.getBigIntNumerator().doubleValue() / v1.getBigIntDenominator().doubleValue());
 		}
 		else
diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index e3c45f9e9..7f258e61f 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -324,7 +324,9 @@ public BitSet G(CSG csg, BitSet b) throws PrismException {
 		return x;
 	}
 	
-	public void buildCoalitions(CSG csg, Coalition coalition, boolean min) throws PrismLangException {
+	public void buildCoalitions(CSG csg, Coalition coalition, boolean min) throws PrismException {
+		if (coalition == null || coalition.isEmpty())
+			throw new PrismException("Coalitions must not be empty");
 		int p;
 		numPlayers = csg.getNumPlayers();
 		coalitionIndexes = new BitSet[2];
@@ -1540,10 +1542,10 @@ public ModelCheckerResult computeCumulativeRewards(CSG csg, CSGRewards csgReward
 		return res;
 	}
 	
-	public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, int[] bounds, boolean min) throws PrismException {
+	public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<ExpressionTemporal> exprs, BitSet[] targets, BitSet[] remain, int[] bounds, boolean min) throws PrismException {
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeBoundedEquilibria(csg, coalitions, null, null, targets, remain, bounds, min);
+		res = csgeq.computeBoundedEquilibria(csg, coalitions, null, exprs, targets, remain, bounds, min);
 		return res;		
 	}
 	
diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 52771bf28..6591767c8 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -136,7 +136,9 @@ public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		// eqssmt = new CSGSupportEnumerationIpopt();
 	}
 
-	public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismLangException {
+	public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismException {
+		if (coalitions == null || coalitions.isEmpty())
+			throw new PrismException("Coalitions must not be empty");
 		int c, p, all;
 		all = 0;
 		numPlayers = csg.getNumPlayers();
@@ -574,10 +576,36 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		long currentTime, timePrecomp;		
 		
 		rew = rewards != null;
-		pindx.set(0, numCoalitions);
+		pindx.set(0, numCoalitions); // review this
+		buildCoalitions(csg, coalitions);
+		
+		// Case next
+		if ((exprs.get(0).getOperator() == ExpressionTemporal.P_X) || (exprs.get(1).getOperator() == ExpressionTemporal.P_X)) {
+			for (i = 0; i < 2; i++) {
+				if (exprs.get(i).getOperator() == ExpressionTemporal.P_X) {
+					for (s = 0; s < csg.getNumStates(); s++) {
+						sol[i][s] = targets[i].get(s)? 1.0 : 0.0;
+					}
+				}
+				else {
+					sol[i] = mdpmc.computeBoundedUntilProbs(csg, remain[i], targets[i], bounds[i]-1, min).soln;
+				}
+			}
+			for (s = 0; s < csg.getNumStates(); s++) {
+				eq = stepEquilibria(csg, null, null, null, eqs, null, sol, s, min);
+				sw = swne(eq, null, min);
+				tmp[0][s] = sw[1];
+				tmp[1][s] = sw[2];
+				r[s] = sw[1] + sw[2];
+			}
+			mainLog.println("\nCoalition results (initial state): (" + tmp[0][csg.getFirstInitialState()] + "," + tmp[1][csg.getFirstInitialState()] + ")");
+			res.soln = r;
+			res.numIters = 1;
+			return res;		
+		}
 		
 		if (!rew) {
-			for (i = 0; i < 2; i++) { //
+			for (i = 0; i < 2; i++) {
 				phi1[i] = new BitSet();
 				if (remain[i] == null) 
 					phi1[i].set(0, csg.getNumStates());
@@ -615,9 +643,7 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		
 			cpy.clear();
 		}
-		
-		buildCoalitions(csg, coalitions);
-		
+				
 		k = Math.abs(bounds[0] - bounds[1]);
 		n1 = (bounds[0] > bounds[1])? k : 0;
 		n2 = (bounds[1] > bounds[0])? k : 0;
diff --git a/prism/src/explicit/ProbModelChecker.java b/prism/src/explicit/ProbModelChecker.java
index 20391171f..bb0cb02c3 100644
--- a/prism/src/explicit/ProbModelChecker.java
+++ b/prism/src/explicit/ProbModelChecker.java
@@ -679,8 +679,6 @@ protected StateValues checkExpressionMultiNash(Model model, ExpressionMultiNash
 					switch (exprTemp.getOperator()) {
 						case ExpressionTemporal.P_X:
 							bounded.set(p);
-							targets[p] = new BitSet();
-							targets[p].set(0, ((CSG) model).getNumStates());
 							bounds[p] = 1;
 							break;
 						case ExpressionTemporal.P_U:
@@ -757,7 +755,7 @@ else if (bounded.cardinality() == formulae.size()) {
 					res = ((CSGModelChecker) this).computeRewBoundedEquilibria((CSG) model, coalitions, rewards, exprs, bounds, min);
 				}
 				else {
-					res = ((CSGModelChecker) this).computeProbBoundedEquilibria((CSG) model, coalitions, targets, remain, bounds, min);				
+					res = ((CSGModelChecker) this).computeProbBoundedEquilibria((CSG) model, coalitions, exprs, targets, remain, bounds, min);			
 				}
 			}
 			else {

From bc9b1c6d2b761ff0c40c6a532344c2e00a58abef Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabrielhrsantos@gmail.com>
Date: Tue, 30 Mar 2021 17:18:41 +0100
Subject: [PATCH 05/30] class for equilibria computation with yices

---
 ...CSGLabeledPolytopesYicesBindingsStack.java | 353 ++++++++++++++++++
 1 file changed, 353 insertions(+)
 create mode 100644 prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java

diff --git a/prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java b/prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java
new file mode 100644
index 000000000..0b7e01ca5
--- /dev/null
+++ b/prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java
@@ -0,0 +1,353 @@
+package explicit;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.HashMap;
+
+import com.sri.yices.Config;
+import com.sri.yices.Context;
+import com.sri.yices.Status;
+import com.sri.yices.Terms;
+import com.sri.yices.Yices;
+
+import prism.PrismSettings;
+
+public class CSGLabeledPolytopesYicesBindingsStack implements CSGLabeledPolytopes {
+
+	private Config cfg;
+	private Context ctx;
+	
+	private int realType;
+	private int boolType;
+	
+	private int zero;
+	private int one;
+	private int ytrue;
+	private int yfalse;
+	
+	private int eq;
+	
+	private int curr;
+	
+	private int[] xlabels;
+	private int[] ylabels;
+		
+	private int[] vars;
+	private int[] xexps;
+	private int[] yexps;
+	
+	private int[] tmpc;
+	private int[] tmpr;
+	
+	private com.sri.yices.Model model;
+	
+	private int xctr;
+	private int yctr;
+	private int c1;
+	private int c2; 
+	
+	private String[] lvp1;
+	private String[] lvp2;
+	
+	private double[][] a;
+	private double[][] b;
+
+	private double[] p1p;
+	private double[] p2p;
+		
+	private int neq;
+	private int nrows;
+	private int ncols;
+	
+	private HashMap<String,ArrayList<Double>> eqs;
+    private ArrayList<ArrayList<Distribution>> strat;
+	
+	protected String eqPolicy;
+    
+    public CSGLabeledPolytopesYicesBindingsStack() {
+    	
+    }
+    
+    public CSGLabeledPolytopesYicesBindingsStack(int nrows, int ncols) {    	
+		cfg = new Config("QF_LRA");
+		cfg.set("mode", "push-pop");
+		ctx = new Context(cfg);
+		cfg.close();
+        eqs = new HashMap<String,ArrayList<Double>>();
+        realType = Yices.realType();
+        boolType = Yices.boolType();
+		zero = Terms.intConst(0);
+		one = Terms.intConst(1);
+		vars = new int[nrows+ncols];
+		lvp1 = new String[nrows];
+		lvp2 = new String[ncols];
+		tmpc = new int[ncols-1];
+		tmpr = new int[nrows-1];
+		xlabels = new int[nrows+ncols];
+		ylabels = new int[nrows+ncols];
+		yexps = new int[nrows];
+		xexps = new int[ncols];
+		xctr = zero;
+		yctr = zero;
+		ytrue = Yices.mkTrue();
+		yfalse = Yices.mkFalse();
+		int i = 0, j = 0;
+		for(; i < nrows; i++) {
+			vars[i] = Terms.newUninterpretedTerm(realType);
+			lvp1[i] = "x_" + i;
+		}
+		for(; j < ncols; j++) {
+			vars[i] = Terms.newUninterpretedTerm(realType);
+			lvp2[j] = "y_" + j;
+			i++;
+		}
+		for(int v : vars) {
+			ctx.assertFormula(Terms.arithLeq(v, one));
+			ctx.assertFormula(Terms.arithGeq(v, zero));
+		}
+    }
+    
+	public void update(int nrows, int ncols, double[][] a, double[][] b) {
+		this.nrows = nrows;
+		this.ncols = ncols;
+		this.a = a;
+		this.b = b;
+	}
+	
+	private void xLabels() {
+		int l = 0;
+		int j = 0;
+		for(int i = 0; i < nrows+ncols; i++) {
+			if(i < nrows) {
+				xlabels[i] = Terms.arithEq(vars[i], zero);
+			}
+			else {
+				for(int k = 0; k < ncols; k++) {
+					if(j != k) {
+						tmpc[l] = Terms.arithGeq(xexps[j], xexps[k]);
+						l++;
+					}
+				}
+				xlabels[i] = tmpc[0];
+				if(ncols-1 > 1) {
+					for(int m = 1; m < ncols-1; m++) {
+						xlabels[i] = Terms.and(xlabels[i], tmpc[m]);
+					}
+				}
+				j++;
+				l = 0;
+			}
+		}
+	}
+	
+	private void yLabels() {
+		int l = 0;
+		int j = 0;
+		for(int i = 0; i < nrows+ncols; i++) {
+			if(i < nrows) {
+				for(int k = 0; k < nrows; k++) {
+					if(j != k) {
+						tmpr[l] = Terms.arithGeq(yexps[j], yexps[k]);
+						l++;
+					}
+				}
+				ylabels[i] = tmpr[0];
+				if(nrows-1 > 1) {
+					for(int m = 1; m < nrows-1; m++) {
+						ylabels[i] = Terms.and(ylabels[i], tmpr[m]);
+					}
+				}
+				j++;
+				l = 0;
+			}
+			else {
+				ylabels[i] = Terms.arithEq(vars[i], zero);
+			}
+		}
+	}
+	
+	private void vMult() {
+		for(int i = 0; i < nrows; i++) {
+			curr = zero;
+			for(int j = 0; j < ncols; j++) {
+				try {
+					curr = Terms.add(curr, Terms.mul(vars[nrows+j], 
+													Terms.parseFloat(String.valueOf(a[i][j]))));
+				}
+				catch(Exception e) {
+					e.printStackTrace();
+				}
+			}
+			yexps[i] = curr;
+		}
+		for(int j = 0; j < ncols; j++) {
+			curr = zero;
+			for(int i = 0; i < nrows; i++) {
+				try {		
+					curr = Terms.add(curr, Terms.mul(vars[i], 
+													Terms.parseFloat(String.valueOf(b[i][j]))));
+				}
+				catch(Exception e) {
+					e.printStackTrace();
+				}
+			}
+			xexps[j] = curr;
+		}
+	}
+
+	public void compEq() {
+		ArrayList<Distribution> dists;
+		Distribution dist1;
+		Distribution dist2;
+		double p;
+		int i, j;		
+		vMult();
+		xLabels();
+		yLabels();
+		ctx.push();
+		eq = ytrue;
+		xctr = zero;
+		yctr = zero;
+		for(i = 0; i < nrows+ncols; i++) {
+			eq = Terms.and(eq, Terms.or(xlabels[i],ylabels[i]));
+		}
+		for(i = 0; i < nrows; i++) {
+			xctr = Terms.add(xctr, vars[i]);
+		}
+		xctr = Terms.arithEq(xctr, one);
+		for(j = i; j < nrows+ncols; j++) {
+			yctr = Terms.add(yctr, vars[j]);
+		}
+		yctr = Terms.arithEq(yctr, one);			
+		ctx.assertFormula(xctr);
+		ctx.assertFormula(yctr);
+		ctx.assertFormula(eq);
+        strat = new ArrayList<ArrayList<Distribution>>();
+		eqs.clear();
+        j = 0; 
+        while (ctx.check() == Status.SAT) {
+        	model = ctx.getModel();        
+            c1 = ytrue;
+            c2 = ytrue;
+            dists = new ArrayList<Distribution>();
+            dist1 = new Distribution();
+            dist2 = new Distribution();
+    		//System.out.println("---");
+            //String prt = "(";
+            for (i = 0; i < nrows+ncols; i++) {            	
+        		//p = model.bigRationalValue(vars[i]).doubleValue();
+            	p = model.doubleValue(vars[i]);
+        		//prt += p;
+        		//if (i < vars.length - 1)
+        			//prt += ",";
+        		//System.out.println(p);
+        		if(p > 0) {
+        			if(i < nrows)
+        				dist1.add(i, p);
+        			else 
+        				dist2.add(i - nrows, p);
+        		}
+                if (j == 0) {
+        			if (i < nrows) {
+                		eqs.put(lvp1[i], new ArrayList<Double>());
+                		eqs.get(lvp1[i]).add(p);
+                	} 
+        			else {
+        	       		eqs.put(lvp2[i-nrows], new ArrayList<Double>());
+        	       		eqs.get(lvp2[i-nrows]).add(p);
+                	}
+                }
+                else {
+        			if (i < nrows) {
+                		eqs.get(lvp1[i]).add(p);
+                	} 
+        			else {
+        				eqs.get(lvp2[i-nrows]).add(p);		
+               		}
+       			}
+            }
+            //prt += ")";
+            //System.out.println(prt);
+            if (eqPolicy == "first_found") {
+                dists.add(0, dist1);
+                dists.add(1, dist2);
+                strat.add(j, dists);
+        		j++;
+        		break;
+            }
+            for(i = 0; i < nrows+ncols; i++) {
+				if (i < nrows) {
+        			//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
+        			if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
+        				c1 = Terms.and(c1, Terms.not(Terms.arithEq(vars[i], zero)));
+        			}
+            		else {
+            			c1 = Terms.and(c1, Terms.arithEq(vars[i], zero));
+            		}
+				} 
+				else {
+    				//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
+    				if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
+    					c2 = Terms.and(c2, Terms.not(Terms.arithEq(vars[i], zero)));
+            		}
+            		else {
+            			c2 = Terms.and(c2, Terms.arithEq(vars[i], zero));
+            		}
+				}
+            }
+            dists.add(0, dist1);
+            dists.add(1, dist2);
+            strat.add(j, dists);
+    		j++;
+            ctx.assertFormula(Terms.or(Terms.not(c1), Terms.not(c2)));
+        }
+        ctx.pop();
+		model.close();
+		//System.out.println(eqs);
+        neq = j;
+        
+        compPayoffs();
+        //System.out.println(Arrays.toString(p1p));
+        //System.out.println(Arrays.toString(p2p));
+	}
+
+	public void compPayoffs() {
+		p1p = new double[neq];
+		p2p = new double[neq];
+		Arrays.fill(p1p, 0.0);
+		Arrays.fill(p2p, 0.0);
+		for(int e = 0; e < neq; e++) {
+        	for(int i = 0; i < nrows; i++) {
+        		for(int j = 0; j < ncols; j++) {
+        			p1p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * a[i][j];
+        			p2p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * b[i][j];
+        		}
+        	}
+        }			
+	}
+
+	public ArrayList<ArrayList<Distribution>> getStrat() {
+		return strat;
+	}
+
+	public double[] getP1p() {
+		return p1p;
+	}
+
+	public double[] getP2p() {
+		return p2p;
+	}
+	
+	public int getNeq() {
+		return neq;
+	}
+
+	public void clear() {
+		
+	}
+
+	public void setPolicy(String s) {
+		this.eqPolicy = s;
+	}
+
+}

From 5f66a979773888f71daffbc6cb03e994ec707650 Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabtos@pc-142-107.customer.ask4.lan>
Date: Thu, 27 May 2021 18:30:05 +0100
Subject: [PATCH 06/30] yices libraries and refactoring

---
 prism/lib/libyices.so.2.6.1                   | Bin 0 -> 2760408 bytes
 prism/lib/libyices2java.dylib                 | Bin 0 -> 213888 bytes
 prism/lib/libyices2java.jnilib                |   1 +
 prism/lib/yices.jar                           | Bin 0 -> 105995 bytes
 prism/src/explicit/CSGLabeledPolytopes.java   |   2 -
 ...ava => CSGLabeledPolytopesYicesStack.java} |  63 +-
 prism/src/explicit/CSGLabeledPolytopesZ3.java |   6 -
 ...h.java => CSGLabeledPolytopesZ3Stack.java} |   6 +-
 .../explicit/CSGModelCheckerEquilibria.java   | 781 +++++-------------
 9 files changed, 276 insertions(+), 583 deletions(-)
 create mode 100755 prism/lib/libyices.so.2.6.1
 create mode 100755 prism/lib/libyices2java.dylib
 create mode 120000 prism/lib/libyices2java.jnilib
 create mode 100644 prism/lib/yices.jar
 rename prism/src/explicit/{CSGLabeledPolytopesYicesBindingsStack.java => CSGLabeledPolytopesYicesStack.java} (85%)
 rename prism/src/explicit/{CSGLabeledPolytopesZ3Push.java => CSGLabeledPolytopesZ3Stack.java} (97%)

diff --git a/prism/lib/libyices.so.2.6.1 b/prism/lib/libyices.so.2.6.1
new file mode 100755
index 0000000000000000000000000000000000000000..f8363634adfb74b71c6cc8149063dee555a6d286
GIT binary patch
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diff --git a/prism/lib/libyices2java.dylib b/prism/lib/libyices2java.dylib
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diff --git a/prism/lib/libyices2java.jnilib b/prism/lib/libyices2java.jnilib
new file mode 120000
index 000000000..46f9c690d
--- /dev/null
+++ b/prism/lib/libyices2java.jnilib
@@ -0,0 +1 @@
+libyices2java.dylib
\ No newline at end of file
diff --git a/prism/lib/yices.jar b/prism/lib/yices.jar
new file mode 100644
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HcmV?d00001

diff --git a/prism/src/explicit/CSGLabeledPolytopes.java b/prism/src/explicit/CSGLabeledPolytopes.java
index 395c36af9..af02dd25e 100644
--- a/prism/src/explicit/CSGLabeledPolytopes.java
+++ b/prism/src/explicit/CSGLabeledPolytopes.java
@@ -17,7 +17,5 @@ public interface CSGLabeledPolytopes {
 	public double[] getP2p(); 
 	
 	public int getNeq();
-
-	public void clear();
 	
 }
diff --git a/prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
similarity index 85%
rename from prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java
rename to prism/src/explicit/CSGLabeledPolytopesYicesStack.java
index 0b7e01ca5..6a75fbd8e 100644
--- a/prism/src/explicit/CSGLabeledPolytopesYicesBindingsStack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
@@ -12,7 +12,7 @@
 
 import prism.PrismSettings;
 
-public class CSGLabeledPolytopesYicesBindingsStack implements CSGLabeledPolytopes {
+public class CSGLabeledPolytopesYicesStack implements CSGLabeledPolytopes {
 
 	private Config cfg;
 	private Context ctx;
@@ -64,11 +64,11 @@ public class CSGLabeledPolytopesYicesBindingsStack implements CSGLabeledPolytope
 	
 	protected String eqPolicy;
     
-    public CSGLabeledPolytopesYicesBindingsStack() {
+    public CSGLabeledPolytopesYicesStack() {
     	
     }
     
-    public CSGLabeledPolytopesYicesBindingsStack(int nrows, int ncols) {    	
+    public CSGLabeledPolytopesYicesStack(int nrows, int ncols) {    	
 		cfg = new Config("QF_LRA");
 		cfg.set("mode", "push-pop");
 		ctx = new Context(cfg);
@@ -107,6 +107,45 @@ public CSGLabeledPolytopesYicesBindingsStack(int nrows, int ncols) {
 		}
     }
     
+    public void clear() {
+		cfg = new Config("QF_LRA"); 
+		cfg.set("mode", "push-pop");
+		ctx = new Context(cfg);
+		cfg.close();
+        eqs = new HashMap<String,ArrayList<Double>>();
+        realType = Yices.realType();
+        boolType = Yices.boolType();
+		zero = Terms.intConst(0);
+		one = Terms.intConst(1);
+		vars = new int[nrows+ncols];
+		lvp1 = new String[nrows];
+		lvp2 = new String[ncols];
+		tmpc = new int[ncols-1];
+		tmpr = new int[nrows-1];
+		xlabels = new int[nrows+ncols];
+		ylabels = new int[nrows+ncols];
+		yexps = new int[nrows];
+		xexps = new int[ncols];
+		xctr = zero;
+		yctr = zero;
+		ytrue = Yices.mkTrue();
+		yfalse = Yices.mkFalse();
+		int i = 0, j = 0;
+		for(; i < nrows; i++) {
+			vars[i] = Terms.newUninterpretedTerm(realType);
+			lvp1[i] = "x_" + i;
+		}
+		for(; j < ncols; j++) {
+			vars[i] = Terms.newUninterpretedTerm(realType);
+			lvp2[j] = "y_" + j;
+			i++;
+		}
+		for(int v : vars) {
+			ctx.assertFormula(Terms.arithLeq(v, one));
+			ctx.assertFormula(Terms.arithGeq(v, zero));
+		}
+    }
+    
 	public void update(int nrows, int ncols, double[][] a, double[][] b) {
 		this.nrows = nrows;
 		this.ncols = ncols;
@@ -200,11 +239,11 @@ public void compEq() {
 		Distribution dist1;
 		Distribution dist2;
 		double p;
-		int i, j;		
+		int i, j;	
+		clear();
 		vMult();
 		xLabels();
 		yLabels();
-		ctx.push();
 		eq = ytrue;
 		xctr = zero;
 		yctr = zero;
@@ -277,7 +316,6 @@ public void compEq() {
             }
             for(i = 0; i < nrows+ncols; i++) {
 				if (i < nrows) {
-        			//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
         			if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
         				c1 = Terms.and(c1, Terms.not(Terms.arithEq(vars[i], zero)));
         			}
@@ -286,7 +324,6 @@ public void compEq() {
             		}
 				} 
 				else {
-    				//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
     				if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
     					c2 = Terms.and(c2, Terms.not(Terms.arithEq(vars[i], zero)));
             		}
@@ -301,14 +338,10 @@ public void compEq() {
     		j++;
             ctx.assertFormula(Terms.or(Terms.not(c1), Terms.not(c2)));
         }
-        ctx.pop();
-		model.close();
-		//System.out.println(eqs);
+        model.close();
         neq = j;
-        
+        Yices.reset();
         compPayoffs();
-        //System.out.println(Arrays.toString(p1p));
-        //System.out.println(Arrays.toString(p2p));
 	}
 
 	public void compPayoffs() {
@@ -342,10 +375,6 @@ public int getNeq() {
 		return neq;
 	}
 
-	public void clear() {
-		
-	}
-
 	public void setPolicy(String s) {
 		this.eqPolicy = s;
 	}
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3.java b/prism/src/explicit/CSGLabeledPolytopesZ3.java
index ddfe8d9d1..2b8bab16c 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3.java
@@ -146,12 +146,6 @@ private void initialize() {
 		}
 	}
 	
-	@Override
-	public void clear() {
-		// TODO Auto-generated method stub
-		
-	}
-	
 	private void xLabels() {
 		/*
 		System.out.println("-- xexps");
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3Push.java b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
similarity index 97%
rename from prism/src/explicit/CSGLabeledPolytopesZ3Push.java
rename to prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
index 76722f62e..29d422fb0 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3Push.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
@@ -16,7 +16,7 @@
 import com.microsoft.z3.Solver;
 import com.microsoft.z3.Status;
 
-public class CSGLabeledPolytopesZ3Push implements CSGLabeledPolytopes {
+public class CSGLabeledPolytopesZ3Stack implements CSGLabeledPolytopes {
 
 	private RealExpr[] payvars;
 	private ArithExpr[] payoffs;
@@ -63,11 +63,11 @@ public class CSGLabeledPolytopesZ3Push implements CSGLabeledPolytopes {
 	private HashMap<String,ArrayList<Double>> eqs;
     private ArrayList<ArrayList<Distribution>> strat;
     
-    public CSGLabeledPolytopesZ3Push() {
+    public CSGLabeledPolytopesZ3Stack() {
     	
     }
     
-    public CSGLabeledPolytopesZ3Push(int nrows, int ncols) {
+    public CSGLabeledPolytopesZ3Stack(int nrows, int ncols) {
     	cfg = new HashMap<String, String>();
         cfg.put("model", "true");
         cfg.put("auto_config", "true");
diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 6591767c8..18243b754 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -44,6 +44,7 @@
 import org.apache.commons.math3.util.Precision;
 
 import explicit.CSGModelCheckerEquilibria.CSGResultStatus;
+import explicit.ProbModelChecker.TermCrit;
 import explicit.rewards.CSGRewards;
 import explicit.rewards.CSGRewardsSimple;
 import explicit.rewards.MDPRewards;
@@ -79,7 +80,8 @@ public class CSGModelCheckerEquilibria extends CSGModelChecker {
 	private ArrayList<Integer> payoffs;	
 	
 	private HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> gradient;
-	private HashMap<Integer, int[]> map;
+	//{action j -> [player i, action j (index)]}
+	private HashMap<Integer, int[]> mapActionIndex;
 	
 	private ArrayList<ArrayList<BitSet>> supports;
 	private ArrayList<BitSet> allSupports;
@@ -88,7 +90,9 @@ public class CSGModelCheckerEquilibria extends CSGModelChecker {
 	protected BitSet[] dominating;
 	protected BitSet players;
 	
-	protected CSGLabeledPolytopes eqs;	
+	//smt solver for labelled polytopes 
+	protected CSGLabeledPolytopes eqslps;
+	//smt solver for support enumeration
 	protected CSGSupportEnumeration eqssmt;
 	
 	protected String smtSolver;
@@ -103,7 +107,7 @@ public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		supports = new ArrayList<ArrayList<BitSet>>();
 		allSupports =  new ArrayList<BitSet>();
 				
-		map = new HashMap<Integer, int[]>();
+		mapActionIndex = new HashMap<Integer, int[]>();
 		products = new ArrayList<ArrayList<ArrayList<Pair<BitSet, Double>>>>();
 		assertions = new HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>>();
 		gradient = new HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>>();
@@ -115,25 +119,23 @@ public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		
 		smtSolver = getSettings().getString(PrismSettings.PRISM_SMT_SOLVER);
 		switch (smtSolver) {
-		case "Z3":
-			//eqs = new CSGLabeledPolytopesZ3();
-			eqs = new CSGLabeledPolytopesZ3Push();
-			eqssmt = new CSGSupportEnumerationZ3();
-			//eqssmt = new CSGNPlayerImpZ3();
-			break;
-		case "Yices":
-			throw new PrismNotSupportedException("The Yices solver is currently not supported");
-			//eqs = new CSGLabeledPolytopesYices();
-//			eqssmt = new CSGSupportEnumerationYices();
-			//eqs = new CSGLabeledPolytopesYicesBindings();
-			//eqs = new CSGLabeledPolytopesYicesPush();
-//			eqs = new CSGLabeledPolytopesYicesPushBindings();
-//			break;
-		default:
-			throw new PrismException("Unknown SMT solver \"" + smtSolver + "\"");
-		}
-		// eqs = new CSGLabeledPolytopesCVC();
-		// eqssmt = new CSGSupportEnumerationIpopt();
+			case "Z3":
+				break;
+			case "Yices":
+				break;
+			default:
+				throw new PrismException("Unknown SMT solver \"" + smtSolver + "\"");
+		}
+	}
+	
+	public void setSolver() throws PrismException {
+		switch (smtSolver) {
+			case "Z3":
+				eqslps = new CSGLabeledPolytopesZ3Stack(maxRows, maxCols);
+				break;
+			case "Yices":
+				eqslps = new CSGLabeledPolytopesYicesStack();
+		}
 	}
 
 	public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismException {
@@ -175,42 +177,47 @@ public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismExc
 	public void buildAllSupports() {
 		BitSet support;
 		for (int p = 0; p < numCoalitions; p++) {
-			if (!dominating[p].isEmpty()) 
+			if (!dominating[p].isEmpty()) {
 				supports.get(p).add(dominating[p]);
-			else
+			}
+			else { 
 				buildSupportsPlayer(new BitSet(), p, 0);
-		
+			}
 		}
-		for (int s = 0; s < supports.get(0).size(); s++) {
+		for (BitSet s : supports.get(0)) {
 			support = new BitSet();
-			support.or(supports.get(0).get(s));
+			support.or(s);
 			buildAllSupportsAux(support, 1);
 		}
 	}
 	
 	public void buildAllSupportsAux(BitSet supp, int p) {
-		for (int s = 0; s < supports.get(p).size(); s++) {
+		for (BitSet s : supports.get(p)) {
 			BitSet curr = (BitSet) supp.clone();
-			curr.or(supports.get(p).get(s));
+			curr.or(s);
 			if(p == numCoalitions - 1) {
-				allSupports.add(curr);
+				if (!allSupports.contains(curr))
+					allSupports.add(curr);
 			}
 			else {
 				buildAllSupportsAux(curr, p + 1);
 			}
-		}	
+		}		
 	}
 
 	public void buildSupportsPlayer(BitSet supp, int p, int a) {
 		BitSet gt0 = (BitSet) supp.clone(); 
-		if (!dominated[p].get(strategies.get(p).get(a)))
+		if (!dominated[p].get(strategies.get(p).get(a))) {
 			gt0.set(strategies.get(p).get(a));
+		}
 		BitSet eq0 = (BitSet) supp.clone();
 		if (a == strategies.get(p).size() - 1) {
 			if (!eq0.isEmpty()) {
 				supports.get(p).add(eq0);
 			}
-			supports.get(p).add(gt0);
+			if (!gt0.isEmpty()) {
+				supports.get(p).add(gt0);
+			}
 		}
 		else {
 			buildSupportsPlayer(eq0, p, a + 1);
@@ -283,6 +290,24 @@ public BitSet findDominating(int p) throws PrismException {
 		return domi;
 	}
 	
+	public int[] findMaxIndexes(double[][] a) {
+		int result[] = new int[2];
+		result[0] = 0;
+		result[1] = 0;	
+		double value = 0.0;
+		for(int r = 0; r < a.length; r++) {
+			for(int c = 0; c < a[r].length; c++) {
+				if(Double.compare(a[r][c], value) > 0) {
+				//if(a[r][c] > value) {
+					value = a[r][c];
+					result[0] = r;
+					result[1] = c;	
+				}
+			}
+		}		
+		return result;
+	}
+	
 	public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, double[][] val, int s, boolean min) throws PrismException {
 		Map<BitSet, Integer> imap = new HashMap<BitSet, Integer>();
 		BitSet jidx;
@@ -360,36 +385,64 @@ public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, B
 		//System.out.println("-- utilities " + utilities);
 	}
 	
-	public ArrayList<ArrayList<ArrayList<Double>>> buildBiMatrixGame(CSG csg, CSGRewards r1, CSGRewards r2, List<Map<Integer, BitSet>> mmap, double[][] val, int s, boolean min) throws PrismException {
+	public ArrayList<ArrayList<ArrayList<Double>>> buildBiMatrixGame(CSG csg, CSGRewards r1, CSGRewards r2, List<Map<Integer, BitSet>> mmap,  List<ArrayList<Integer>> nmap, double[][] val, int s, boolean min) throws PrismException {
 		ArrayList<ArrayList<ArrayList<Double>>> bmgame = new ArrayList<ArrayList<ArrayList<Double>>>();
 		ArrayList<CSGRewards> rewards = null;
-        BitSet action = new BitSet();
-		int col, p, row;
-        if (numCoalitions > 2) 
-        	throw new PrismLangException("Multiplayer game not supported by this method");
-        if (r1 != null || r2 != null) {
-        	rewards = new ArrayList<CSGRewards>();
-        	rewards.add(0, r1);
-        	rewards.add(1, r2);
-        }
-        buildStepGame(csg, rewards, mmap, val, s, min);
+		BitSet action = new BitSet();
+		int col, p, row, irow, icol;
+		if (numCoalitions > 2) 
+			throw new PrismLangException("Multiplayer game not supported by this method");
+		if (r1 != null || r2 != null) {
+			rewards = new ArrayList<CSGRewards>();
+			rewards.add(0, r1);
+			rewards.add(1, r2);
+		}
+		buildStepGame(csg, rewards, mmap, val, s, min);
+		//System.out.println("-- utilities " + utilities);
+		//System.out.println("-- strategies " + strategies);
+		//System.out.println("-- mmap " + mmap);
+		clear();
+		computeAssertions();
+		//System.out.println("-- assertions " + assertions);
+		//System.out.println("-- gradient " + gradient);
+		for (p = 0; p < numCoalitions; p++) {
+			dominated[p] = findDominated(p);
+			dominating[p] = findDominating(p);
+			//System.out.println("-- dominated " + p + ": " + dominated[p]);
+			//System.out.println("-- dominating " + p + ": " + dominating[p]);
+		}
+		buildAllSupports();
+		//System.out.println("-- supports " + allSupports);
 		for (p = 0; p < 2; p++) {
-        	bmgame.add(p, new ArrayList<ArrayList<Double>>());
-        	for (row = 0; row < strategies.get(0).size(); row++) {
-        		bmgame.get(p).add(row, new ArrayList<Double>());
-        		action.clear();
-        		action.set(strategies.get(0).get(row));
-        		for (col = 0; col < strategies.get(1).size(); col++) {
-            		action.set(strategies.get(1).get(col));
-        			if (utilities.containsKey(action))
-        				bmgame.get(p).get(row).add(col, utilities.get(action).get(p));
-        			else 
-        				throw new PrismException("Error in building bimatrix game");
-        			action.clear(strategies.get(1).get(col));
-        		}	
-        	}
-        }
-        return bmgame;
+			bmgame.add(p, new ArrayList<ArrayList<Double>>());
+			irow = 0;
+			for (row = 0; row < strategies.get(0).size(); row++) {
+				if (!dominated[0].get(strategies.get(0).get(row))) {
+					bmgame.get(p).add(irow, new ArrayList<Double>());
+					action.clear();
+					action.set(strategies.get(0).get(row));
+					icol = 0;
+					for (col = 0; col < strategies.get(1).size(); col++) {
+						if (!dominated[1].get(strategies.get(1).get(col))) {
+							action.set(strategies.get(1).get(col));
+							if (utilities.containsKey(action))
+								bmgame.get(p).get(irow).add(icol, utilities.get(action).get(p));
+							else 
+								throw new PrismException("Error in building bimatrix game");
+							action.clear(strategies.get(1).get(col));
+							if (p == 0 && irow == 0)
+								nmap.get(1).add(icol, col);
+							icol++;
+						}
+					}
+					if (p == 0)
+						nmap.get(0).add(irow, row);
+					irow++;
+				}
+			}
+		}
+		//System.out.println("-- nmap " + nmap);
+		return bmgame;
 	}
 	
 	public void clear() {
@@ -399,7 +452,7 @@ public void clear() {
 		assertions.clear();
 		gradient.clear();
 		payoffs.clear();
-		map.clear();
+		mapActionIndex.clear();
 		for(int c = 0; c < numCoalitions; c++) {
 			supports.add(c, new ArrayList<BitSet>());
 			products.add(c, new ArrayList<ArrayList<Pair<BitSet, Double>>>());
@@ -407,7 +460,7 @@ public void clear() {
 			gradient.put(c, new HashMap<Integer, ArrayList<Pair<BitSet, Double>>>());
 			for(int a = 0; a < strategies.get(c).size(); a++) {
 				products.get(c).add(a, new ArrayList<Pair<BitSet, Double>>());
-				map.put(strategies.get(c).get(a), new int[] {c, a});
+				mapActionIndex.put(strategies.get(c).get(a), new int[] {c, a});
 			}
 		}
 		for(int c = 0; c < numCoalitions; c++) { // strategies allocated first
@@ -416,7 +469,7 @@ public void clear() {
 		}
 	}
 	
-	public void computeAssertions() {
+	public void computeAssertions() throws PrismException {
 		int c, q;
 		BitSet ps;
 		BitSet acts = new BitSet();
@@ -455,7 +508,7 @@ public void computeAssertions() {
 		*/
 	}
 	
-	public ArrayList<Pair<BitSet, Double>> prodAction(BitSet prod, BitSet sp, int act, int p) {
+	public ArrayList<Pair<BitSet, Double>> prodAction(BitSet prod, BitSet sp, int act, int p) throws PrismException {
 		prodAction(new Pair<BitSet, Double>(new BitSet(), 0.0), prod, sp, act, p);
 		ArrayList<Pair<BitSet, Double>> sum = new ArrayList<Pair<BitSet, Double>>();		
 		for(int j = 0; j < products.get(p).get(act).size(); j++) {
@@ -465,33 +518,25 @@ public ArrayList<Pair<BitSet, Double>> prodAction(BitSet prod, BitSet sp, int ac
 		return sum;
 	}
 	
-	public void prodAction(Pair<BitSet, Double> expr, BitSet prod, BitSet sp, int act, int p) {
-		//HashSet<Integer> set;
+	public void prodAction(Pair<BitSet, Double> expr, BitSet prod, BitSet sp, int act, int p) throws PrismException {
 		BitSet set;
 		BitSet curr = (BitSet) sp.clone();
 		Pair<BitSet, Double> nexpr;
 		if(products.get(p) == null) 
 			products.add(p, new ArrayList<ArrayList<Pair<BitSet, Double>>>());
 		else if(products.get(p).get(act) == null)
-			products.get(p).add(act, new ArrayList<Pair<BitSet, Double>>());	
+			products.get(p).add(act, new ArrayList<Pair<BitSet, Double>>());
 		for(int cp = sp.nextSetBit(0); cp < sp.size() && cp != -1; cp = sp.nextSetBit(cp + 1)) {
 			curr.clear(cp);
 			for(int a = 0; a < actions.get(cp).size(); a++) {
-				//set = new HashSet<Integer>();
-				//set.addAll(prod);
-				//set.add(strategies.get(cp).get(a));
 				set = new BitSet();
 				set.or(prod);
 				set.set(strategies.get(cp).get(a));		
 				nexpr = new Pair<BitSet, Double>(new BitSet(), 0.0);
-				//nexpr.first.addAll(expr.first);
-				//nexpr.first.add(strategies.get(cp).get(a));
 				nexpr.first.or(expr.first);
 				nexpr.first.set(strategies.get(cp).get(a));
 				prodAction(nexpr, set, curr, act, p);
-				if(sp.cardinality() == 1 && set.cardinality() == numCoalitions) { // should have to check for set size?					
-					//nexpr.first.addAll(expr.first);
-					//nexpr.first.add(strategies.get(cp).get(a));
+				if(sp.cardinality() == 1 && set.cardinality() == numCoalitions) { // should have to check for set size?	
 					nexpr.first.or(expr.first);
 					nexpr.first.set(strategies.get(cp).get(a));
 					nexpr.second = utilities.get(set).get(p);			
@@ -500,33 +545,22 @@ else if(products.get(p).get(act) == null)
 						gradient.get(p).put(act, new ArrayList<Pair<BitSet, Double>>());	
 					if(nexpr.second != 0.0)
 						gradient.get(p).get(act).add(nexpr);
-					//HashSet<Integer> der = new HashSet<Integer>();
 					BitSet der = new BitSet();
-					//for(int i : nexpr.first) {
 					for(int i = nexpr.first.nextSetBit(0); i >= 0; i = nexpr.first.nextSetBit(i + 1)) {
-						//der.addAll(nexpr.first);
-						//der.add(strategies.get(p).get(act));
-						//der.remove(i);
 						der.or(nexpr.first);
 						der.set(strategies.get(p).get(act));
 						der.clear(i);
-						//System.out.println(der);
-						if(gradient.get(map.get(i)[0]).get(map.get(i)[1]) == null)
-							gradient.get(map.get(i)[0]).put(map.get(i)[1], new ArrayList<Pair<BitSet, Double>>());
+						if(gradient.get(mapActionIndex.get(i)[0]).get(mapActionIndex.get(i)[1]) == null)
+							gradient.get(mapActionIndex.get(i)[0]).put(mapActionIndex.get(i)[1], new ArrayList<Pair<BitSet, Double>>());
 						if(nexpr.second != 0.0)
-							gradient.get(map.get(i)[0]).get(map.get(i)[1]).add(new Pair<BitSet, Double>((BitSet) der.clone(), nexpr.second));
+							gradient.get(mapActionIndex.get(i)[0]).get(mapActionIndex.get(i)[1]).add(new Pair<BitSet, Double>((BitSet) der.clone(), nexpr.second));
 						der.clear();
 					}
-					
-				}
-				else {
-					// should throw an exception
 				}
 			}
 		}
 	}
 	
-	
 	public double[][] computeBoundedReachProbs(CSG csg, BitSet target, int n) {
 		double[][] sol = new double[n][csg.getNumStates()];
 		double[] sol1 = new double[csg.getNumStates()];
@@ -559,12 +593,11 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		if (generateStrategy || exportAdv) {
 			throw new PrismException("Strategy synthesis for bounded properties is not supported yet.");
 		}
-		//System.out.println("\n-- Bounded Equilibria");
 		ModelCheckerResult res = new ModelCheckerResult();
+		List<CSGRewards> newRewards= null;
 		BitSet[] only = new BitSet[coalitions.size()];
 		BitSet[] phi1 = new BitSet[3];
 		BitSet cpy =  new BitSet();
-		BitSet pindx = new BitSet();
 		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
 		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
 		double[][] val = new double[coalitions.size()][csg.getNumStates()];
@@ -576,8 +609,12 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		long currentTime, timePrecomp;		
 		
 		rew = rewards != null;
-		pindx.set(0, numCoalitions); // review this
+		
 		buildCoalitions(csg, coalitions);
+		findMaxRowsCols(csg);
+		setSolver();
+		dominated = new BitSet[numCoalitions];
+		dominating = new BitSet[numCoalitions];
 		
 		// Case next
 		if ((exprs.get(0).getOperator() == ExpressionTemporal.P_X) || (exprs.get(1).getOperator() == ExpressionTemporal.P_X)) {
@@ -592,7 +629,7 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 				}
 			}
 			for (s = 0; s < csg.getNumStates(); s++) {
-				eq = stepEquilibria(csg, null, null, null, eqs, null, sol, s, min);
+				eq = stepEquilibria(csg, null, null, null, eqslps, null, sol, s, min);
 				sw = swne(eq, null, min);
 				tmp[0][s] = sw[1];
 				tmp[1][s] = sw[2];
@@ -630,23 +667,23 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 			}
 		}
 		
+		k = Math.abs(bounds[0] - bounds[1]);
+		n1 = (bounds[0] > bounds[1])? k : 0;
+		n2 = (bounds[1] > bounds[0])? k : 0;
+		
 		if (!rew) {
 			phi1[2] = new BitSet();
 			phi1[2].or(phi1[0]); 
 			phi1[2].and(phi1[1]); // intersection of phi1(1) and phi1(2)
-		
 			cpy.clear();
 			cpy.or(phi1[0]);
-		
 			phi1[0].andNot(phi1[1]); // phi1(1) minus phi1(2)
 			phi1[1].andNot(cpy); // phi1(2) minus phi1(1)
-		
 			cpy.clear();
 		}
-				
-		k = Math.abs(bounds[0] - bounds[1]);
-		n1 = (bounds[0] > bounds[1])? k : 0;
-		n2 = (bounds[1] > bounds[0])? k : 0;
+		else {
+			newRewards = new ArrayList<CSGRewards>();
+		}
 		
 		//System.out.println("for bounds[0]");
 		//double[][] pre0 = computeBoundedReachProbs(csg, targets[0], bounds[0]); 
@@ -673,13 +710,11 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		findMaxRowsCols(csg);
 		switch (smtSolver) {
 			case "Z3":
-				eqs = new CSGLabeledPolytopesZ3Push(maxRows, maxCols);
-			break;
+				eqslps = new CSGLabeledPolytopesZ3Stack(maxRows, maxCols);
+				break;
 			case "Yices":
-				throw new PrismNotSupportedException("The Yices solver is currently not supported");
-				//eqs = new CSGLabeledPolytopesYicesPushBindings(maxRows, maxCols);
+				eqslps = new CSGLabeledPolytopesYicesStack();
 		}
-		//eqs = new CSGLabeledPolytopesYicesPush(maxRows, maxCols);
 		
 		while (true) {
 			currentTime = System.currentTimeMillis();
@@ -700,41 +735,17 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 			timePrecomp += System.currentTimeMillis() - currentTime;
 			if (Math.min(n1, n2) > 0) {
 				for (s = 0; s < csg.getNumStates(); s++) {
-					//System.out.print(s + "--");
 					if (rew) {
-						if (targets[0].get(s) && targets[1].get(s)) {
-							tmp[0][s] = 0.0;
-							tmp[1][s] = 0.0;					
-						}
-						else if (only[0].get(s)) {
-							tmp[0][s] = 0.0;
-							tmp[1][s] = val[1][s];
-						}
-						else if (only[1].get(s)) {
-							tmp[0][s] = val[0][s];
-							tmp[1][s] = 0.0;		
-						}
-						else {
-							eq = stepEquilibria(csg, 
-												(exprs.get(0).getOperator() == ExpressionTemporal.R_C)? rewards.get(0) : null, 
-												(exprs.get(1).getOperator() == ExpressionTemporal.R_C)? rewards.get(1) : null, 
-												null, 
-												eqs, null, sol, s, min);
-							sw = swne(eq, null, min);
-							/*
-							//if (s == csg.getFirstInitialState()) {	
-							System.out.println("-- equilibria for state " + s);
-							for (int e = 0; e < eq.length; e++) {
-								System.out.println(e + " " + Arrays.toString(eq[e]));
-							}
-							
-							System.out.println("-- selected from " + eq.length);
-							System.out.println(Arrays.toString(sw));
-							//}
-							*/
-							tmp[0][s] = sw[1];
-							tmp[1][s] = sw[2];
+						newRewards.clear();
+						for (i = 0; i < 2; i++) {
+							newRewards.add(i, rewards.get(i));
+							if (!(exprs.get(i).getOperator() == ExpressionTemporal.R_C))
+								newRewards.set(i, null);
 						}
+						eq = stepEquilibria(csg, newRewards.get(0), newRewards.get(1), null, eqslps, null, sol, s, min);	
+						sw = swne(eq, null, min);
+						tmp[0][s] = sw[1];
+						tmp[1][s] = sw[2];
 					} 
 					else {
 						if (targets[0].get(s) && targets[1].get(s)) {
@@ -762,20 +773,8 @@ else if(!phi1[2].get(s)) {
 							tmp[1][s] = 0.0;
 						}
 						else {
-							eq = stepEquilibria(csg, null, null, null, eqs, null, sol, s, min);
-							//sw = swne(eq, null, min, false);
+							eq = stepEquilibria(csg, null, null, null, eqslps, null, sol, s, min);
 							sw = swne(eq, null, min);
-							/*
-							//if (s == csg.getFirstInitialState()) {	
-								System.out.println("-- equilibria");
-								for (int e = 0; e < eq.length; e++) {
-									System.out.println(e + " " + Arrays.toString(eq[e]));
-								}
-								
-								System.out.println("-- selected from " + eq.length);
-								System.out.println(Arrays.toString(sw));
-							//}
-							*/
 							tmp[0][s] = sw[1];
 							tmp[1][s] = sw[2];
 						}
@@ -841,7 +840,6 @@ else if (n1 == 0) {
 		mainLog.println("Coalition results (initial state): (" + sol[0][csg.getFirstInitialState()] + "," + sol[1][csg.getFirstInitialState()] + ")");
 		res.soln = r;
 		res.numIters = k;
-		eqs.clear();
 		return res;		
 	}
 
@@ -865,14 +863,6 @@ public ModelCheckerResult computeMultiReachEquilibria(CSG csg, List<Coalition> c
 		boolean done, rew;
 		
 		rew = rewards != null;
-	
-		//System.out.println("-- targets");
-		//for (i = 0; i < coalitions.size(); i++) {
-		//	System.out.println("-- " + i + " " + targets[i]);
-		//}
-		
-		//System.out.println("-- rewards");
-		//System.out.println(rewards);
 		
 		buildCoalitions(csg, coalitions);
 		dominated = new BitSet[numCoalitions];
@@ -982,9 +972,7 @@ public ModelCheckerResult computeMultiReachEquilibria(CSG csg, List<Coalition> c
 		csg.exportToDotFile(pflog, null, true);
 		
 		mainLog.print("\n" + newmodel.infoStringTable() + "\n");
-		
-		//System.exit(1);
-		
+				
 		sol = new double[coalitions.size()][newmodel.getNumStates()];
 		val = new double[coalitions.size()][newmodel.getNumStates()];
 		tmp = new double[coalitions.size()][newmodel.getNumStates()];
@@ -1226,8 +1214,7 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		BitSet[] only = new BitSet[targets.length];
 		BitSet[] phi1 = new BitSet[3];
 		BitSet known = new BitSet();
-		BitSet cpy =  new BitSet();
-		BitSet pindx = new BitSet();
+		BitSet temp =  new BitSet();
 		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
 		double[][] val = new double[coalitions.size()][csg.getNumStates()];
 		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
@@ -1238,7 +1225,6 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		boolean done, rew;
 		long timePrecomp;
 				
-		pindx.set(0, numCoalitions);
 		// player -> iteration -> state -> indexes -> value
 		if (generateStrategy || exportAdv) {
 			//mdpmc.setGenerateStrategy(true);
@@ -1255,9 +1241,7 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 				}
 			} 
 		}
-		
 		rew = rewards != null;
-		
 		for (i = 0; i < targets.length; i++) {
 			only[i] = new BitSet();
 			only[i].or(targets[i]);
@@ -1267,7 +1251,6 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 			}
 			known.or(targets[i]);
 		}		
-		
 		if (!rew) {
 			for (i = 0; i < 2; i++) {
 				phi1[i] = new BitSet();
@@ -1279,38 +1262,23 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 			phi1[2] = new BitSet();
 			phi1[2].or(phi1[0]); 
 			phi1[2].and(phi1[1]); // intersection of phi1(1) and phi1(2)
-		
-			cpy.clear();
-			cpy.or(phi1[0]);
-		
+			temp.clear();
+			temp.or(phi1[0]);
 			phi1[0].andNot(phi1[1]); // phi1(1) minus phi1(2)
-			phi1[1].andNot(cpy); // phi1(2) minus phi1(1)
-		
+			phi1[1].andNot(temp); // phi1(2) minus phi1(1)
 			known.or(phi1[0]);
 			known.or(phi1[1]);
-
-			cpy.clear();
-			cpy.set(0, csg.getNumStates());
-			cpy.andNot(phi1[2]);
-		
-			known.or(cpy);
-		}
-		
+			temp.clear();
+			temp.set(0, csg.getNumStates());
+			temp.andNot(phi1[2]);
+			known.or(temp);
+		}		
 		buildCoalitions(csg, coalitions);
+		dominated = new BitSet[numCoalitions];
+		dominating = new BitSet[numCoalitions];
 		mainLog.println();
-
 		findMaxRowsCols(csg);
-		switch (smtSolver) {
-			case "Z3":
-				eqs = new CSGLabeledPolytopesZ3Push(maxRows, maxCols);
-			break;
-			case "Yices":
-				throw new PrismNotSupportedException("The Yices solver is currently not supported");
-				//eqs = new CSGLabeledPolytopesYicesPushBindings(maxRows, maxCols);
-		}
-		//eqs = new CSGLabeledPolytopesYicesPush();
-		//eqs = new CSGLabeledPolytopesYicesPush(maxRows, maxCols);
-		
+		setSolver();
 		// Add an exception somewhere for reachability rewards and states with positive rewards that do not reach the targets
 		k = 0;
 		if (rew) {
@@ -1380,40 +1348,21 @@ else if (!phi1[2].get(s)) {
 		dominating = new BitSet[numCoalitions];
 		while (true) {
 			for (s = 0; s < csg.getNumStates(); s++) {
-				//System.out.print(s + "-");
-				//System.out.println("-- state " + s);
 				if (!known.get(s)) {
 					if (generateStrategy || exportAdv) {
 						sstrat = new ArrayList<List<Map<BitSet, Double>>>();
-						/*
-						for (p = 0; p < coalitions.size(); p++) {
-			        		mmap.get(p).clear();
-						}
-						*/
 						mmap.clear();
 			    		for (p = 0; p < 2; p++) {
 			        		mmap.add(p, new HashMap<Integer, BitSet>());
 			        	}
 					}
 					if (rew) {
-						eq = stepEquilibria(csg, rewards.get(0), rewards.get(1), mmap, eqs, sstrat, sol, s, min);
-						//eq = stepEquilibria(csg, rewards, mmap, sstrat, sol, s, min);
+						eq = stepEquilibria(csg, rewards.get(0), rewards.get(1), mmap, eqslps, sstrat, sol, s, min);
 					}
 					else {
-						eq = stepEquilibria(csg, null, null, mmap, eqs, sstrat, sol, s, min);
-						//eq = stepEquilibria(csg, null,  mmap, sstrat, sol, s, min);
+						eq = stepEquilibria(csg, null, null, mmap, eqslps, sstrat, sol, s, min);
 					}
 					sw = swne(eq, sstrat, min);
-					/*
-					if (s == csg.getFirstInitialState()) {	
-						System.out.println("-- equilibria");
-						for (int e = 0; e < eq.length; e++) {
-							System.out.println(e + " " + Arrays.toString(eq[e]));
-						}
-						System.out.println("-- selected from " + eq.length);
-						System.out.println(Arrays.toString(sw));
-					}
-					*/
 					val[0][s] = sw[1];
 					val[1][s] = sw[2];
 					// player -> iteration -> state -> indexes -> value
@@ -1448,13 +1397,8 @@ else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(p)) && checkEquil
 			}
 			mainLog.println(k + ": " + sols);
 			*/
-			/*
-			for (p = 0; p < numCoalitions; p++) {
-				System.out.println(Arrays.toString(sol[p]));
-			}
-			*/
-			done = done & PrismUtils.doublesAreClose(sol[0], tmp[0], 1e-6, true);
-			done = done & PrismUtils.doublesAreClose(sol[1], tmp[1], 1e-6, true);
+			done = done & PrismUtils.doublesAreClose(sol[0], tmp[0], termCritParam, termCrit == TermCrit.ABSOLUTE);
+			done = done & PrismUtils.doublesAreClose(sol[1], tmp[1], termCritParam, termCrit == TermCrit.ABSOLUTE);
 			if (done) {
 				break;
 			}
@@ -1479,7 +1423,6 @@ else if (!done && k == maxIters) {
 				res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_P);
 		}
 		res.numIters = k;
-		eqs.clear();
 		return res;		
 	}
 	
@@ -1495,12 +1438,10 @@ public double[] swne(double[][] eqs, List<List<Map<BitSet, Double>>> strats, boo
 			eq[p+1] = eqs[0][p];
 		}
 		isw.set(0);
-		if (strats != null)
+		if (strats != null) { 
 			dist = strats.get(0);
-		//if (eqs.length > 1)
-		//	System.out.println("\nequilibria");
+		}
 		for (int i = 1; i < eqs.length; i++) { // if there are more than one
-		//	System.out.println(Arrays.toString(eqs[i]));
 			sum = 0.0;
 			for (p = 0; p < numCoalitions; p++) { // computes the sum
 				sum += eqs[i][p];
@@ -1522,18 +1463,6 @@ else if (Double.compare(sum, eq[0]) == 0) {
 		}
 		if (isw.cardinality() != 1) {
 			int idx = findMaxEqIndexes(isw, eqs, eq);
-			/*
-			if (idx < 0) {
-				System.out.println("-- isw");
-				System.out.println(isw);
-				System.out.println("-- eqs");
-				for (int i = 0; i < eqs.length; i++) {
-					System.out.println(i + ": " + Arrays.toString(eqs[i]));
-				}
-				System.out.println("-- eq");
-				System.out.println(Arrays.toString(eq));
-			}
-			*/
 			sum = 0.0;
 			for (p = 0; p < numCoalitions; p++) { // computes the sum
 				sum += eqs[idx][p];
@@ -1574,11 +1503,6 @@ else if (Double.compare(eqs[i][p], max) == 0) {
 		}
 		if (maxindexes[0].cardinality() == 1) {
 			idx =  maxindexes[0].nextSetBit(0);
-			/*
-			if (idx < 0) {
-				System.out.println("max 1");
-			}
-			*/
 			return idx;
 		}
 		else {
@@ -1587,22 +1511,11 @@ else if (Double.compare(eqs[i][p], max) == 0) {
 				tmp.and(maxindexes[p]);
 				if (tmp.cardinality() == 1) {
 					idx = tmp.nextSetBit(0);
-					/*
-					if (idx < 0) {
-						System.out.println("max 2");
-					}
-					*/
 					return idx;
 				}
 			}
 			// if this part of the code is reached, all players get the same payoff for all equilibria in tmp
 			idx = maxindexes[0].nextSetBit(0);
-			/*
-			if (idx < 0) {
-				System.out.println("max 3");
-				System.out.println(Arrays.toString(eq));
-				System.out.println(tmp);
-			*/
 			return idx;
 		}
 	}
@@ -1622,6 +1535,15 @@ public void extractStrategyFromSupport(ArrayList<Map<BitSet, Double>> eqstrat, L
 		}
 	}
 	
+	public void addStateRewards(double[][] eqs, CSGRewards csgRewards1, CSGRewards csgRewards2, int s, boolean min) {
+		for (int e = 0; e < eqs.length; e++) {
+			if (csgRewards1 != null)
+				eqs[e][0] += ((min)? -1 * csgRewards1.getStateReward(s) : csgRewards1.getStateReward(s));
+			if (csgRewards2 != null)
+				eqs[e][1] += ((min)? -1 * csgRewards2.getStateReward(s) : csgRewards2.getStateReward(s));
+		}
+	}
+	
 	public void addStateRewards(double[][] eqs, List<CSGRewards> rewards, int s, boolean min) {
 		int e, p;
 		for (e = 0; e < eqs.length; e++) {
@@ -1645,15 +1567,7 @@ public double[][] stepEquilibria(CSG csg, List<CSGRewards> rewards, List<Map<Int
 		int n, p, p1, p2;
 			
 		buildStepGame(csg, rewards, mmap, val, s, min);
-		//active = csg.getActivePlayers(s);
 		active = csg.getConcurrentPlayers(s);
-		
-		//active = new BitSet();
-		//active.set(0);
-		//active.set(1);
-		
-		//System.out.println("\n## " + s);
-		//System.out.println("-- mmap " + mmap);
 
 		time = System.currentTimeMillis();
 		if (active.cardinality() == 1) { // in case just one player has a choice
@@ -1748,7 +1662,7 @@ else if (utilities.get(entry).get(p1) == v && sumv > sumt) { // case utility for
 			eqssmt.setIndexes(strategies);
 			eqssmt.setNumPlayers(numCoalitions);
 			eqssmt.init();
-			eqssmt.translateAssertions(assertions, map);
+			eqssmt.translateAssertions(assertions, mapActionIndex);
 			
 			/*
 			eqss.setNumPlayers(numCoalitions);
@@ -1812,7 +1726,7 @@ else if (utilities.get(entry).get(p1) == v && sumv > sumt) { // case utility for
 					//if (allSupports.get(supp).cardinality() == 25)
 					//System.out.println("\n ## Support " + allSupports.get(supp));
 					//System.out.println("## Support " + allSupports.get(supp));
-					eqsresult = eqssmt.computeEquilibria(allSupports.get(supp), map, s);
+					eqsresult = eqssmt.computeEquilibria(allSupports.get(supp), mapActionIndex, s);
 					//eqsresult = new Pair<CSGResultStatus, ArrayList<Double>>(CSGResultStatus.UNKNOWN, new ArrayList<Double>());
 					if (eqsresult.first == CSGResultStatus.SAT) {
 						/*
@@ -1886,48 +1800,34 @@ else if (eqsresult.first == CSGResultStatus.UNKNOWN) {// && allSupports.get(supp
 		return result;
 	}
 	
-	public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csgRewards2, 
-										List<Map<Integer, BitSet>> mmap,
-										CSGLabeledPolytopes nash,
-										List<List<Map<BitSet, Double>>> strats,
-										double[][] val, int s, boolean min) throws PrismException {
+	public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csgRewards2, List<Map<Integer, BitSet>> mmap, CSGLabeledPolytopes nash,
+			List<List<Map<BitSet, Double>>> strats, double[][] val, int s, boolean min) throws PrismException {
 		Map<BitSet, Double> d1 = null;
 		Map<BitSet, Double> d2 = null;
 		ArrayList<Map<BitSet, Double>> eqstrat;
+		ArrayList<ArrayList<Integer>> nmap;
 		ArrayList<ArrayList<ArrayList<Double>>> bmgame;
 		double[][] val1s, val2s, result;
-		double val1, val2;
+		double val1, val2, ent1, ent2;
 		int[] mIndxs;
 		int nrows, ncols, mrow, mcol;
-		boolean zeroA, zeroB, bMaxRow, bMaxCol, uRow, uCol;
+		boolean equalA, equalB;
 
 		mmap = new ArrayList<Map<Integer, BitSet>>();
-		for (int i = 0; i < 2; i++) {
-        	mmap.add(i, new HashMap<Integer, BitSet>());
+		nmap = new ArrayList<ArrayList<Integer>>();
+		for (int p = 0; p < 2; p++) {
+			mmap.add(p, new HashMap<Integer, BitSet>());
+			nmap.add(p, new ArrayList<Integer>());
 		}
-		
-		bmgame = buildBiMatrixGame(csg, csgRewards1, csgRewards2, mmap, val, s, min);	
-		
+		bmgame = buildBiMatrixGame(csg, csgRewards1, csgRewards2, mmap, nmap, val, s, min);	
 		nrows = bmgame.get(0).size();
 		ncols = bmgame.get(0).get(0).size();
 		val1s = new double[nrows][ncols];
 		val2s = new double[nrows][ncols];
 
-		val1 = 0.0;
-		val2 = 0.0;
-		
-		int maxRow[] = new int[ncols];
-		Arrays.fill(maxRow, 0);
-		int maxCol[] = new int[nrows];
-		Arrays.fill(maxCol, 0);
-
-		bMaxRow = false;
-		bMaxCol = false;
-		uRow = true;
-		uCol = true;
-		
 		/*
-		if (s == csg.getFirstInitialState()) {
+		// --- Uncomment to print matrices ---
+		//if (s == csg.getFirstInitialState()) {
 			System.out.println("\n-- matrices for state " + s + " " + csg.getStatesList().get(s));
 			for (int p = 0; p < 2; p++) {
 				System.out.println("-- player " + p);
@@ -1949,182 +1849,50 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 				}
 			}
 			System.out.println();
-		//}  
+		//} 
 		*/
-		
-		if (nrows > 1 && ncols > 1) {
-			zeroA = true;
-			zeroB = true;
+
+		if (nrows > 1 && ncols > 1) { // both players have choices
+			equalA = true;
+			equalB = true;
+			ent1 = bmgame.get(0).get(0).get(0);
+			ent2 = bmgame.get(1).get(0).get(0);
 			for (int r = 0; r < nrows; r++) {
 				for (int c = 0; c < ncols; c++) {
 					val1 = bmgame.get(0).get(r).get(c);
 					val2 = bmgame.get(1).get(r).get(c);
-					zeroA = zeroA && val1 == 0.0;
-					zeroB = zeroB && val2 == 0.0;
+					equalA = equalA && Double.compare(ent1, val1) == 0;
+					equalB = equalB && Double.compare(ent2, val2) == 0;
 					val1s[r][c] = val1;
 					val2s[r][c] = val2;		
 				}
 			}
-
-			if (!zeroA) {
-				for (int r = 1; r < nrows; r++) {
-					for (int c = 0; c < ncols; c++) {
-						//maxRow[c] = (val1s[r][c] > val1s[maxRow[c]][c])? r : maxRow[c]; 
-						maxRow[c] = (Double.compare(val1s[r][c], val1s[maxRow[c]][c]) > 0)? r : maxRow[c]; 
-					}
-				}
-				bMaxRow = allEqual(maxRow);
-				if (bMaxRow) {
-					int maxr = maxRow[0];
-					/*
-					if (maxr != 0) {	
-						for (int r = 0; r < nrows; r++) { // is this actually needed?
-							if (r != maxr) 
-								uRow = uRow && !Arrays.equals(val1s[r], val1s[maxRow[0]]);
-						}	 
-					}
-					else {*/
-						for (int r = 0; r < nrows; r++) { 
-							if (r != maxr) {
-								for (int c = 0; c < ncols; c++) {
-									//uRow = uRow && val1s[maxr][c] > val1s[r][c];
-									uRow = uRow && Double.compare(val1s[maxr][c], val1s[r][c]) > 0;
-								}
-							}
-						} 
-					//}
-				}
-				bMaxRow = bMaxRow && uRow; // maximal and unique
-				
-				/*
-				//if (s== ?) {
-					if (bMaxRow) {
-						System.out.println("-- maxRow");
-						System.out.println(Arrays.toString(maxRow));
-					}
-				//}
-				*/
-			}
-			else {
-				bMaxRow = true;
-			}
-			
-			if (!zeroB) { 
-				for (int c = 1; c < ncols; c++) {
-					for (int r = 0; r < nrows; r++) {
-						//maxCol[r] = (val2s[r][c] > val2s[r][maxCol[r]])? c : maxCol[r];
-						maxCol[r] = (Double.compare(val2s[r][c], val2s[r][maxCol[r]]) > 0)? c : maxCol[r];
-					}
-				}
-				bMaxCol = allEqual(maxCol);
-				if(bMaxCol) {
-					int maxc = maxCol[0];
-					/*
-					if (maxc != 0) {
-						for (int c = 0; c < ncols; c++) { // is this actually needed?
-							if (c != maxc) {
-								uCol = uCol && !Arrays.equals(getCol(val2s,c), getCol(val2s,maxCol[0]));
-							}
-						}
-					}
-					else {*/
-						for (int c = 0; c < ncols; c++) { // is this actually needed?
-							if (c != maxc) {
-								for (int r = 0; r < nrows; r++) {
-									//uCol = uCol && val2s[r][maxc] > val2s[r][c];
-									uCol = uCol && (Double.compare(val2s[r][maxc], val2s[r][c]) > 0);
-								}
-							}
-						} 
-					//}
-				}
-				bMaxCol = bMaxCol && uCol; // maximal and unique
-				
-				/*
-				//if (s== ?) {
-					if (bMaxCol) {
-						System.out.println("-- maxCol");
-						System.out.println(Arrays.toString(maxCol));
-					}				
-				//}
-				*/
-			}
-			else {
-				bMaxCol = true;
-			}
-			
-			/*
-			System.out.println("-- zeroA " + zeroA);
-			System.out.println("-- zeroB " + zeroB);
-			System.out.println("-- bMaxRow " + bMaxRow);
-			System.out.println("-- bMaxCol " + bMaxCol);
-			*/
-			
-			if (!(zeroA && zeroB)) {
-				result = new double[1][2];
-				if(bMaxRow || bMaxCol) {
-					double v1 = Double.NEGATIVE_INFINITY;
-					double v2 = Double.NEGATIVE_INFINITY;
-					double vsum = Double.NEGATIVE_INFINITY; 
-					double tv1 = Double.NEGATIVE_INFINITY;
-					double tv2 = Double.NEGATIVE_INFINITY;
-					double tvsum = Double.NEGATIVE_INFINITY;  
-					if (zeroA) {
+			if (!(equalA && equalB)) { // at least one has different entries
+				if(equalA || equalB) { // if all entries of one of them are the same
+					result = new double[1][2];
+					if (equalA) { 
 						mIndxs = findMaxIndexes(val2s);
 						mrow = mIndxs[0];
 						mcol = mIndxs[1];
 					}
-					else if (zeroB) {
+					else {
 						mIndxs = findMaxIndexes(val1s);
 						mrow = mIndxs[0];
 						mcol = mIndxs[1];
 					}
-					else if (bMaxRow && bMaxCol) {
-						mrow = maxRow[0];
-						mcol = maxCol[0];
-					} 
-					else if (bMaxRow) {
-						mrow = maxRow[0];
-						mcol = -1;
-						for (int c = 0; c < ncols; c++) {
-							tv1 = val1s[mrow][c];
-							tv2 = val2s[mrow][c];
-							tvsum = tv1 + tv2;
-							if (Double.compare(tv2, v2) > 0 || (Double.compare(tv2, v2) == 0 && Double.compare(tvsum, vsum) > 0)) {
-					 			mcol = c;
-								v2 = tv2;
-								vsum = tvsum;
-							}       
-						}
-					}
-					else {
-						mrow = -1;
-						mcol = maxCol[0];
-						for (int r = 0; r < nrows; r++) {
-							tv1 = val1s[r][mcol];
-							tv2 = val2s[r][mcol];
-							tvsum = tv1 + tv2;
-							if (Double.compare(tv1, v1) > 0 || (Double.compare(tv1, v1) == 0 && Double.compare(tvsum, vsum) > 0)) {
-								mrow = r;
-								v1 = tv1;
-								vsum = tvsum;
-							}       
-						}
-					}
 					result[0][0] = val1s[mrow][mcol];
 					result[0][1] = val2s[mrow][mcol];
-					if(generateStrategy || exportAdv) {
+					if (generateStrategy || exportAdv) {
 						eqstrat = new ArrayList<Map<BitSet, Double>>();
 						eqstrat.add(0, new HashMap<BitSet, Double>());
-						eqstrat.get(0).put(mmap.get(0).get(mrow), 1.0);
+						eqstrat.get(0).put(mmap.get(0).get(nmap.get(0).get(mrow)), 1.0);
 						eqstrat.add(1, new HashMap<BitSet, Double>());
-						eqstrat.get(1).put(mmap.get(1).get(mcol), 1.0);
+						eqstrat.get(1).put(mmap.get(1).get(nmap.get(1).get(mcol)), 1.0);
 						strats.add(0, eqstrat);
 					}
 					addStateRewards(result, csgRewards1, csgRewards2, s, min);
 				}
-				else {
-					//System.out.println("equilibria state " + s);
+				else { // both players have choices and matrices are not trivial, call solver
 					nash.update(nrows, ncols, val1s, val2s);
 					nash.compEq();
 					nash.compPayoffs();
@@ -2136,46 +1904,33 @@ else if (bMaxRow) {
 							eqstrat = new ArrayList<Map<BitSet, Double>>();
 							for (int p = 0; p < 2; p++) {
 								eqstrat.add(p, new HashMap<BitSet, Double>());
+								//System.out.println("-- strat from solver " + nash.getStrat().get(e).get(p).getSupport());
 								for (int t : nash.getStrat().get(e).get(p).getSupport()) {
-									eqstrat.get(p).put(mmap.get(p).get(t), nash.getStrat().get(e).get(p).get(t));
-								}								
+									eqstrat.get(p).put(mmap.get(p).get(nmap.get(p).get(t)), nash.getStrat().get(e).get(p).get(t));
+								}
 							} 
 							strats.add(e, eqstrat);
 						}
 					}
 					addStateRewards(result, csgRewards1, csgRewards2, s, min);
-					/*
-					double[] sw = swne(result, null, false);
-					if (sw[2] > sw[1]) {
-						System.out.println("-- state " + s);
-						for (int p = 0; p < 2; p++) {
-							System.out.println("-- player " + p);
-							for (int r = 0; r < nrows; r++) {
-								System.out.println("-- row " + r + " " + bmgame.get(p).get(r));
-							}
-						}
-						System.out.println("-- sw" + Arrays.toString(sw));
-						System.exit(1);
-					}
-					*/
 				}
 			}
-			else {
+			else { // all entries in both are the same
 				result = new double[1][2];
-				result[0][0] = 0.0;
-				result[0][1] = 0.0;
+				result[0][0] = ent1;
+				result[0][1] = ent2;
 				if (generateStrategy || exportAdv) {
 					eqstrat = new ArrayList<Map<BitSet, Double>>();
 					eqstrat.add(0, new HashMap<BitSet, Double>());
-					eqstrat.get(0).put(mmap.get(0).get(0), 1.0);
+					eqstrat.get(0).put(mmap.get(0).get(nmap.get(0).get(0)), 1.0);
 					eqstrat.add(1, new HashMap<BitSet, Double>());
-					eqstrat.get(1).put(mmap.get(1).get(0), 1.0);
+					eqstrat.get(1).put(mmap.get(1).get(nmap.get(0).get(0)), 1.0);
 					strats.add(0, eqstrat);
 				}
 				addStateRewards(result, csgRewards1, csgRewards2, s, min);
 			}
-		}
-		else {
+		} 
+		else { // just one of the players have choices
 			result = new double[1][2];
 			double vt1, vt2, sumv, sumt;
 			if(generateStrategy || exportAdv) {
@@ -2191,10 +1946,9 @@ else if (bMaxRow) {
 					vt2 = bmgame.get(1).get(r).get(0);
 					sumt = vt1 + vt2;
 					if (Double.compare(vt1, val1) > 0 || (Double.compare(vt1, val1) == 0 && Double.compare(sumt, sumv) > 0)) {
-					//if ((vt1 > val1) || (vt1 == val1 && sumt > sumv)) {
 						if(generateStrategy || exportAdv) {
 							d1.clear();
-							d1.put(mmap.get(0).get(r), 1.0);
+							d1.put(mmap.get(0).get(nmap.get(0).get(r)), 1.0);
 						}
 						val2 = vt2;
 						val1 = vt1;
@@ -2202,7 +1956,7 @@ else if (bMaxRow) {
 					}
 				}
 				if(generateStrategy || exportAdv) 
-					d2.put(mmap.get(1).get(0), 1.0);
+					d2.put(mmap.get(1).get(nmap.get(1).get(0)), 1.0);
 			} 
 			else if (nrows == 1 && ncols > 1) {
 				for (int c = 0; c < ncols; c++) {
@@ -2210,10 +1964,9 @@ else if (nrows == 1 && ncols > 1) {
 					vt2 = bmgame.get(1).get(0).get(c);
 					sumt = vt1 + vt2;
 					if (Double.compare(vt2, val2) > 0 || (Double.compare(vt2, val2) == 0 && Double.compare(sumt, sumv) > 0)) {
-					//if (vt2 > val2 || (vt2 == val2 && sumt > sumv)) {
 						if(generateStrategy || exportAdv) {
 							d2.clear();
-							d2.put(mmap.get(1).get(c), 1.0);
+							d2.put(mmap.get(1).get(nmap.get(1).get(c)), 1.0);
 						}
 						val2 = vt2;
 						val1 = vt1;
@@ -2221,14 +1974,14 @@ else if (nrows == 1 && ncols > 1) {
 					}
 				}
 				if(generateStrategy || exportAdv) 
-					d1.put(mmap.get(0).get(0), 1.0);
+					d1.put(mmap.get(0).get(nmap.get(0).get(0)), 1.0);
 			} 
 			else if (nrows == 1 && ncols == 1) {
 				val1 = bmgame.get(0).get(0).get(0);
 				val2 = bmgame.get(1).get(0).get(0);
 				if(generateStrategy || exportAdv) {
-					d1.put(mmap.get(0).get(0), 1.0);
-					d2.put(mmap.get(1).get(0), 1.0);
+					d1.put(mmap.get(0).get(nmap.get(0).get(0)), 1.0);
+					d2.put(mmap.get(1).get(nmap.get(1).get(0)), 1.0);
 				}
 			} 
 			else {
@@ -2244,88 +1997,6 @@ else if (nrows == 1 && ncols == 1) {
 			result[0][1] = val2;
 			addStateRewards(result, csgRewards1, csgRewards2, s, min);
 		}
-		/*
-		if (s == 3041) {
-			for (int e = 0; e < result.length; e++) {
-				System.out.println(">> eq " + e);
-				for (int p = 0; p < 2; p++) {
-					System.out.println(">> result " + p + " " + result[e][p]);
-				}
-			} 
-		}
-		*/
-		return result;
-	}
-	
-	public void addStateRewards(double[][] eqs, CSGRewards csgRewards1, CSGRewards csgRewards2, int s, boolean min) {
-		for (int e = 0; e < eqs.length; e++) {
-			if (csgRewards1 != null)
-				eqs[e][0] += ((min)? -1 * csgRewards1.getStateReward(s) : csgRewards1.getStateReward(s));
-			if (csgRewards2 != null)
-				eqs[e][1] += ((min)? -1 * csgRewards2.getStateReward(s) : csgRewards2.getStateReward(s));
-		}
-	}
-	
-	public boolean allEqual(int[] a) {
-		boolean r = true;
-		for(int e = 0; e < a.length-1; e++) {
-			r = r && (a[e] == a[e+1]);
-		}
-		return r;
-	}
-	
-	public boolean allEqual(double[][] a) {
-		boolean result = true;
-		double e = a[0][0];
-		for(int r = 0; r < a.length; r++) {
-			for(int c = 0; c < a[r].length; c++) {
-				if(e != a[r][c]) {
-					return false;
-				}
-				else {
-					e = a[r][c];
-				}
-			}
-		}
-		return result;
-	}
-	
-	public double[] getCol(double[][] a, int c) {
-		double[] col = new double[a.length];
-		for(int r = 0; r < a.length; r++) {
-			col[r] = a[r][c];
-		}
-		return col;
-	}
-	
-	public int getMaxIndex(double[] a) {
-		int r = 0;
-		double e = a[0];
-		for(int l = 1; l < a.length; l++) {
-			if(Double.compare(a[l], e) > 0) {
-			//if(a[l] > e) {
-				r = l;
-				e = a[l];
-			}
-		}
-		return r;
-	}
-	
-	public int[] findMaxIndexes(double[][] a) {
-		int result[] = new int[2];
-		result[0] = 0;
-		result[1] = 0;	
-		double value = 0.0;
-		for(int r = 0; r < a.length; r++) {
-			for(int c = 0; c < a[r].length; c++) {
-				if(Double.compare(a[r][c], value) > 0) {
-				//if(a[r][c] > value) {
-					value = a[r][c];
-					result[0] = r;
-					result[1] = c;	
-				}
-			}
-		}		
 		return result;
 	}
 	

From 293842b874dfac4640745f380dd603df1bcd7a46 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabrielhrsantos@gmail.com>
Date: Sat, 3 Apr 2021 08:18:39 +0100
Subject: [PATCH 07/30] update linux libraries

---
 prism/lib/libyices.so.2.6 | Bin 0 -> 1917544 bytes
 prism/lib/yices.jar       | Bin 105995 -> 105745 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100755 prism/lib/libyices.so.2.6

diff --git a/prism/lib/libyices.so.2.6 b/prism/lib/libyices.so.2.6
new file mode 100755
index 0000000000000000000000000000000000000000..e5c1c10fb6864725562962d8b94369802cb24288
GIT binary patch
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From fc29d4e87ba3575c33c07168d3129251b1e703d2 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabrielhrsantos@gmail.com>
Date: Sat, 3 Apr 2021 09:17:12 +0100
Subject: [PATCH 08/30] missing yices linux file

---
 prism/lib/libyices2java.so | Bin 0 -> 297488 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100755 prism/lib/libyices2java.so

diff --git a/prism/lib/libyices2java.so b/prism/lib/libyices2java.so
new file mode 100755
index 0000000000000000000000000000000000000000..0d9faf7c245a3c2c94230f7f8a3d51b570517449
GIT binary patch
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HcmV?d00001


From 0413257415d5e272d3159b9e5a9ad250503fb6f8 Mon Sep 17 00:00:00 2001
From: Gabriel Santos <gabtos@pc-142-107.customer.ask4.lan>
Date: Wed, 7 Jul 2021 11:49:20 +0100
Subject: [PATCH 09/30] missing yices mac file

---
 prism/lib/libyices.2.dylib | Bin 0 -> 1342856 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100755 prism/lib/libyices.2.dylib

diff --git a/prism/lib/libyices.2.dylib b/prism/lib/libyices.2.dylib
new file mode 100755
index 0000000000000000000000000000000000000000..532872836debea5f0d22e055586ec250e0cdbc45
GIT binary patch
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HcmV?d00001


From 3bc1f615d44e335fee45ac3ecaefe73cee8e6535 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 12 Apr 2022 17:55:46 +0100
Subject: [PATCH 10/30] small fixes

---
 prism/src/explicit/CSGLabeledPolytopesZ3.java | 522 +++++++++---------
 .../explicit/CSGLabeledPolytopesZ3Stack.java  | 331 ++++++-----
 .../src/explicit/CSGSupportEnumerationZ3.java |  91 +--
 3 files changed, 503 insertions(+), 441 deletions(-)

diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3.java b/prism/src/explicit/CSGLabeledPolytopesZ3.java
index 31f727fbd..d1dae2b2d 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3.java
@@ -3,7 +3,7 @@
 //	Copyright (c) 2002-
 //	Authors:
 //	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
-//  	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
 //	
 //------------------------------------------------------------------------------
 //	
@@ -43,6 +43,8 @@
 import java.math.BigDecimal;
 
 public class CSGLabeledPolytopesZ3 implements CSGLabeledPolytopes {
+
+	private final String solverName = "Z3";
 	
 	private RealExpr[] payvars;
 	private ArithExpr[] payoffs;
@@ -65,48 +67,48 @@ public class CSGLabeledPolytopesZ3 implements CSGLabeledPolytopes {
 	private double[] p2p;
 	private double[][] a;
 	private double[][] b;
-    
+
 	private String[] lvp1;
-   	private String[] lvp2;
-    
-    	private HashMap<String, String> cfg;
-    	private Context ctx;
-    	private Solver s;
-    
-    	private ArithExpr cp1;
-    	private ArithExpr cp2;
-    	private double time;
-        
-    	private int ndigits = 9;
-    
-    	private ArrayList<ArrayList<Distribution>> strat;
-    
-    public CSGLabeledPolytopesZ3() {
-    	cfg = new HashMap<String, String>();
-        cfg.put("model", "true");
-        ctx = new Context(cfg);
-        s = ctx.mkSolver();        
-    }
-    
-    public CSGLabeledPolytopesZ3(int nrows, int ncols, double[][] a, double[][] b) {
-    	cfg = new HashMap<String, String>();
-        cfg.put("model", "true");
-        ctx = new Context(cfg);
-        s = ctx.mkSolver();
-        this.nrows = nrows;
-        this.ncols = ncols;
-        this.a = a;
-        this.b = b;
-        initialize();
-    }
-        
-    public void update(int nrows, int ncols, double[][] a, double[][] b) {
-        s.reset();
-        this.nrows = nrows;
-        this.ncols = ncols;
-        this.a = a;
-        this.b = b;
-        /*
+	private String[] lvp2;
+
+	private HashMap<String, String> cfg;
+	private Context ctx;
+	private Solver s;
+
+	private ArithExpr cp1;
+	private ArithExpr cp2;
+	private double time;
+
+	private int ndigits = 9;
+
+	private ArrayList<ArrayList<Distribution>> strat;
+
+	public CSGLabeledPolytopesZ3() {
+		cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		ctx = new Context(cfg);
+		s = ctx.mkSolver();        
+	}
+
+	public CSGLabeledPolytopesZ3(int nrows, int ncols, double[][] a, double[][] b) {
+		cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		ctx = new Context(cfg);
+		s = ctx.mkSolver();
+		this.nrows = nrows;
+		this.ncols = ncols;
+		this.a = a;
+		this.b = b;
+		initialize();
+	}
+
+	public void update(int nrows, int ncols, double[][] a, double[][] b) {
+		s.reset();
+		this.nrows = nrows;
+		this.ncols = ncols;
+		this.a = a;
+		this.b = b;
+		/*
         System.out.println("-- matrix a");
         for (int row = 0; row < nrows; row++) {
             System.out.println("-- row " + row + " " + Arrays.toString(a[row]));
@@ -115,13 +117,13 @@ public void update(int nrows, int ncols, double[][] a, double[][] b) {
         for (int row = 0; row < nrows; row++) {
             System.out.println("-- row " + row + " " + Arrays.toString(b[row]));
         }
-        */
-        initialize();
-    }
-    
+		 */
+		initialize();
+	}
+
 	private void initialize() {
 		zero = ctx.mkInt(0);
-	    	one = ctx.mkInt(1);
+		one = ctx.mkInt(1);
 		vars = new RealExpr[nrows+ncols];
 		p1vars = new RealExpr[nrows];
 		p2vars = new RealExpr[ncols];
@@ -145,14 +147,14 @@ private void initialize() {
 			s.add(ctx.mkGe(v, zero));
 		}
 	}
-	
+
 	private void xLabels() {
 		/*
 		System.out.println("-- xexps");
 		for (int l = 0; l < xexps.length; l++) {
 			System.out.println(l + ": " + xexps[l]);
 		}
-		*/
+		 */
 		BoolExpr[] tmp = new BoolExpr[ncols-1];
 		int l = 0;
 		int j = 0;
@@ -179,14 +181,14 @@ private void xLabels() {
 			}
 		}
 	}
-	
+
 	private void yLabels() {
 		/*
 		System.out.println("-- yexps");
 		for (int l = 0; l < yexps.length; l++) {
 			System.out.println(l + ": " + yexps[l]);
 		}
-		*/
+		 */
 		BoolExpr[] tmp = new BoolExpr[nrows-1];
 		int l = 0;
 		int j = 0;
@@ -213,7 +215,7 @@ private void yLabels() {
 			}
 		}
 	}
-	
+
 	private void vMult() {
 		yexps = new ArithExpr[nrows];
 		xexps = new ArithExpr[ncols];
@@ -248,86 +250,86 @@ private void vMult() {
 			xexps[j] = curr;
 		}
 	}
-	
+
 	public void compEq() {
-        	ArrayList<Distribution> dists;
-        	Distribution dist1;
-        	Distribution dist2;
-        	double p;
-        	Model model = null;                
-        	BoolExpr rstr;
-        	BoolExpr prstr;
-        	long start, end;
+		ArrayList<Distribution> dists;
+		Distribution dist1;
+		Distribution dist2;
+		double p;
+		Model model = null;                
+		BoolExpr rstr;
+		BoolExpr prstr;
+		long start, end;
 		int i,j;
-        
-        	BoolExpr c1;
-        	BoolExpr c2;
-        
-        	BoolExpr p1;
-        	BoolExpr p2; 
-		
-        	//in order to check for indifference
-        	BoolExpr xeqrst = ctx.mkTrue();
-        	BoolExpr yeqrst = ctx.mkTrue();
-        
-        	start = new Date().getTime();
-        
-		vMult();
-		xLabels();
-		yLabels();
-		
-		eq = ctx.mkTrue();
-		for(i = 0; i < nrows+ncols; i++) {
-			eq = ctx.mkAnd(eq, ctx.mkOr(xlabels[i], ylabels[i]));
-		}
-		
-		Expr xctr = zero;
-		Expr yctr = zero;
-		
-		for(i = 0; i < nrows; i++) {
-			xctr = ctx.mkAdd((ArithExpr) xctr, vars[i]);
-		}
-		xctr = ctx.mkEq(xctr, one);
-		
-		for(j = i; j < nrows+ncols; j++) {
-			yctr = ctx.mkAdd((ArithExpr) yctr, vars[j]);
-		}
-		yctr = ctx.mkEq(yctr, one);		
-		
-		s.add((BoolExpr) xctr); 
-		s.add((BoolExpr) yctr); 
-		s.add(eq);
-	
-        j = 0; 
 
-        strat = new ArrayList<ArrayList<Distribution>>();
-        eqs = new HashMap<String,ArrayList<Double>> ();
-        
-        /*
+		BoolExpr c1;
+		BoolExpr c2;
+
+		BoolExpr p1;
+		BoolExpr p2; 
+
+		//in order to check for indifference
+		BoolExpr xeqrst = ctx.mkTrue();
+				BoolExpr yeqrst = ctx.mkTrue();
+
+				start = new Date().getTime();
+
+				vMult();
+				xLabels();
+				yLabels();
+
+				eq = ctx.mkTrue();
+				for(i = 0; i < nrows+ncols; i++) {
+					eq = ctx.mkAnd(eq, ctx.mkOr(xlabels[i], ylabels[i]));
+				}
+
+				Expr xctr = zero;
+				Expr yctr = zero;
+
+				for(i = 0; i < nrows; i++) {
+					xctr = ctx.mkAdd((ArithExpr) xctr, vars[i]);
+				}
+				xctr = ctx.mkEq(xctr, one);
+
+				for(j = i; j < nrows+ncols; j++) {
+					yctr = ctx.mkAdd((ArithExpr) yctr, vars[j]);
+				}
+				yctr = ctx.mkEq(yctr, one);		
+
+				s.add((BoolExpr) xctr); 
+				s.add((BoolExpr) yctr); 
+				s.add(eq);
+
+				j = 0; 
+
+				strat = new ArrayList<ArrayList<Distribution>>();
+				eqs = new HashMap<String,ArrayList<Double>> ();
+
+				/*
     	System.out.println("-- xlabels");
         for (int l = 0; l < xlabels.length; l++) {
         	System.out.println(l + ": " + xlabels[l]);
         }
-        
+
     	System.out.println("-- ylabels");
         for (int l = 0; l < ylabels.length; l++) {
         	System.out.println(l + ": " + ylabels[l]);        	
         }
-        */
-        
-        /*
+				 */
+
+				/*
         for(int nv = 0; nv < p1vars.length - 1; nv++) {
         	xeqrst = ctx.mkAnd(xeqrst, ctx.mkEq(p1vars[nv], p1vars[nv+1]));
         }
-        
+
         for(int nv = 0; nv < p2vars.length - 1; nv++) {
         	yeqrst = ctx.mkAnd(yeqrst, ctx.mkEq(p2vars[nv], p2vars[nv+1]));
         }
-        */
-       
-        /*** Too strong? ***/
-       
-       /* 
+				 */
+
+				/*** Too strong? ***/
+
+				/* 
         for(int nv = 0; nv < p1vars.length; nv++) {
             for(int nnv = 0; nnv < p1vars.length; nnv++) {
             	xeqrst = ctx.mkAnd(xeqrst, 
@@ -339,7 +341,7 @@ public void compEq() {
             						);
             }
         }
-        
+
         for(int nv = 0; nv < p2vars.length; nv++) {
             for(int nnv = 0; nnv < p2vars.length; nnv++) {
             	xeqrst = ctx.mkAnd(xeqrst, 
@@ -351,34 +353,34 @@ public void compEq() {
             						);
             }
         }
-        */
-        
-        /*** Too strong? ***/
-        
-        xeqrst = ctx.mkNot(xeqrst);
-        yeqrst = ctx.mkNot(yeqrst);
-        
-        boolean indif = false;
-        
-        addPayoffs();
-        
-        /*
+				 */
+
+				/*** Too strong? ***/
+
+				xeqrst = ctx.mkNot(xeqrst);
+				yeqrst = ctx.mkNot(yeqrst);
+
+				boolean indif = false;
+
+				addPayoffs();
+
+				/*
         Optimize opt = ctx.mkOptimize();
         opt.Add(ctx.mkEq(payoffs[0],  payvars[0]));
         opt.Add(ctx.mkEq(payoffs[1],  payvars[1]));
         opt.MkMaximize(payvars[0]);
         Optimize.Handle mx = opt.MkMaximize(payvars[0]);
         Optimize.Handle my = opt.MkMaximize(payvars[1]);
-        */
-        
-        while (Status.SATISFIABLE == s.check()) {
-            model = s.getModel();
-            rstr = ctx.mkFalse();
-
-            c1 = ctx.mkTrue();
-            c2 = ctx.mkTrue();
-                     
-            /*
+				 */
+
+				while (Status.SATISFIABLE == s.check()) {
+					model = s.getModel();
+					rstr = ctx.mkFalse();
+
+					c1 = ctx.mkTrue();
+					c2 = ctx.mkTrue();
+
+					/*
             if(j > 0) {          	
             	if(((BoolExpr) model.eval(xeqrst, true)).isFalse()) {
             		System.out.println("## Player 1 is indifferent. ##");
@@ -391,100 +393,100 @@ public void compEq() {
             		//break;	
             	}      	            	
             }
-            */
-            
-            //System.out.println(getDoubleValue(model, payvars[0]));
-            //System.out.println(getDoubleValue(model, payvars[1]));
-            //compPayoffs(model);
-                        
-            dists = new ArrayList<Distribution>();
-            dist1 = new Distribution();
-            dist2 = new Distribution();
-            
-            for(i = 0; i < vars.length; i++) {
-            		p = getDoubleValue(model, vars[i]);
-            		if(p > 0) {
-            			if(i < nrows)
-            				dist1.add(i, p);
-            			else 
-            				dist2.add(i - nrows, p);
-            		}
-            		if(j == 0) {
-            			eqs.put(vars[i].getSExpr(), new ArrayList<Double> ());
-            			eqs.get(vars[i].getSExpr()).add(p);
-            		}
-            		else {
-            			//System.out.println((RatNum) model.getConstInterp(vars[i]));
-            			eqs.get(vars[i].getSExpr().toString()).add(p);	
-            		}
-            	//rstr = ctx.mkOr(rstr, ctx.mkNot(ctx.mkEq(vars[i], (RealExpr) model.getConstInterp(vars[i]))));
-            }
-            
-            for(i = 0; i < p1vars.length; i++) {
-            		if(((BoolExpr) model.eval(ctx.mkEq(p1vars[i], zero), true)).isFalse()) {
-            			c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(p1vars[i], zero)));
-            		}
-            		else {
-            			c1 = ctx.mkAnd(c1, ctx.mkEq(p1vars[i], zero));
-            		}
-            }
-            
-            for(i = 0; i < p2vars.length; i++) {
-            		if(((BoolExpr) model.eval(ctx.mkEq(p2vars[i], zero), true)).isFalse()) {
-            			c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(p2vars[i], zero)));
-            		}
-            		else {
-            			c2 = ctx.mkAnd(c2, ctx.mkEq(p2vars[i], zero));
-            		}
-            }            
-            
-            /*
+					 */
+
+					//System.out.println(getDoubleValue(model, payvars[0]));
+					//System.out.println(getDoubleValue(model, payvars[1]));
+					//compPayoffs(model);
+
+					dists = new ArrayList<Distribution>();
+					dist1 = new Distribution();
+					dist2 = new Distribution();
+
+					for(i = 0; i < vars.length; i++) {
+						p = getDoubleValue(model, vars[i]);
+						if(p > 0) {
+							if(i < nrows)
+								dist1.add(i, p);
+							else 
+								dist2.add(i - nrows, p);
+						}
+						if(j == 0) {
+							eqs.put(vars[i].getSExpr(), new ArrayList<Double> ());
+							eqs.get(vars[i].getSExpr()).add(p);
+						}
+						else {
+							//System.out.println((RatNum) model.getConstInterp(vars[i]));
+							eqs.get(vars[i].getSExpr().toString()).add(p);	
+						}
+						//rstr = ctx.mkOr(rstr, ctx.mkNot(ctx.mkEq(vars[i], (RealExpr) model.getConstInterp(vars[i]))));
+					}
+
+					for(i = 0; i < p1vars.length; i++) {
+						if(((BoolExpr) model.eval(ctx.mkEq(p1vars[i], zero), true)).isFalse()) {
+							c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(p1vars[i], zero)));
+						}
+						else {
+							c1 = ctx.mkAnd(c1, ctx.mkEq(p1vars[i], zero));
+						}
+					}
+
+					for(i = 0; i < p2vars.length; i++) {
+						if(((BoolExpr) model.eval(ctx.mkEq(p2vars[i], zero), true)).isFalse()) {
+							c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(p2vars[i], zero)));
+						}
+						else {
+							c2 = ctx.mkAnd(c2, ctx.mkEq(p2vars[i], zero));
+						}
+					}            
+
+					/*
             p1 = ctx.mkAnd(c2, ctx.mkEq(payvars[0], model.getConstInterp(payvars[0])));
             p2 = ctx.mkAnd(c1, ctx.mkEq(payvars[1], model.getConstInterp(payvars[1])));
-            */
+					 */
 
-            /*
+					/*
         	prstr = ctx.mkAnd(ctx.mkEq(payvars[0], model.getConstInterp(payvars[0])), ctx.mkEq(payvars[1], model.getConstInterp(payvars[1])));
-            */
-            
-            //System.out.println(opt.Check()); 
-            //System.out.println(mx.getValue());
-            //System.out.println(my.getValue());
-            
-            /*
+					 */
+
+					//System.out.println(opt.Check()); 
+					//System.out.println(mx.getValue());
+					//System.out.println(my.getValue());
+
+					/*
 			System.out.println("--");
 			for(String v : eqs.keySet()) {
 				System.out.println(v + " " + eqs.get(v).get(j));
 			}
 			System.out.println("--");
-            */
-            
-            //System.out.println("$$ dist1 " + dist1);
-            //System.out.println("$$ dist2 " + dist2);
-            
-            
-            dists.add(0,dist1);
-            dists.add(1,dist2);
-            strat.add(j,dists);
-    		
-            j++;
-    		s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
-    		
-    		//s.add(rstr);
-            //s.add(ctx.mkNot(p2));
-            //s.add(ctx.mkNot(p1));
-        }
-        end = new Date().getTime();
-        time = (end - start)/1000.000;
-        //System.out.println("Time: " + time); 
-        if(!indif) {
-        	//System.out.println(j + " equilibrium(a)");
-        }
-        else {
-        	//System.out.println(j-1 + " equilibrium(a)");
-        	//System.out.println("## One of the players is indifferent. ##");
-        }
-        neq = j;
+					 */
+
+					//System.out.println("$$ dist1 " + dist1);
+					//System.out.println("$$ dist2 " + dist2);
+
+
+					dists.add(0,dist1);
+					dists.add(1,dist2);
+					strat.add(j,dists);
+
+					j++;
+					s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
+
+					//s.add(rstr);
+					//s.add(ctx.mkNot(p2));
+					//s.add(ctx.mkNot(p1));
+				}
+				end = new Date().getTime();
+				time = (end - start)/1000.000;
+				//System.out.println("Time: " + time); 
+				if(!indif) {
+					//System.out.println(j + " equilibrium(a)");
+				}
+				else {
+					//System.out.println(j-1 + " equilibrium(a)");
+					//System.out.println("## One of the players is indifferent. ##");
+				}
+				neq = j;
 	}
 
 	public void addPayoffs() {
@@ -507,43 +509,43 @@ public void addPayoffs() {
 	public void compPayoffs(Model model) {	
 		double p1p = 0.0;
 		double p2p = 0.0;
-        for(int i = 0; i < nrows; i++) {
-        	for(int j = 0; j < ncols; j++) {
-        		p1p += getDoubleValue(model, p1vars[i])*
-        			   getDoubleValue(model, p2vars[j])*a[i][j];
-        		p2p += getDoubleValue(model, p1vars[i])*
-        			   getDoubleValue(model, p2vars[j])*b[i][j];
-        	}
-        }	
-        cp1 = getRealValue(p1p);
-        cp2 = getRealValue(p2p);
+		for(int i = 0; i < nrows; i++) {
+			for(int j = 0; j < ncols; j++) {
+				p1p += getDoubleValue(model, p1vars[i])*
+						getDoubleValue(model, p2vars[j])*a[i][j];
+				p2p += getDoubleValue(model, p1vars[i])*
+						getDoubleValue(model, p2vars[j])*b[i][j];
+			}
+		}	
+		cp1 = getRealValue(p1p);
+		cp2 = getRealValue(p2p);
 	}
-	
+
 	public void compPayoffs() {	
 		p1p = new double[neq];
 		p2p = new double[neq];
 		Arrays.fill(p1p, 0.0);
 		Arrays.fill(p2p, 0.0);
 		for(int e = 0; e < neq; e++) {
-        	for(int i = 0; i < nrows; i++) {
-        		for(int j = 0; j < ncols; j++) {
-           			//p1p[e] += eqs.get(lvp1[i].toString()).get(e) * eqs.get(lvp2[j].toString()).get(e) * Precision.round(a[i][j], 9, BigDecimal.ROUND_HALF_EVEN);
-        			//p2p[e] += eqs.get(lvp1[i].toString()).get(e) * eqs.get(lvp2[j].toString()).get(e) * Precision.round(b[i][j], 9, BigDecimal.ROUND_HALF_EVEN);
-        			p1p[e] += eqs.get(p1vars[i].toString()).get(e) * eqs.get(p2vars[j].toString()).get(e) * a[i][j];
-        			p2p[e] += eqs.get(p1vars[i].toString()).get(e) * eqs.get(p2vars[j].toString()).get(e) * b[i][j];
-        		}
-        	}
-        }		
+			for(int i = 0; i < nrows; i++) {
+				for(int j = 0; j < ncols; j++) {
+					//p1p[e] += eqs.get(lvp1[i].toString()).get(e) * eqs.get(lvp2[j].toString()).get(e) * Precision.round(a[i][j], 9, BigDecimal.ROUND_HALF_EVEN);
+					//p2p[e] += eqs.get(lvp1[i].toString()).get(e) * eqs.get(lvp2[j].toString()).get(e) * Precision.round(b[i][j], 9, BigDecimal.ROUND_HALF_EVEN);
+					p1p[e] += eqs.get(p1vars[i].toString()).get(e) * eqs.get(p2vars[j].toString()).get(e) * a[i][j];
+					p2p[e] += eqs.get(p1vars[i].toString()).get(e) * eqs.get(p2vars[j].toString()).get(e) * b[i][j];
+				}
+			}
+		}		
 	}
-	
+
 	public void print() {
-			for(int i = 0; i < neq; i++) {
-				for(String v : eqs.keySet()) {
-					System.out.println(v + " " + eqs.get(v).get(i));
-				}
-				System.out.println("p1 " + p1p[i]);
-				System.out.println("p2 " + p2p[i]);
-        }
+		for(int i = 0; i < neq; i++) {
+			for(String v : eqs.keySet()) {
+				System.out.println(v + " " + eqs.get(v).get(i));
+			}
+			System.out.println("p1 " + p1p[i]);
+			System.out.println("p2 " + p2p[i]);
+		}
 	}
 
 	public double getDoubleValue(Model model, Expr expr) {
@@ -561,7 +563,7 @@ else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 		else
 			return Double.NaN;
 	}
-	
+
 	public ArithExpr getRealValue(double v) {
 		BigFraction fr;
 		ArithExpr result = null;
@@ -576,10 +578,10 @@ public ArithExpr getRealValue(double v) {
 		catch (Exception e) {
 			e.printStackTrace();
 		}
-		*/
+		 */
 		return result;
 	}
-	
+
 	public RealExpr[] getP1vars() {
 		return p1vars;
 	}
@@ -595,7 +597,7 @@ public double[] getP1p() {
 	public double[] getP2p() {
 		return p2p;
 	}
-	
+
 	public int getNeq() {
 		return neq;
 	}
@@ -603,7 +605,7 @@ public int getNeq() {
 	public ArrayList<ArrayList<Distribution>> getStrat() {
 		return strat;
 	}
-	
+
 	public HashMap<String, ArrayList<Double>> getEqs() {
 		return eqs;
 	}
@@ -615,5 +617,11 @@ public String[] getLvp1() {
 	public String[] getLvp2() {
 		return lvp2;
 	}
-	
+
+	@Override
+	public String getSolverName()
+	{
+		return solverName;
+	}
+
 }
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
index 85880f92c..eaf16c99f 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
@@ -1,3 +1,30 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
+//	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
 package explicit;
 
 import java.util.ArrayList;
@@ -22,8 +49,8 @@
 
 public class CSGLabeledPolytopesZ3Stack implements CSGLabeledPolytopes
 {
-	private String solverName = "Z3";
-	
+	private final String solverName = "Z3";
+
 	private RealExpr[] payvars;
 	private ArithExpr[] payoffs;
 	private RealExpr[] vars;
@@ -42,102 +69,102 @@ public class CSGLabeledPolytopesZ3Stack implements CSGLabeledPolytopes
 	private BoolExpr eq;
 	private int nrows = 0;
 	private int ncols = 0;
-	
+
 	private BoolExpr[] tmpc;
 	private BoolExpr[] tmpr;
-	
+
 	private Model model;
-	
+
 	private Expr xctr;
 	private Expr yctr;
 	private BoolExpr c1;
 	private BoolExpr c2; 
-	
+
 	private int neq = 0;
 	private double[] p1p;
 	private double[] p2p;
 	private double[][] a;
 	private double[][] b;
-	
+
 	private String[] lvp1;
 	private String[] lvp2;
-    
-    	private Context ctx;
-    	private Solver s;
-	
+
+	private Context ctx;
+	private Solver s;
+
 	private HashMap<String,ArrayList<Double>> eqs;
-    	private ArrayList<ArrayList<Distribution>> strat;
-   
- 
+	private ArrayList<ArrayList<Distribution>> strat;
+
+
 	public CSGLabeledPolytopesZ3Stack() {
-    	
-    	}
-    
-   public CSGLabeledPolytopesZ3Stack(int nrows, int ncols) throws PrismException
-   {
-    	initSolver();
-        s = ctx.mkSolver(); 
-        eqs = new HashMap<String,ArrayList<Double>>();
-	zero = ctx.mkInt(0);
-	one = ctx.mkInt(1);
-	vars = new RealExpr[nrows+ncols];
-	lvp1 = new String[nrows];
-	lvp2 = new String[ncols];
-	tmpc = new BoolExpr[ncols-1];
-	tmpr = new BoolExpr[nrows-1];
-	xlabels = new BoolExpr[nrows+ncols];
-	ylabels = new BoolExpr[nrows+ncols];
-	yexps = new ArithExpr[nrows];
-	xexps = new ArithExpr[ncols];
-	xctr = zero;
-	yctr = zero;
-	ytrue = ctx.mkTrue();
-	yfalse = ctx.mkFalse();
-	int i = 0, j = 0;
-	for(; i < nrows; i++) {
-		vars[i] = ctx.mkRealConst("x" + i);
-		lvp1[i] = "x_" + i;
+
 	}
-	for(; j < ncols; j++) {
-		vars[i] = ctx.mkRealConst("y" + j);
-		lvp2[j] = "y_" + j;
-		i++;
+
+	public CSGLabeledPolytopesZ3Stack(int nrows, int ncols) throws PrismException
+	{
+		initSolver();
+		s = ctx.mkSolver(); 
+		eqs = new HashMap<String,ArrayList<Double>>();
+		zero = ctx.mkInt(0);
+		one = ctx.mkInt(1);
+		vars = new RealExpr[nrows+ncols];
+		lvp1 = new String[nrows];
+		lvp2 = new String[ncols];
+		tmpc = new BoolExpr[ncols-1];
+		tmpr = new BoolExpr[nrows-1];
+		xlabels = new BoolExpr[nrows+ncols];
+		ylabels = new BoolExpr[nrows+ncols];
+		yexps = new ArithExpr[nrows];
+		xexps = new ArithExpr[ncols];
+		xctr = zero;
+		yctr = zero;
+		ytrue = ctx.mkTrue();
+		yfalse = ctx.mkFalse();
+		int i = 0, j = 0;
+		for(; i < nrows; i++) {
+			vars[i] = ctx.mkRealConst("x" + i);
+			lvp1[i] = "x_" + i;
+		}
+		for(; j < ncols; j++) {
+			vars[i] = ctx.mkRealConst("y" + j);
+			lvp2[j] = "y_" + j;
+			i++;
+		}
+		for(RealExpr v : vars) {
+			s.add(ctx.mkLe(v, one));
+			s.add(ctx.mkGe(v, zero));
+		}
 	}
-	for(RealExpr v : vars) {
-		s.add(ctx.mkLe(v, one));
-		s.add(ctx.mkGe(v, zero));
+
+	/**
+	 * Initialise the solver
+	 */
+	private void initSolver() throws PrismException
+	{
+		HashMap<String, String> cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		cfg.put("auto_config", "true");
+		try {
+			ctx = new Context(cfg);
+			solverName = Version.getFullVersion();
+		} catch (UnsatisfiedLinkError e) {
+			throw new PrismException("Could not initialise Z3: " + e.getMessage());
+		}
+	}
+
+	@Override
+	public String getSolverName()
+	{
+		return solverName;
 	}
-    }
-    
-    /**
-     * Initialise the solver
-     */
-    private void initSolver() throws PrismException
-    {
-    	HashMap<String, String> cfg = new HashMap<String, String>();
-        cfg.put("model", "true");
-        cfg.put("auto_config", "true");
-        try {
-        	ctx = new Context(cfg);
-        	solverName = Version.getFullVersion();
-        } catch (UnsatisfiedLinkError e) {
-        	throw new PrismException("Could not initialise Z3: " + e.getMessage());
-        }
-    }
-    
-    @Override
-    public String getSolverName()
-    {
-    	return solverName;
-    }
-    
+
 	public void update(int nrows, int ncols, double[][] a, double[][] b) {
 		this.nrows = nrows;
 		this.ncols = ncols;
 		this.a = a;
 		this.b = b;
 	}
-	
+
 	private void xLabels() {
 		int l = 0;
 		int j = 0;
@@ -163,7 +190,7 @@ private void xLabels() {
 			}
 		}
 	}
-	
+
 	private void yLabels() {
 		int l = 0;
 		int j = 0;
@@ -189,7 +216,7 @@ private void yLabels() {
 			}
 		}
 	}
-    
+
 	private void vMult() {
 		for(int i = 0; i < nrows; i++) {
 			curr = zero;
@@ -220,7 +247,7 @@ private void vMult() {
 			xexps[j] = curr;
 		}
 	}
-	
+
 	public void compEq() {
 		ArrayList<Distribution> dists;
 		Distribution dist1;
@@ -238,7 +265,7 @@ public void compEq() {
 			/*
 			if (st == 1)
 				System.out.println(xlabels[i]);
-			*/
+			 */
 			eq = ctx.mkAnd(eq, ctx.mkOr(xlabels[i], ylabels[i]));
 		}
 		for(i = 0; i < nrows; i++) {
@@ -252,75 +279,75 @@ public void compEq() {
 		s.add((BoolExpr) xctr);
 		s.add((BoolExpr) yctr);
 		s.add(eq);
-        	strat = new ArrayList<ArrayList<Distribution>>();
+		strat = new ArrayList<ArrayList<Distribution>>();
 		eqs.clear();
-        j = 0; 
-        while (Status.SATISFIABLE == s.check()) {
-            model = s.getModel();
-            c1 = ytrue;
-            c2 = ytrue;
-            dists = new ArrayList<Distribution>();
-            dist1 = new Distribution();
-            dist2 = new Distribution();
-    		//System.out.println("---");
-            for (i = 0; i < nrows+ncols; i++) {            	
-        		//p = model.bigRationalValue(vars[i]).doubleValue();
-            	p = getDoubleValue(model, vars[i]);
-        		//System.out.println(p);
-        		if(p > 0) {
-        			if(i < nrows)
-        				dist1.add(i, p);
-        			else 
-        				dist2.add(i - nrows, p);
-        		}
-                if (j == 0) {
-        			if (i < nrows) {
-                		eqs.put(lvp1[i], new ArrayList<Double>());
-                		eqs.get(lvp1[i]).add(p);
-                	} 
-        			else {
-        	       		eqs.put(lvp2[i-nrows], new ArrayList<Double>());
-        	       		eqs.get(lvp2[i-nrows]).add(p);
-                	}
-                }
-                else {
-        			if (i < nrows) {
-                		eqs.get(lvp1[i]).add(p);
-                	} 
-        			else {
-        				eqs.get(lvp2[i-nrows]).add(p);		
-               		}
-       			}
-            }
-            for(i = 0; i < nrows+ncols; i++) {
+		j = 0; 
+		while (Status.SATISFIABLE == s.check()) {
+			model = s.getModel();
+			c1 = ytrue;
+			c2 = ytrue;
+			dists = new ArrayList<Distribution>();
+			dist1 = new Distribution();
+			dist2 = new Distribution();
+			//System.out.println("---");
+			for (i = 0; i < nrows+ncols; i++) {            	
+				//p = model.bigRationalValue(vars[i]).doubleValue();
+				p = getDoubleValue(model, vars[i]);
+				//System.out.println(p);
+				if(p > 0) {
+					if(i < nrows)
+						dist1.add(i, p);
+					else 
+						dist2.add(i - nrows, p);
+				}
+				if (j == 0) {
+					if (i < nrows) {
+						eqs.put(lvp1[i], new ArrayList<Double>());
+						eqs.get(lvp1[i]).add(p);
+					} 
+					else {
+						eqs.put(lvp2[i-nrows], new ArrayList<Double>());
+						eqs.get(lvp2[i-nrows]).add(p);
+					}
+				}
+				else {
+					if (i < nrows) {
+						eqs.get(lvp1[i]).add(p);
+					} 
+					else {
+						eqs.get(lvp2[i-nrows]).add(p);		
+					}
+				}
+			}
+			for(i = 0; i < nrows+ncols; i++) {
 				if (i < nrows) {
-        			//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
-        			if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
-        				c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(vars[i], zero)));
-        			}
-            		else {
-            			c1 = ctx.mkAnd(c1, ctx.mkEq(vars[i], zero));
-            		}
+					//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
+					if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
+						c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(vars[i], zero)));
+					}
+					else {
+						c1 = ctx.mkAnd(c1, ctx.mkEq(vars[i], zero));
+					}
 				} 
 				else {
-    				//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
-    				if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
-    					c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(vars[i], zero)));
-            		}
-            		else {
-            			c2 = ctx.mkAnd(c2, ctx.mkEq(vars[i], zero));
-            		}
+					//if (Double.compare(model.bigRationalValue(vars[i]).doubleValue(), 0.0) != 0) {
+					if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
+						c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(vars[i], zero)));
+					}
+					else {
+						c2 = ctx.mkAnd(c2, ctx.mkEq(vars[i], zero));
+					}
 				}
-            }
-            dists.add(0, dist1);
-            dists.add(1, dist2);
-            strat.add(j, dists);
-	    j++;
-            s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
-        }
-	//System.out.println(eqs);
-        s.pop();
-        neq = j;
+			}
+			dists.add(0, dist1);
+			dists.add(1, dist2);
+			strat.add(j, dists);
+			j++;
+			s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
+		}
+		//System.out.println(eqs);
+		s.pop();
+		neq = j;
 	}
 
 	public void compPayoffs() {
@@ -329,13 +356,13 @@ public void compPayoffs() {
 		Arrays.fill(p1p, 0.0);
 		Arrays.fill(p2p, 0.0);
 		for(int e = 0; e < neq; e++) {
-        	for(int i = 0; i < nrows; i++) {
-        		for(int j = 0; j < ncols; j++) {
-        			p1p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * a[i][j];
-        			p2p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * b[i][j];
-        		}
-        	}
-        }			
+			for(int i = 0; i < nrows; i++) {
+				for(int j = 0; j < ncols; j++) {
+					p1p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * a[i][j];
+					p2p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * b[i][j];
+				}
+			}
+		}			
 	}
 
 	public double getDoubleValue(Model model, Expr expr) {
@@ -353,7 +380,7 @@ else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 		else
 			return Double.NaN;
 	}
-	
+
 	public ArrayList<ArrayList<Distribution>> getStrat() {
 		return strat;
 	}
@@ -365,13 +392,13 @@ public double[] getP1p() {
 	public double[] getP2p() {
 		return p2p;
 	}
-	
+
 	public int getNeq() {
 		return neq;
 	}
 
 	public void clear() {
-		
+
 	}
-	
+
 }
diff --git a/prism/src/explicit/CSGSupportEnumerationZ3.java b/prism/src/explicit/CSGSupportEnumerationZ3.java
index 91d44773f..a9a10c6d8 100644
--- a/prism/src/explicit/CSGSupportEnumerationZ3.java
+++ b/prism/src/explicit/CSGSupportEnumerationZ3.java
@@ -1,3 +1,30 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
+//	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
 package explicit;
 
 import java.util.ArrayList;
@@ -24,8 +51,8 @@ public class CSGSupportEnumerationZ3 implements CSGSupportEnumeration {
 
 	private HashMap<String, String> cfg;
 	private Context ctx;
-    private Solver s;
-    
+	private Solver s;
+
 	private ArrayList<ArithExpr> payoffs;	
 	private ArrayList<ArrayList<ArithExpr>> strategies;
 	private HashMap<Integer, HashMap<Integer, ArithExpr>> assertions;
@@ -33,38 +60,38 @@ public class CSGSupportEnumerationZ3 implements CSGSupportEnumeration {
 
 	private IntNum zero;
 	private IntNum one;
-	
+
 	private BitSet players;
 	private BoolExpr support;
-	
+
 	private int numPlayers;
 	private Params params;
-	
-    private ArrayList<Distribution> strat;
-    
-    private int ndigits = 9;
-	
+
+	private ArrayList<Distribution> strat;
+
+	private int ndigits = 9;
+
 	public CSGSupportEnumerationZ3() {
-    	cfg = new HashMap<String, String>();
-        cfg.put("model", "true");
-        ctx = new Context(cfg);
-        s = ctx.mkSolver();        
-        
-        params = ctx.mkParams();
+		cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		ctx = new Context(cfg);
+		s = ctx.mkSolver();        
+
+		params = ctx.mkParams();
 		params.add("timeout", 20);
 		s.setParameters(params);
-		
+
 		assertions = new HashMap<Integer, HashMap<Integer, ArithExpr>>();
 		strategies = new ArrayList<ArrayList<ArithExpr>>();
 		payoffs = new ArrayList<ArithExpr>();
 		players = new BitSet();
 		strat = new ArrayList<Distribution>();
 	}
-	
+
 	public void init() {
 		s.reset();
 		s.setParameters(params);
-		
+
 		players.clear();
 		players.set(0, numPlayers);
 		strategies.clear();
@@ -88,7 +115,7 @@ public void init() {
 		//System.out.println(indexes);
 		//System.out.println(strategies);
 	}
-	
+
 	public void computeConstraints(BitSet supp) {
 		for(int p = 0; p < indexes.size(); p++) {
 			for(int a = 0; a < indexes.get(p).size(); a++) {
@@ -116,7 +143,7 @@ public void computeSupport(BitSet supp, HashMap<Integer, int[]> map) {
 		}
 		s.add(support);
 	}
-	
+
 	public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, HashMap<Integer, int[]> map, int st) {
 		s.push();
 		computeConstraints(supp);
@@ -126,12 +153,12 @@ public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, H
 		for(int i = 0; i < s.getNumAssertions(); i++) {
 			System.out.println(s.getAssertions()[i]);
 		}
-		*/
+		 */
 		Model model;
 		ArrayList<Double> eq = new ArrayList<>();
 		Distribution d;
 		double v;
-		
+
 		Status result = s.check();
 		if(result == Status.SATISFIABLE) {
 			model = s.getModel();
@@ -149,10 +176,10 @@ public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, H
 		}
 		s.pop();
 		return new Pair<CSGResultStatus, ArrayList<Double>>((result == Status.SATISFIABLE)? CSGResultStatus.SAT : 
-															(result == Status.UNKNOWN)? CSGResultStatus.UNKNOWN :
-																						CSGResultStatus.UNSAT, new ArrayList<Double>(eq));	
+			(result == Status.UNKNOWN)? CSGResultStatus.UNKNOWN :
+				CSGResultStatus.UNSAT, new ArrayList<Double>(eq));	
 	}
-	
+
 	public double getDoubleValue(Model model, Expr expr) {
 		RatNum v1;
 		AlgebraicNum v2;
@@ -168,7 +195,7 @@ else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 		else
 			return Double.NaN;
 	}
-  	
+
 	public void translateAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> assertionsIdx, HashMap<Integer, int[]> map) {
 		assertions.clear();
 		ArithExpr sum, prod;
@@ -188,18 +215,18 @@ public void translateAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair
 			}
 		}
 	}
-	
+
 	public ArithExpr getRealValue(double v) {
 		ArithExpr result;
 		result = ctx.mkReal((long) (Math.pow(10, ndigits) * v));
 		result = ctx.mkDiv(result, ctx.mkReal((long) (Math.pow(10, ndigits))));
 		return result;
 	}
-	
+
 	public void setNumPlayers(int n) {
 		this.numPlayers = n;
 	}
-	
+
 	public void setIndexes(ArrayList<ArrayList<Integer>> a) {
 		this.indexes = a;
 	}
@@ -207,17 +234,17 @@ public void setIndexes(ArrayList<ArrayList<Integer>> a) {
 	public ArrayList<Distribution> getStrat() {
 		return new ArrayList<Distribution>(this.strat);
 	}
-	
+
 	@Override
 	public void setGradient(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> gradient) {
 		// TODO Auto-generated method stub
-		
+
 	}
 
 	@Override
 	public void setAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> assertions) {
 		// TODO Auto-generated method stub
-		
+
 	}
 
 }

From 32f4fe005dad30a0e3d5f35de6fb7e04884d2f18 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 12 Apr 2022 18:00:43 +0100
Subject: [PATCH 11/30] small fixes

---
 .../CSGLabeledPolytopesYicesStack.java        | 294 +++++++++---------
 .../explicit/CSGLabeledPolytopesZ3Stack.java  |   2 +-
 2 files changed, 148 insertions(+), 148 deletions(-)

diff --git a/prism/src/explicit/CSGLabeledPolytopesYicesStack.java b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
index eff9e244c..ec0c8a36c 100644
--- a/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
@@ -17,68 +17,68 @@
 
 public class CSGLabeledPolytopesYicesStack implements CSGLabeledPolytopes
 {
-	private String solverName = "Yices";
+	private String solverName;
 
 	private Config cfg;
 	private Context ctx;
-	
+
 	private int realType;
 	private int boolType;
-	
+
 	private int zero;
 	private int one;
 	private int ytrue;
 	private int yfalse;
-	
+
 	private int eq;
-	
+
 	private int curr;
-	
+
 	private int[] xlabels;
 	private int[] ylabels;
-		
+
 	private int[] vars;
 	private int[] xexps;
 	private int[] yexps;
-	
+
 	private int[] tmpc;
 	private int[] tmpr;
-	
+
 	private com.sri.yices.Model model;
-	
+
 	private int xctr;
 	private int yctr;
 	private int c1;
 	private int c2; 
-	
+
 	private String[] lvp1;
 	private String[] lvp2;
-	
+
 	private double[][] a;
 	private double[][] b;
 
 	private double[] p1p;
 	private double[] p2p;
-		
+
 	private int neq;
 	private int nrows;
 	private int ncols;
-	
+
 	private HashMap<String,ArrayList<Double>> eqs;
 	private ArrayList<ArrayList<Distribution>> strat;
-	
+
 	protected String eqPolicy;
-    
-   	public CSGLabeledPolytopesYicesStack() {
-    	
-    	}
-    
-    	public CSGLabeledPolytopesYicesStack(int nrows, int ncols) throws PrismException
-    	{
-    		initSolver();
-        	eqs = new HashMap<String,ArrayList<Double>>();
-        	realType = Yices.realType();
-        	boolType = Yices.boolType();
+
+	public CSGLabeledPolytopesYicesStack() {
+
+	}
+
+	public CSGLabeledPolytopesYicesStack(int nrows, int ncols) throws PrismException
+	{
+		initSolver();
+		eqs = new HashMap<String,ArrayList<Double>>();
+		realType = Yices.realType();
+		boolType = Yices.boolType();
 		zero = Terms.intConst(0);
 		one = Terms.intConst(1);
 		vars = new int[nrows+ncols];
@@ -108,14 +108,14 @@ public CSGLabeledPolytopesYicesStack(int nrows, int ncols) throws PrismException
 			ctx.assertFormula(Terms.arithLeq(v, one));
 			ctx.assertFormula(Terms.arithGeq(v, zero));
 		}
-    	}
-    
+	}
+
 	public void clear() throws PrismException
-    	{
-    		initSolver();
-        	eqs = new HashMap<String,ArrayList<Double>>();
-        	realType = Yices.realType();
-        	boolType = Yices.boolType();
+	{
+		initSolver();
+		eqs = new HashMap<String,ArrayList<Double>>();
+		realType = Yices.realType();
+		boolType = Yices.boolType();
 		zero = Terms.intConst(0);
 		one = Terms.intConst(1);
 		vars = new int[nrows+ncols];
@@ -145,37 +145,37 @@ public void clear() throws PrismException
 			ctx.assertFormula(Terms.arithLeq(v, one));
 			ctx.assertFormula(Terms.arithGeq(v, zero));
 		}
-    	}
-    
-    	/**
-	* Initialise the solver
-     	*/
-    	private void initSolver() throws PrismException
-    	{
-        	try {
-        		Config cfg = new Config("QF_LRA");
-    			cfg.set("mode", "push-pop");
-    			ctx = new Context(cfg);
-    			cfg.close();
-        		solverName = "Yices " + Version.versionString;
-        	} catch (UnsatisfiedLinkError e) {
-        		throw new PrismException("Could not initialise Yices: " + e.getMessage());
-        	}
-    	}
-    
-    	@Override
-    	public String getSolverName()
-    	{
-    		return solverName;
-    	}
-    
+	}
+
+	/**
+	 * Initialise the solver
+	 */
+	private void initSolver() throws PrismException
+	{
+		try {
+			Config cfg = new Config("QF_LRA");
+			cfg.set("mode", "push-pop");
+			ctx = new Context(cfg);
+			cfg.close();
+			solverName = "Yices " + Version.versionString;
+		} catch (UnsatisfiedLinkError e) {
+			throw new PrismException("Could not initialise Yices: " + e.getMessage());
+		}
+	}
+
+	@Override
+	public String getSolverName()
+	{
+		return solverName;
+	}
+
 	public void update(int nrows, int ncols, double[][] a, double[][] b) {
 		this.nrows = nrows;
 		this.ncols = ncols;
 		this.a = a;
 		this.b = b;
 	}
-	
+
 	private void xLabels() {
 		int l = 0;
 		int j = 0;
@@ -201,7 +201,7 @@ private void xLabels() {
 			}
 		}
 	}
-	
+
 	private void yLabels() {
 		int l = 0;
 		int j = 0;
@@ -227,14 +227,14 @@ private void yLabels() {
 			}
 		}
 	}
-	
+
 	private void vMult() {
 		for(int i = 0; i < nrows; i++) {
 			curr = zero;
 			for(int j = 0; j < ncols; j++) {
 				try {
 					curr = Terms.add(curr, Terms.mul(vars[nrows+j], 
-													Terms.parseFloat(String.valueOf(a[i][j]))));
+							Terms.parseFloat(String.valueOf(a[i][j]))));
 				}
 				catch(Exception e) {
 					e.printStackTrace();
@@ -247,7 +247,7 @@ private void vMult() {
 			for(int i = 0; i < nrows; i++) {
 				try {		
 					curr = Terms.add(curr, Terms.mul(vars[i], 
-													Terms.parseFloat(String.valueOf(b[i][j]))));
+							Terms.parseFloat(String.valueOf(b[i][j]))));
 				}
 				catch(Exception e) {
 					e.printStackTrace();
@@ -285,88 +285,88 @@ public void compEq() throws PrismException
 		ctx.assertFormula(xctr);
 		ctx.assertFormula(yctr);
 		ctx.assertFormula(eq);
-        	strat = new ArrayList<ArrayList<Distribution>>();
+		strat = new ArrayList<ArrayList<Distribution>>();
 		eqs.clear();
-        
-	j = 0; 
-        while (ctx.check() == Status.SAT) {
-            model = ctx.getModel();        
-            c1 = ytrue;
-            c2 = ytrue;
-            dists = new ArrayList<Distribution>();
-            dist1 = new Distribution();
-            dist2 = new Distribution();
-    	    //System.out.println("---");
-            //String prt = "(";
-            for (i = 0; i < nrows+ncols; i++) {            	
-        	//p = model.bigRationalValue(vars[i]).doubleValue();
-            	p = model.doubleValue(vars[i]);
-        	//prt += p;
-        	//if (i < vars.length - 1)
-        		//prt += ",";
-        	//System.out.println(p);
-        	if(p > 0) {
-        		if(i < nrows)
-        			dist1.add(i, p);
-        		else 
-        			dist2.add(i - nrows, p);
-        	}
-                if (j == 0) {
-        			if (i < nrows) {
-                		eqs.put(lvp1[i], new ArrayList<Double>());
-                		eqs.get(lvp1[i]).add(p);
-                	} 
-        			else {
-        	       		eqs.put(lvp2[i-nrows], new ArrayList<Double>());
-        	       		eqs.get(lvp2[i-nrows]).add(p);
-                	}
-                }
-                else {
-        			if (i < nrows) {
-                		eqs.get(lvp1[i]).add(p);
-                	} 
-        			else {
-        				eqs.get(lvp2[i-nrows]).add(p);		
-               		}
-       			}
-            }
-            //prt += ")";
-            //System.out.println(prt);
-            if (eqPolicy == "first_found") {
-                dists.add(0, dist1);
-                dists.add(1, dist2);
-                strat.add(j, dists);
-        		j++;
-        		break;
-            }
-            for(i = 0; i < nrows+ncols; i++) {
+
+		j = 0; 
+		while (ctx.check() == Status.SAT) {
+			model = ctx.getModel();        
+			c1 = ytrue;
+			c2 = ytrue;
+			dists = new ArrayList<Distribution>();
+			dist1 = new Distribution();
+			dist2 = new Distribution();
+			//System.out.println("---");
+			//String prt = "(";
+			for (i = 0; i < nrows+ncols; i++) {            	
+				//p = model.bigRationalValue(vars[i]).doubleValue();
+				p = model.doubleValue(vars[i]);
+				//prt += p;
+				//if (i < vars.length - 1)
+				//prt += ",";
+				//System.out.println(p);
+				if(p > 0) {
+					if(i < nrows)
+						dist1.add(i, p);
+					else 
+						dist2.add(i - nrows, p);
+				}
+				if (j == 0) {
+					if (i < nrows) {
+						eqs.put(lvp1[i], new ArrayList<Double>());
+						eqs.get(lvp1[i]).add(p);
+					} 
+					else {
+						eqs.put(lvp2[i-nrows], new ArrayList<Double>());
+						eqs.get(lvp2[i-nrows]).add(p);
+					}
+				}
+				else {
+					if (i < nrows) {
+						eqs.get(lvp1[i]).add(p);
+					} 
+					else {
+						eqs.get(lvp2[i-nrows]).add(p);		
+					}
+				}
+			}
+			//prt += ")";
+			//System.out.println(prt);
+			if (eqPolicy == "first_found") {
+				dists.add(0, dist1);
+				dists.add(1, dist2);
+				strat.add(j, dists);
+				j++;
+				break;
+			}
+			for(i = 0; i < nrows+ncols; i++) {
 				if (i < nrows) {
-        			if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
-        				c1 = Terms.and(c1, Terms.not(Terms.arithEq(vars[i], zero)));
-        			}
-            		else {
-            			c1 = Terms.and(c1, Terms.arithEq(vars[i], zero));
-            		}
+					if (Double.compare(eqs.get(lvp1[i]).get(j), 0.0) != 0) {
+						c1 = Terms.and(c1, Terms.not(Terms.arithEq(vars[i], zero)));
+					}
+					else {
+						c1 = Terms.and(c1, Terms.arithEq(vars[i], zero));
+					}
 				} 
 				else {
-    				if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
-    					c2 = Terms.and(c2, Terms.not(Terms.arithEq(vars[i], zero)));
-            		}
-            		else {
-            			c2 = Terms.and(c2, Terms.arithEq(vars[i], zero));
-            		}
+					if (Double.compare(eqs.get(lvp2[i-nrows]).get(j), 0.0) != 0) {
+						c2 = Terms.and(c2, Terms.not(Terms.arithEq(vars[i], zero)));
+					}
+					else {
+						c2 = Terms.and(c2, Terms.arithEq(vars[i], zero));
+					}
 				}
-            }
-            dists.add(0, dist1);
-            dists.add(1, dist2);
-            strat.add(j, dists);
-    		j++;
-            ctx.assertFormula(Terms.or(Terms.not(c1), Terms.not(c2)));
-        }
-        model.close();
-        neq = j;
-        Yices.reset();
-        compPayoffs();
+			}
+			dists.add(0, dist1);
+			dists.add(1, dist2);
+			strat.add(j, dists);
+			j++;
+			ctx.assertFormula(Terms.or(Terms.not(c1), Terms.not(c2)));
+		}
+		model.close();
+		neq = j;
+		Yices.reset();
+		compPayoffs();
 	}
 
 	public void compPayoffs() {
@@ -375,13 +375,13 @@ public void compPayoffs() {
 		Arrays.fill(p1p, 0.0);
 		Arrays.fill(p2p, 0.0);
 		for(int e = 0; e < neq; e++) {
-        	for(int i = 0; i < nrows; i++) {
-        		for(int j = 0; j < ncols; j++) {
-        			p1p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * a[i][j];
-        			p2p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * b[i][j];
-        		}
-        	}
-        }			
+			for(int i = 0; i < nrows; i++) {
+				for(int j = 0; j < ncols; j++) {
+					p1p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * a[i][j];
+					p2p[e] += eqs.get(lvp1[i]).get(e) * eqs.get(lvp2[j]).get(e) * b[i][j];
+				}
+			}
+		}			
 	}
 
 	public ArrayList<ArrayList<Distribution>> getStrat() {
@@ -395,7 +395,7 @@ public double[] getP1p() {
 	public double[] getP2p() {
 		return p2p;
 	}
-	
+
 	public int getNeq() {
 		return neq;
 	}
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
index eaf16c99f..d07ad5cf4 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
@@ -49,7 +49,7 @@
 
 public class CSGLabeledPolytopesZ3Stack implements CSGLabeledPolytopes
 {
-	private final String solverName = "Z3";
+	private String solverName;
 
 	private RealExpr[] payvars;
 	private ArithExpr[] payoffs;

From e3279a65ca889839c490427b65527efd5e6174b3 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 25 Apr 2022 18:44:02 +0100
Subject: [PATCH 12/30] change assumption check for two player equilibria

---
 .../src/explicit/CSGModelCheckerEquilibria.java | 17 ++++++++++++++---
 1 file changed, 14 insertions(+), 3 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index cfb309f9d..56b104df7 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -3,7 +3,7 @@
 //	Copyright (c) 2002-
 //	Authors:
 //	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
-//  	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
 //	
 //------------------------------------------------------------------------------
 //	
@@ -1274,9 +1274,20 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		
 		mainLog.println("Starting equilibria computation (solver=" + eqslps.getSolverName() + ")...");
 		
-		// Add an exception somewhere for reachability rewards and states with positive rewards that do not reach the targets
+		mainLog.println("Checking whether all objctives are reachable...");
+		for (i = 0; i < targets.length; i++) {
+			BitSet target_check = new BitSet();
+			if (!rew) {
+				target_check.or(remain[i]);
+				target_check.flip(0, csg.getNumStates());
+			}
+			target_check.or(targets[i]);
+			if (mdpmc.prob1((MDP) csg, null, target_check, true, null).cardinality() != csg.numStates)
+				throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
+		}
+		
 		k = 0;
-		if (rew) {
+		if (rew) {			
 			// Precompuation for rewards
 			timePrecomp = System.currentTimeMillis();
 			for (i = 0; i < targets.length; i++) {

From 0a4bbd7a0b39dcb0254792edc8901120bb9cf24a Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 25 Apr 2022 19:31:55 +0100
Subject: [PATCH 13/30] change assumption check for two player equilibria

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 56b104df7..e66470baa 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1275,14 +1275,17 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		mainLog.println("Starting equilibria computation (solver=" + eqslps.getSolverName() + ")...");
 		
 		mainLog.println("Checking whether all objctives are reachable...");
+		
 		for (i = 0; i < targets.length; i++) {
-			BitSet target_check = new BitSet();
+			temp.clear();
 			if (!rew) {
-				target_check.or(remain[i]);
-				target_check.flip(0, csg.getNumStates());
+				temp.or(remain[i]);
+				temp.flip(0, csg.getNumStates());
 			}
-			target_check.or(targets[i]);
-			if (mdpmc.prob1((MDP) csg, null, target_check, true, null).cardinality() != csg.numStates)
+			temp.or(targets[i]);
+			System.out.println(temp);
+			System.out.println(mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality());
+			if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)
 				throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
 		}
 		

From b7bc5e39e8ea9d792436ca3fdf9322f3b6e9bf0d Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 25 Apr 2022 19:32:44 +0100
Subject: [PATCH 14/30] change assumption check for two player equilibria

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 2 --
 1 file changed, 2 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index e66470baa..5bdfe3dae 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1283,8 +1283,6 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 				temp.flip(0, csg.getNumStates());
 			}
 			temp.or(targets[i]);
-			System.out.println(temp);
-			System.out.println(mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality());
 			if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)
 				throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
 		}

From 54e4041bc2df4d8ce354a5302821fae10366f5b7 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Wed, 27 Apr 2022 14:30:34 +0100
Subject: [PATCH 15/30] fix null remain for probabilistic

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 5bdfe3dae..6fd3c872d 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1279,7 +1279,8 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		for (i = 0; i < targets.length; i++) {
 			temp.clear();
 			if (!rew) {
-				temp.or(remain[i]);
+				if (remain[i] != null)
+					temp.or(remain[i]);
 				temp.flip(0, csg.getNumStates());
 			}
 			temp.or(targets[i]);

From bec8c132f5ccae16fe8d03e52e9e54b3d71d5c93 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Fri, 29 Apr 2022 16:04:40 +0100
Subject: [PATCH 16/30] fix check for probabilistic

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 6fd3c872d..6bbd64110 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1276,12 +1276,13 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		
 		mainLog.println("Checking whether all objctives are reachable...");
 		
-		for (i = 0; i < targets.length; i++) {
+   		for (i = 0; i < targets.length; i++) {
 			temp.clear();
 			if (!rew) {
-				if (remain[i] != null)
+				if (remain[i] != null) {
 					temp.or(remain[i]);
-				temp.flip(0, csg.getNumStates());
+					temp.flip(0, csg.getNumStates());
+				}
 			}
 			temp.or(targets[i]);
 			if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)

From 7f86ac55aa38178e66628a7f3210e4ce15fe1b60 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 3 May 2022 19:28:10 +0100
Subject: [PATCH 17/30] switch for equilibria assumption check

---
 .../explicit/CSGModelCheckerEquilibria.java   | 28 +++++++++++--------
 prism/src/prism/PrismSettings.java            | 14 ++++++++--
 2 files changed, 28 insertions(+), 14 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 6bbd64110..b9c296d2b 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -97,6 +97,8 @@ public class CSGModelCheckerEquilibria extends CSGModelChecker {
 	
 	protected String smtSolver;
 		
+	protected boolean assumptionCheck = true;
+	
 	public enum CSGResultStatus {
 		SAT, UNKNOWN, UNSAT;
 	}
@@ -117,6 +119,8 @@ public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		mdpmc.setVerbosity(0);
 		mdpmc.setSilentPrecomputations(true);
 		
+		assumptionCheck = getSettings().getBoolean(PrismSettings.PRISM_EQ_ASSUMPTION_CHECK);
+
 		smtSolver = getSettings().getString(PrismSettings.PRISM_SMT_SOLVER);
 		switch (smtSolver) {
 			case "Z3":
@@ -1276,17 +1280,19 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		
 		mainLog.println("Checking whether all objctives are reachable...");
 		
-   		for (i = 0; i < targets.length; i++) {
-			temp.clear();
-			if (!rew) {
-				if (remain[i] != null) {
-					temp.or(remain[i]);
-					temp.flip(0, csg.getNumStates());
-				}
-			}
-			temp.or(targets[i]);
-			if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)
-				throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
+		if (assumptionCheck) {
+   			for (i = 0; i < targets.length; i++) {
+   				temp.clear();
+   				if (!rew) {
+   					if (remain[i] != null) {
+   						temp.or(remain[i]);
+   						temp.flip(0, csg.getNumStates());
+   					}
+   				}
+   				temp.or(targets[i]);
+   				if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)
+   					throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
+   			}
 		}
 		
 		k = 0;
diff --git a/prism/src/prism/PrismSettings.java b/prism/src/prism/PrismSettings.java
index c7dbb1507..ee4d80fba 100644
--- a/prism/src/prism/PrismSettings.java
+++ b/prism/src/prism/PrismSettings.java
@@ -134,7 +134,8 @@ public class PrismSettings implements Observer
 
 	// csg and equilibria
 	public static final String PRISM_ZS_LP_SCALE_FACTOR			= "prism.lpscalefactor";
-
+	public static final String PRISM_EQ_ASSUMPTION_CHECK 			= "prism.eqassumptioncheck";
+	
     // multi-objective synthesis for games
 	public static final     String PRISM_MULTI_GAUSS_SEIDEL					= "prism.multiGaussSeidel";
         // iteration control
@@ -145,7 +146,7 @@ public class PrismSettings implements Observer
         public static final	String PRISM_MULTI_MIN_M         		= "prism.multiMinM";
         public static final	String PRISM_MULTI_MAX_M         		= "prism.multiMaxM";
         // rounding
-	public static final     String PRISM_MULTI_ROUNDING					= "prism.multiRounding";
+        public static final String PRISM_MULTI_ROUNDING					= "prism.multiRounding";
         public static final	String PRISM_MULTI_BASELINE_ACCURACY 		= "prism.baselineAccuracy";
         public static final	String PRISM_MULTI_INCREASE_FACTOR		= "prism.increaseFactor";
         // logging
@@ -368,7 +369,8 @@ public class PrismSettings implements Observer
 			// CSG ZERO-SUM LP SCALE FACTOR
 			{ DOUBLE_TYPE,		PRISM_ZS_LP_SCALE_FACTOR, 					"Scale factor for LPs",			"4.5", 				Double.valueOf(1.0), 			"1,",
 																			"Scale factor used when building linear programs for solving matrix games"},
-
+			{ BOOLEAN_TYPE,		PRISM_EQ_ASSUMPTION_CHECK, 					"Assumption check for equilirbia",			"4.5", 				Boolean.valueOf(true), 			"",
+																			"Assumption check for unbouded equilibria formulae."},
 			// OUTPUT OPTIONS:
 			{ BOOLEAN_TYPE,		PRISM_VERBOSE,							"Verbose output",						"2.1",		Boolean.valueOf(false),															"",																							
 																			"Display verbose output to log." },
@@ -1175,6 +1177,8 @@ else if (sw.equals("power") || sw.equals("pow") || sw.equals("pwr")) {
 			set(PRISM_MDP_SOLN_METHOD, "Linear programming");
 			set(PRISM_MDP_MULTI_SOLN_METHOD, "Linear programming");
 		}
+		
+		// CSG-specific 
 		else if (sw.equals("lpscalefactor")) {// Scale factor for LPs (zero-sum)
 			if (i < args.length - 1) {
 				try {
@@ -1189,6 +1193,10 @@ else if (sw.equals("lpscalefactor")) {// Scale factor for LPs (zero-sum)
 				throw new PrismException("No value specified for -" + sw + " switch");
 			}
 		}
+		
+		else if (sw.equals("eqassumptioncheck")) {
+			set(PRISM_EQ_ASSUMPTION_CHECK, false); 
+		}
 
 		// Interval iterations
 		else if (sw.equals("intervaliter") ||

From 0ebab2b33cc1772e1a4f05f0c1e8fe82114ca04e Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Fri, 10 Feb 2023 21:47:45 +0000
Subject: [PATCH 18/30] Fix and strategy synthesis for next

---
 prism/src/explicit/CSGModelChecker.java       | 64 +++++++++++++++++--
 .../explicit/CSGModelCheckerEquilibria.java   |  2 +-
 2 files changed, 59 insertions(+), 7 deletions(-)

diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index 0ddd5eb0b..7a50d61f8 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -146,17 +146,72 @@ public CSGModelChecker(PrismComponent parent) throws PrismException
 	 */
 	public ModelCheckerResult computeNextProbs(CSG csg, BitSet target, boolean min1, boolean min2, Coalition coalition) throws PrismException
 	{
-		ModelCheckerResult res = null;
+		ModelCheckerResult res = new ModelCheckerResult();
+		LpSolve lp;
+		ArrayList<ArrayList<Double>> mgame = new ArrayList<ArrayList<Double>>();
+		Map<Integer, BitSet> mmap = null;
+		List<List<List<Map<BitSet, Double>>>> lstrat = null;
+		List<Map<BitSet, Double>> kstrat = null;
+		double[] nsol = new double[csg.getNumStates()];
+		long timer;
+		int s, i;
+		if (genStrat || exportAdv) {
+			mmap = new HashMap<Integer, BitSet>();
+			kstrat = new ArrayList<Map<BitSet, Double>>();
+			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>(1);
+			lstrat.add(0, new ArrayList<List<Map<BitSet, Double>>>());
+			lstrat.get(0).add(0, new ArrayList<Map<BitSet, Double>>());
+			for (i = 0; i < csg.getNumStates(); i++) {
+				lstrat.get(0).get(0).add(i, null);
+				kstrat.add(i, null);
+			}
+		}
 		if (verbosity >= 1)
 			mainLog.println("\nStarting next probabilistic reachability for CSGs...");
+		timer = System.currentTimeMillis();
 		buildCoalitions(csg, coalition, min1);
 		switch (solnMethod) {
 		case VALUE_ITERATION:
-			res = computeReachProbsValIter(csg, new BitSet(), new BitSet(), 1, true, min1);
+			for (s = 0; s < csg.getNumStates(); s++) {
+				nsol[s] = target.get(s)? 1.0 : 0.0;
+			}
+			try {
+				lp = LpSolve.makeLp(maxCols + 1, maxRows + 1);
+				lp.setVerbose(LpSolve.CRITICAL);
+				if (min1)
+					lp.resizeLp(0, maxCols + 1);
+				else
+					lp.resizeLp(0, maxRows + 1);
+				
+			} catch (Exception e) {
+				e.printStackTrace();
+				throw new PrismException(e.toString());
+			}
+			for (s = 0; s < csg.getNumStates(); s++) {
+				mgame = buildMatrixGame(csg, null, mmap, nsol, s, min1);
+				nsol[s] = val(lp, mgame, kstrat, mmap, s, true, min1);
+				if ((genStrat || exportAdv)) {
+					// player -> iteration -> state -> indexes -> value
+					if (lstrat.get(0).get(0).get(s) == null) {
+						lstrat.get(0).get(0).set(s, kstrat.get(s));
+					} else if (!lstrat.get(0).get(0).get(s).equals(kstrat.get(s))) {
+						lstrat.get(0).get(0).set(s, kstrat.get(s));
+					}
+				}
+			}
 			break;
 		default:
 			throw new PrismException("Unknown CSG solution method " + solnMethod);
 		}
+		timer = System.currentTimeMillis() - timer;
+		mainLog.println("Next probability computation took " + 1 + " iters and " + timer / 1000.0 + " seconds.");
+		res.soln = nsol;
+		res.lastSoln = null;
+		res.numIters = 1;
+		res.timeTaken = timer / 1000.0;
+		res.timePre = 0.0;
+		if (genStrat || exportAdv)
+			res.strat = new CSGStrategy(csg, lstrat, new BitSet(), target, new BitSet(), CSGStrategyType.ZERO_SUM);
 		return res;
 	}
 
@@ -1868,7 +1923,7 @@ public double val(LpSolve lp, ArrayList<ArrayList<Double>> mgame, List<Map<BitSe
 				}
 			}
 			if (genStrat || exportAdv) {
-				d.put(rmap.get(srow), 1.0); // in case of min, rmap is actually "cmap"
+				d.put(rmap.get(srow), 1.0); // In case of min, rmap maps columns not rows
 				strat.set(s, d);
 			}
 			return res;
@@ -1887,7 +1942,6 @@ public double val(LpSolve lp, ArrayList<ArrayList<Double>> mgame, List<Map<BitSe
 			}
 			return res;
 		} else {
-			// System.out.println("$$ state " + s + " is concurrent");
 			// Should add check for trivial games
 			int infty;
 			infty = valInfinity(mgame);
@@ -1930,8 +1984,6 @@ public double val(LpSolve lp, ArrayList<ArrayList<Double>> mgame, List<Map<BitSe
 						throw new PrismException("lpSolve could not find an optimal solution for state " + s);
 					}
 				} catch (Exception e) {
-					//e.printStackTrace();
-					//lp.printLp();
 					mainLog.println(
 							"Exception raised by lpSolve when computing value for state " + s + ". lpSolve status: " + lp.getStatustext(lp.getStatus()));
 					mainLog.println("Rounding up entries...");
diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 863dfffb5..7e0dc48a6 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1294,7 +1294,7 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
    					}
    				}
    				temp.or(targets[i]);
-   				if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.numStates)
+   				if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.getNumStates())
    					throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");
    			}
 		}

From 4b58ffc1d9c99ffb8c0952bf5a04d621da428ba4 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 13 Feb 2023 13:39:44 +0000
Subject: [PATCH 19/30] Slightly more relaxed assumptions for equilibria

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 7e0dc48a6..354dcfe2d 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1291,8 +1291,10 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
    					if (remain[i] != null) {
    						temp.or(remain[i]);
    						temp.flip(0, csg.getNumStates());
+   						temp.andNot(targets[i]);
    					}
    				}
+				temp.or(mdpmc.prob0((MDP) csg, null, targets[i], false, null));
    				temp.or(targets[i]);
    				if (mdpmc.prob1((MDP) csg, null, temp, true, null).cardinality() != csg.getNumStates())
    					throw new PrismException("At least one of the objectives is not reachable with probability 1 from all states");

From f56302f007cdc609432691f193afc9b31cce0d01 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 13 Feb 2023 16:53:19 +0000
Subject: [PATCH 20/30] Improved precomp for until, tidying, commenting

---
 prism/src/explicit/CSGModelChecker.java       | 244 ++++++++++++++----
 .../explicit/CSGModelCheckerEquilibria.java   |   3 +-
 prism/src/explicit/ProbModelChecker.java      |   2 +-
 3 files changed, 190 insertions(+), 59 deletions(-)

diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index 7a50d61f8..2b903c004 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -314,7 +314,7 @@ public ModelCheckerResult computeReachProbs(CSG csg, BitSet target, boolean min1
 
 		yes.or(target);
 
-		// If <<C>>Pmax=?[F phi], sets coaltiion to compute <<N\C>>Pmax>=1 [G ¬phi] to compute the set "no", that is, the 
+		// If <<C>>Pmax=?[F phi], sets coalition to compute <<N\C>>Pmax>=1 [G ¬phi] to compute the set "no", that is, the 
 		// set of states from which N\C can ensure that C will not to reach phi
 		// If <<C>>Pmin=?[F phi], sets coalition to compute <<C>>Pmax>=1 [G ¬phi] to compute the set "no", that is, the 
 		// set of states from which C can ensure not to reach phi
@@ -380,7 +380,7 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 		ModelCheckerResult res = null;
 		BitSet no, tmp, yes;
 		int n, numYes, numNo;
-		long timerProb0;
+		long timerProb0, timerProb1;
 		if (verbosity >= 1)
 			mainLog.println("\nStarting probabilistic reachability (until)...");
 		n = csg.getNumStates();
@@ -393,10 +393,10 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 		tmp.andNot(target);
 		tmp.andNot(remain);
 
-		// If <<C>>Pmax=?[F phi], sets coaltiion to compute <<N\C>>Pmax>=1 [G ¬phi] to compute the set "no", that is, the 
-		// set of states from which N\C can ensure that C will not to reach phi
-		// If <<C>>Pmin=?[F phi], sets coalition to compute <<C>>Pmax>=1 [G ¬phi] to compute the set "no", that is, the 
-		// set of states from which C can ensure not to reach phi
+		// If <<C>>Pmax=?[phi1 U phi2], sets coalition to compute <<N\C>>Pmax>=1 [G ¬phi2] to compute the set "no", that is, the 
+		// set of states from which N\C can ensure that C will not to reach phi2
+		// If <<C>>Pmin=?[phi1 U phi2], sets coalition to compute <<C>>Pmax>=1 [G ¬phi2] to compute the set "no", that is, the 
+		// set of states from which C can ensure not to reach phi2
 
 		buildCoalitions(csg, coalition, !min1);
 		timerProb0 = System.currentTimeMillis();
@@ -406,15 +406,29 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 			no = G(csg, no);
 		}
 		timerProb0 = System.currentTimeMillis() - timerProb0;
-
 		no.or(tmp);
 		tmp.clear();
+		tmp.set(0, n);
+		tmp.andNot(remain);
+		tmp.andNot(target);
+		no.or(tmp);
+		
+		// If <<C>>Pmax=?[phi1 U ph2], sets coalition to compute <<C>>Pmax>=1 [F phi2] to compute the set "yes"", that is, the
+		// set of states from which C can reach phi with proability 1 while remaining in phi1
+		// If <<C>>Pmin=? [phi1 U phi2], sets coalition to compute <<N\C>>Pmax>=1 [F phi2] to compute the set "yes", that is, the
+		// set of state from which N\C can force C to reach phi with probability 1 while remaining in phi1
+
+		buildCoalitions(csg, coalition, min1);
+		timerProb1 = System.currentTimeMillis();
+		if (precomp && prob1) {
+			yes.or(AF(csg, remain, target));
+		}
+		timerProb1 = System.currentTimeMillis() - timerProb1;
 		yes.or(target);
+		
 		numYes = yes.cardinality();
 		numNo = no.cardinality();
 
-		buildCoalitions(csg, coalition, min1);
-
 		if (verbosity >= 1)
 			mainLog.println("target=" + target.cardinality() + ", yes=" + numYes + ", no=" + numNo + ", maybe=" + (n - (numYes + numNo)));
 		switch (solnMethod) {
@@ -426,8 +440,9 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 		}
 
 		res.timeProb0 = timerProb0 / 1000.0;
+		res.timePre = (timerProb0 + timerProb1) / 1000.0;				
 		if (verbosity >= 1)
-			mainLog.println("Precomputation took " + timerProb0 / 1000.0 + " seconds.");
+			mainLog.println("Precomputation took " +  res.timePre / 1000.0 + " seconds.");
 		return res;
 	}
 
@@ -638,20 +653,6 @@ public ModelCheckerResult computeCumulativeRewards(CSG csg, CSGRewards csgReward
 		return res;
 	}
 
-	/**
-	 * Compute expected total rewards,
-	 * i.e. compute the min/max expected reward accumulated.
-	 * @param csg The CSG
-	 * @param csgRewards The rewards
-	 * @param coalition The coalition of players which define player 1
-	 * @param min1 Min or max probabilities for player 1 (true=min, false=max)
-	 * @param min2 Min or max probabilities for player 2 (true=min, false=max)
-	 */
-	public ModelCheckerResult computeTotalRewards(CSG csg, CSGRewards csgRewards, boolean min1, boolean min2, Coalition coalition) throws PrismException
-	{
-		return computeTotalRewards(csg, csgRewards, coalition, min1, min2);
-	}
-
 	/**
 	 * Compute expected total rewards,
 	 * i.e. compute the min/max expected reward accumulated.
@@ -735,23 +736,6 @@ public ModelCheckerResult computeTotalRewards(CSG csg, CSGRewards rewards, Coali
 		return res;
 	}
 
-	/**
-	 * Compute expected reachability rewards.
-	 * i.e. compute the min/max reward accumulated to reach a state in {@code target}.
-	 * @param csg The CSG
-	 * @param rewards The rewards
-	 * @param target Target states
-	 * @param unreachingSemantics How to handle paths not reaching target
-	 * @param min1 Min or max probabilities for player 1 (true=min, false=max)
-	 * @param min2 Min or max probabilities for player 2 (true=min, false=max)
-	 * @param coalition The coalition of players which define player 1
-	 */
-	public ModelCheckerResult computeReachRewards(CSG csg, CSGRewards rewards, BitSet target, int unreachingSemantics, boolean min1, boolean min2,
-			Coalition coalition) throws PrismException
-	{
-		return computeReachRewards(csg, coalition, rewards, target, min1, min2, unreachingSemantics);
-	}
-
 	/**
 	 * Compute expected reachability rewards.
 	 * i.e. compute the min/max reward accumulated to reach a state in {@code target}.
@@ -763,8 +747,8 @@ public ModelCheckerResult computeReachRewards(CSG csg, CSGRewards rewards, BitSe
 	 * @param min2 Min or max probabilities for player 2 (true=min, false=max)
 	 * @param unreachingSemantics How to handle paths not reaching target
 	 */
-	public ModelCheckerResult computeReachRewards(CSG csg, Coalition coalition, CSGRewards rewards, BitSet target, boolean min1, boolean min2,
-			int unreachingSemantics) throws PrismException
+	public ModelCheckerResult computeReachRewards(CSG csg, CSGRewards rewards, BitSet target, int unreachingSemantics, boolean min1, boolean min2,
+			Coalition coalition) throws PrismException
 	{
 		// TODO: confirm that the case min1==min2 is not handled  
 		switch (unreachingSemantics) {
@@ -1138,7 +1122,19 @@ public ModelCheckerResult computeReachRewardsValIter(CSG csg, CSGRewards rewards
 		res.timeTaken = timer / 1000.0;
 		return res;
 	}
-
+	
+	/**
+	 * Deal with two-player bounded probabilistic reachability formulae
+	 * @param csg The CSG
+	 * @param coalitions A list of two coalitions
+	 * @param exprs The list of objectives
+	 * @param targets The list of sets of target states
+	 * @param remain The list of sets of states we need to remain in (in case of until)
+	 * @param bounds The list of the objectives' bounds (if applicable)
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<ExpressionTemporal> exprs, BitSet[] targets,
 			BitSet[] remain, int[] bounds, boolean min) throws PrismException
 	{
@@ -1148,6 +1144,16 @@ public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition>
 		return res;
 	}
 
+	/**
+	 * Deal with two-player probabilistic reachability formulae
+	 * @param csg The CSG
+	 * @param coalitions A list of two coalitions
+	 * @param targets The list of sets of target states
+	 * @param remain The list of sets of states we need to remain in (in case of until)
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, boolean min)
 			throws PrismException
 	{
@@ -1157,6 +1163,17 @@ public ModelCheckerResult computeProbReachEquilibria(CSG csg, List<Coalition> co
 		return res;
 	}
 
+	/**
+	 * Deal with two-player bounded reachability rewards
+	 * @param csg The CSG
+	 * @param coalitions A list of two coalitions
+	 * @param rewards The list of reward structures
+	 * @param exprs The list of objectives
+	 * @param bounds The list of the objectives' bounds (if applicable)
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeRewBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs,
 			int[] bounds, boolean min) throws PrismException
 	{
@@ -1166,6 +1183,16 @@ public ModelCheckerResult computeRewBoundedEquilibria(CSG csg, List<Coalition> c
 		return res;
 	}
 
+	/**
+	 * Deal with two-player reachability rewards formulae
+	 * @param csg The CSG
+	 * @param coalitions A list of two coalitions
+	 * @param rewards The list of reward structures
+	 * @param targets The list of sets of target states
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, boolean min)
 			throws PrismException
 	{
@@ -1175,6 +1202,16 @@ public ModelCheckerResult computeRewReachEquilibria(CSG csg, List<Coalition> coa
 		return res;
 	}
 
+	/**
+	 * Deal with multi-player probabilistic reachability formulae
+	 * @param csg The CSG
+	 * @param coalitions The list of coalitions
+	 * @param targets The list of sets of target states
+	 * @param remain The list of sets of states we need to remain in (in case of until)
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeMultiProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, boolean min)
 			throws PrismException
 	{
@@ -1184,6 +1221,16 @@ public ModelCheckerResult computeMultiProbReachEquilibria(CSG csg, List<Coalitio
 		return res;
 	}
 
+	/**
+	 * Deal with multi-player reachability rewards formulae
+	 * @param csg The CSG
+	 * @param coalitions The list of coalitions
+	 * @param rewards The list of reward structures
+	 * @param targets The list of sets of target states
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeMultiRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, boolean min)
 			throws PrismException
 	{
@@ -1193,6 +1240,20 @@ public ModelCheckerResult computeMultiRewReachEquilibria(CSG csg, List<Coalition
 		return res;
 	}
 
+	/**
+	 * Deal with computing mixed bounded and unbounded equilibria.
+	 * @param csg The CSG
+	 * @param coalitions The list of coalitions
+	 * @param rewards The list of reward structures
+	 * @param exprs The list of objectives
+	 * @param bounded Index of the objectives which are bounded
+	 * @param targets The list of sets of target states
+	 * @param remain The list of sets of states we need to remain in (in case of until)
+	 * @param bounds The list of the objectives' bounds (if applicable)
+	 * @param min Whether we're minimising for the first coalition
+	 * @return
+	 * @throws PrismException
+	 */
 	public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs,
 			BitSet bounded, BitSet[] targets, BitSet[] remain, int[] bounds, boolean min) throws PrismException
 	{
@@ -1238,7 +1299,9 @@ public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalit
 		AcceptanceType[] allowedAcceptance = { AcceptanceType.RABIN, AcceptanceType.REACH, AcceptanceType.BUCHI, AcceptanceType.STREETT,
 				AcceptanceType.GENERIC };
 
-		//csg.exportToDotFile(path + "/model.dot");
+		/*
+		csg.exportToDotFile(path + "/model.dot");
+		*/
 
 		if (rew) {
 			BitSet all = new BitSet();
@@ -1249,10 +1312,10 @@ public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalit
 			targets[index] = all;
 			switch (exprs.get(index).getOperator()) {
 			case ExpressionTemporal.R_I:
-				da = constructDRAForInstant("L0", false, new IntegerBound(null, false, bounds[index] + 1, false));
+				da = constructDRAForInstant("L0", new IntegerBound(null, false, bounds[index] + 1, false));
 				break;
 			case ExpressionTemporal.R_C:
-				da = constructDRAForInstant("L0", false, new IntegerBound(null, false, bounds[index], false));
+				da = constructDRAForInstant("L0", new IntegerBound(null, false, bounds[index], false));
 				break;
 			}
 
@@ -1282,7 +1345,9 @@ public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalit
 		((ModelExplicit) product.productModel).clearInitialStates();
 		((ModelExplicit) product.productModel).addInitialState(product.getModelState(csg.getFirstInitialState()));
 
-		//product.productModel.exportToDotFile(path + "/product.dot");
+		/*
+		product.productModel.exportToDotFile(path + "/product.dot");
+		*/
 
 		/*
 		try {
@@ -1395,8 +1460,11 @@ public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalit
 		return res;
 	}
 
-	// Precomputation methods
+	// Precomputation methods (almost surely)
 	
+	/*
+	 * Auxiliary method (as defined in L. Alfaro and T. Henzinger, Concurrent Omega-Regular Games)
+	 */
 	public BitSet A(ArrayList<ArrayList<Distribution>> mdist, BitSet v2, BitSet y)
 	{
 		BitSet result = new BitSet();
@@ -1414,6 +1482,9 @@ public BitSet A(ArrayList<ArrayList<Distribution>> mdist, BitSet v2, BitSet y)
 		return result;
 	}
 
+	/*
+	 * Auxiliary method (as defined in L. Alfaro and T. Henzinger, Concurrent Omega-Regular Games)
+	 */
 	public BitSet B(ArrayList<ArrayList<Distribution>> mdist, BitSet v1, BitSet x)
 	{
 		BitSet result = new BitSet();
@@ -1432,6 +1503,10 @@ public BitSet B(ArrayList<ArrayList<Distribution>> mdist, BitSet v1, BitSet x)
 		return result;
 	}
 
+
+	/*
+	 * Auxiliary method for AF (as defined in L. Alfaro and T. Henzinger, Concurrent Omega-Regular Games)
+	 */
 	public BitSet apreXY(CSG csg, BitSet x, BitSet y) throws PrismException
 	{
 		ArrayList<ArrayList<Distribution>> mdist;
@@ -1444,6 +1519,9 @@ public BitSet apreXY(CSG csg, BitSet x, BitSet y) throws PrismException
 		return result;
 	}
 
+	/*
+	 * Eventually B
+	 */
 	public BitSet AF(CSG csg, BitSet b) throws PrismException
 	{
 		int n = csg.getNumStates();
@@ -1471,7 +1549,42 @@ public BitSet AF(CSG csg, BitSet b) throws PrismException
 		}
 		return y;
 	}
+	
+	/*
+	 * Eventually b, while remaining in a
+	 */
+	public BitSet AF(CSG csg, BitSet a, BitSet b) throws PrismException
+	{
+		int n = csg.getNumStates();
+		BitSet x, y, sol1;
+		x = new BitSet();
+		y = new BitSet();
+		y.set(0, n);
+		sol1 = new BitSet();
+		boolean done_x, done_y;
+		done_y = false;
+		while (!done_y) {
+			done_x = false;
+			x.clear();
+			while (!done_x) {
+				sol1.clear();
+				sol1.or(apreXY(csg, x, y));
+				sol1.and(a);
+				sol1.or(b);
+				done_x = x.equals(sol1);
+				x.clear();
+				x.or(sol1);
+			}
+			done_y = y.equals(x);
+			y.clear();
+			y.or(x);
+		}
+		return y;
+	}
 
+	/*
+	 * Auxiliary method for AFG (as defined in L. Alfaro and T. Henzinger, Concurrent Omega-Regular Games)
+	 */
 	public boolean apreXYZ(ArrayList<ArrayList<Distribution>> mdist, BitSet x, BitSet y, BitSet z)
 	{
 		BitSet a, ab, e, v;
@@ -1494,6 +1607,9 @@ public boolean apreXYZ(ArrayList<ArrayList<Distribution>> mdist, BitSet x, BitSe
 		return !(v.isEmpty());
 	}
 
+	/*
+	 * Auxiliary method for AFG (as defined in L. Alfaro and T. Henzinger, Concurrent Omega-Regular Games)
+	 */
 	public BitSet apreXYZ(CSG csg, BitSet x, BitSet y, BitSet z) throws PrismException
 	{
 		ArrayList<ArrayList<Distribution>> mdist;
@@ -1505,6 +1621,9 @@ public BitSet apreXYZ(CSG csg, BitSet x, BitSet y, BitSet z) throws PrismExcepti
 		return result;
 	}
 
+	/*
+	 * Eventually globally b
+	 */
 	public BitSet AFG(CSG csg, BitSet b) throws PrismException
 	{
 		int n = csg.getNumStates();
@@ -1571,7 +1690,10 @@ public void pre1(CSG csg, BitSet x, BitSet sol) throws PrismException
 			sol.set(s, pre1(mdist, x));
 		}
 	}
-
+	
+	/*
+	 * Globally b
+	 */
 	public BitSet G(CSG csg, BitSet b) throws PrismException
 	{
 		int n = csg.getNumStates();
@@ -1654,6 +1776,7 @@ public void buildCoalitions(CSG csg, Coalition coalition, boolean min) throws Pr
 	 * Find the max size of the matrix game needed across any CSG state,
 	 * for the current coalition (as stored in coalitionIndexes).
 	 * Also compute/report the average number of actions for each coalition across all CSG states.
+	 * @param csg The CSG
 	 */
 	public void findMaxRowsCols(CSG csg)
 	{
@@ -1682,6 +1805,13 @@ public void findMaxRowsCols(CSG csg)
 				+ PrismUtils.formatDouble2dp(avgNumActions[1]) + ")");
 	}
 
+	/**
+	 * Build a matrix game with the transition distributions for state s. 
+	 * @param csg The CSG
+	 * @param s Index of state to build matrix game for 
+	 * @return
+	 * @throws PrismException
+	 */
 	public ArrayList<ArrayList<Distribution>> buildMatrixDist(CSG csg, int s) throws PrismException
 	{
 		ArrayList<ArrayList<Distribution>> mdist = new ArrayList<ArrayList<Distribution>>();
@@ -2149,7 +2279,13 @@ public void buildLPLpsolve(LpSolve lp, ArrayList<ArrayList<Double>> mgame, boole
 		//lp.printLp();
 	}
 
-	public static DA<BitSet, AcceptanceRabin> constructDRAForInstant(String labelA, boolean negateA, IntegerBound bounds)
+	/**
+	 * Constructs the DRA for the CSGxDRA product when computing mixed bounded equilibria.
+	 * @param labelA Label for accepting states
+	 * @param bounds Bound for either cumulative or instant rewards
+	 * @return
+	 */
+	public static DA<BitSet, AcceptanceRabin> constructDRAForInstant(String labelA, IntegerBound bounds)
 	{
 		DA<BitSet, AcceptanceRabin> dra;
 		List<String> apList = new ArrayList<String>();
@@ -2173,11 +2309,7 @@ public static DA<BitSet, AcceptanceRabin> constructDRAForInstant(String labelA,
 		// edge not labeled with the target label
 		edge_no = new BitSet();
 
-		if (negateA) {
-			edge_no.set(0); // no = a, yes = !a
-		} else {
-			edge_yes.set(0); // yes = a, no = !a
-		}
+		edge_yes.set(0); // yes = a, no = !a
 
 		int yes_state = states - 1;
 		int next_counter;
diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 354dcfe2d..db293b10e 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1281,7 +1281,6 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		setSolver();
 		
 		mainLog.println("Starting equilibria computation (solver=" + eqslps.getSolverName() + ")...");
-		
 		mainLog.println("Checking whether all objctives are reachable...");
 		
 		if (assumptionCheck) {
@@ -1602,7 +1601,7 @@ public double[][] stepEquilibria(CSG csg, List<CSGRewards> rewards, List<Map<Int
 				for (p2 = 0; p2 < numCoalitions; p2++) {
 					sumv += utilities.get(entry).get(p2); // computes sum of utilities
 				}
-				if (utilities.get(entry).get(p1) > v) { // maximizes for player who has a choice
+				if (utilities.get(entry).get(p1) > v) { // maximises for player who has a choice
 					support = entry;
 					sumt = 0.0;
 					v = utilities.get(entry).get(p1);
diff --git a/prism/src/explicit/ProbModelChecker.java b/prism/src/explicit/ProbModelChecker.java
index 137bcdf07..37c729c28 100644
--- a/prism/src/explicit/ProbModelChecker.java
+++ b/prism/src/explicit/ProbModelChecker.java
@@ -1402,7 +1402,7 @@ protected StateValues checkRewardTotal(Model model, Rewards modelRewards, Expres
 			res = ((MDPModelChecker) this).computeTotalRewards((MDP) model, (MDPRewards) modelRewards, minMax.isMin());
 			break;
 		case CSG:
-			res = ((CSGModelChecker) this).computeTotalRewards((CSG) model, (CSGRewards) modelRewards, minMax.isMin1(), minMax.isMin2(), minMax.getCoalition());
+			res = ((CSGModelChecker) this).computeTotalRewards((CSG) model, (CSGRewards) modelRewards, minMax.getCoalition(), minMax.isMin1(), minMax.isMin2());
 			break;
 		default:
 			throw new PrismNotSupportedException("Explicit engine does not yet handle the " + expr.getOperatorSymbol() + " reward operator for " + model.getModelType()

From ac2fedc3dff9f82f5d0b0cf094c08ad58a460e74 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Mon, 3 Apr 2023 11:31:02 +0100
Subject: [PATCH 21/30] Changes to parser and settings for equilibria

---
 prism/src/parser/ParseException.java          |   48 +-
 prism/src/parser/PrismParser.java             | 2616 +++++++++--------
 prism/src/parser/PrismParser.jj               |   27 +-
 prism/src/parser/PrismParserConstants.java    |  244 +-
 prism/src/parser/PrismParserTokenManager.java |  917 +++---
 prism/src/parser/SimpleCharStream.java        |   12 +-
 prism/src/parser/Token.java                   |    7 +-
 prism/src/parser/TokenMgrError.java           |   26 +-
 prism/src/parser/ast/ExpressionMultiNash.java |   41 +-
 prism/src/prism/PrismSettings.java            |   55 +-
 10 files changed, 2058 insertions(+), 1935 deletions(-)

diff --git a/prism/src/parser/ParseException.java b/prism/src/parser/ParseException.java
index 839bcc293..0f7f16284 100644
--- a/prism/src/parser/ParseException.java
+++ b/prism/src/parser/ParseException.java
@@ -1,5 +1,5 @@
-/* Generated By:JavaCC: Do not edit this line. ParseException.java Version 7.0 */
-/* JavaCCOptions:KEEP_LINE_COLUMN=true */
+/* Generated By:JavaCC: Do not edit this line. ParseException.java Version 6.0 */
+/* JavaCCOptions:KEEP_LINE_COL=null */
 package parser;
 
 /**
@@ -20,11 +20,6 @@ public class ParseException extends Exception {
    */
   private static final long serialVersionUID = 1L;
 
-  /**
-   * The end of line string for this machine.
-   */
-  protected static String EOL = System.getProperty("line.separator", "\n");
-
   /**
    * This constructor is used by the method "generateParseException"
    * in the generated parser.  Calling this constructor generates
@@ -65,7 +60,7 @@ public ParseException(String message) {
   /**
    * This is the last token that has been consumed successfully.  If
    * this object has been created due to a parse error, the token
-   * following this token will (therefore) be the first error token.
+   * followng this token will (therefore) be the first error token.
    */
   public Token currentToken;
 
@@ -93,8 +88,8 @@ public ParseException(String message) {
   private static String initialise(Token currentToken,
                            int[][] expectedTokenSequences,
                            String[] tokenImage) {
-
-    StringBuilder expected = new StringBuilder();
+    String eol = System.getProperty("line.separator", "\n");
+    StringBuffer expected = new StringBuffer();
     int maxSize = 0;
     for (int i = 0; i < expectedTokenSequences.length; i++) {
       if (maxSize < expectedTokenSequences[i].length) {
@@ -106,7 +101,7 @@ private static String initialise(Token currentToken,
       if (expectedTokenSequences[i][expectedTokenSequences[i].length - 1] != 0) {
         expected.append("...");
       }
-      expected.append(EOL).append("    ");
+      expected.append(eol).append("    ");
     }
     String retval = "Encountered \"";
     Token tok = currentToken.next;
@@ -122,26 +117,21 @@ private static String initialise(Token currentToken,
       retval += " \"";
       tok = tok.next;
     }
-    if (currentToken.next != null) {
-      retval += "\" at line " + currentToken.next.beginLine + ", column " + currentToken.next.beginColumn;
-    }
-    retval += "." + EOL;
-    
-    
-    if (expectedTokenSequences.length == 0) {
-        // Nothing to add here
+    retval += "\" at line " + currentToken.next.beginLine + ", column " + currentToken.next.beginColumn;
+    retval += "." + eol;
+    if (expectedTokenSequences.length == 1) {
+      retval += "Was expecting:" + eol + "    ";
     } else {
-	    if (expectedTokenSequences.length == 1) {
-	      retval += "Was expecting:" + EOL + "    ";
-	    } else {
-	      retval += "Was expecting one of:" + EOL + "    ";
-	    }
-	    retval += expected.toString();
+      retval += "Was expecting one of:" + eol + "    ";
     }
-    
+    retval += expected.toString();
     return retval;
   }
 
+  /**
+   * The end of line string for this machine.
+   */
+  protected String eol = System.getProperty("line.separator", "\n");
 
   /**
    * Used to convert raw characters to their escaped version
@@ -149,11 +139,13 @@ private static String initialise(Token currentToken,
    * string literal.
    */
   static String add_escapes(String str) {
-      StringBuilder retval = new StringBuilder();
+      StringBuffer retval = new StringBuffer();
       char ch;
       for (int i = 0; i < str.length(); i++) {
         switch (str.charAt(i))
         {
+           case 0 :
+              continue;
            case '\b':
               retval.append("\\b");
               continue;
@@ -192,4 +184,4 @@ static String add_escapes(String str) {
    }
 
 }
-/* JavaCC - OriginalChecksum=8dbcceed9d408427f9932dcf43e59aaa (do not edit this line) */
+/* JavaCC - OriginalChecksum=83512206aea6c09dd76f640dc4cc775b (do not edit this line) */
diff --git a/prism/src/parser/PrismParser.java b/prism/src/parser/PrismParser.java
index e8b6885fa..739a47f58 100644
--- a/prism/src/parser/PrismParser.java
+++ b/prism/src/parser/PrismParser.java
@@ -27,7 +27,7 @@ public class PrismParser implements PrismParserConstants {
         static {
                 keywordList.clear();
                 for (int i = PrismParserConstants.COMMENT+1; i < PrismParserConstants.NOT; i++) {
-                        keywordList.add(PrismParserConstants.tokenImage[i].replaceAll("\"", ""));
+                        keywordList.add(PrismParserConstants.tokenImage[i].replaceAll("\u005c"", ""));
                 }
         }
 
@@ -54,26 +54,26 @@ public static void main(String[] args)
                         p = new PrismParser();
                         str = (args.length > 1) ? new FileInputStream(args[1]) : System.in;
                         src = (args.length > 1) ? "file "+args[1] : "stdin";
-                        System.out.println("Reading from "+src+"...\n");
+                        System.out.println("Reading from "+src+"...\u005cn");
 
                         if (args[0].equals("-modulesfile") || args[0].equals("-mf")) {
                                 ModulesFile mf = p.parseModulesFile(str);
-                                System.out.print("Modules file:\n=============\n\n" + mf);
-                                System.out.print("\nTree:\n=====\n" + mf.toTreeString());
+                                System.out.print("Modules file:\u005cn=============\u005cn\u005cn" + mf);
+                                System.out.print("\u005cnTree:\u005cn=====\u005cn" + mf.toTreeString());
                                 mf.tidyUp();
-                                System.out.print("\nAnd after expansion:\n====================\n\n" +mf);
+                                System.out.print("\u005cnAnd after expansion:\u005cn====================\u005cn\u005cn" +mf);
                         }
                         else if (args[0].equals("-propertiesfile") || args[0].equals("-pf")) {
                                 PropertiesFile pf = p.parsePropertiesFile(new ModulesFile(), str);
-                                System.out.print("Properties file:\n================\n\n" + pf);
-                                System.out.print("\nTree:\n=====\n" + pf.toTreeString());
+                                System.out.print("Properties file:\u005cn================\u005cn\u005cn" + pf);
+                                System.out.print("\u005cnTree:\u005cn=====\u005cn" + pf.toTreeString());
                                 pf.tidyUp();
-                                System.out.print("\nAnd after expansion:\n====================\n\n" + pf);
+                                System.out.print("\u005cnAnd after expansion:\u005cn====================\u005cn\u005cn" + pf);
                         }
                         else if (args[0].equals("-expression") || args[0].equals("-e")) {
                                 Expression expr = p.parseSingleExpression(str);
                                 System.out.println("Expression: " + expr.toString());
-                                System.out.print("Tree:\n=====\n" + expr.toTreeString());
+                                System.out.print("Tree:\u005cn=====\u005cn" + expr.toTreeString());
                                 expr.typeCheck();
                                 expr.semanticCheck();
                                 System.out.println("Type: " + expr.getType().getTypeString());
@@ -88,7 +88,7 @@ public Object visit(ExpressionIdent e) throws PrismLangException
                                         }
                                 });
                                 System.out.println("LTL formula: " + expr.toString());
-                                System.out.print("Tree:\n=====\n" + expr.toTreeString());
+                                System.out.print("Tree:\u005cn=====\u005cn" + expr.toTreeString());
                                 expr.typeCheck();
                                 //expr.semanticCheck();
                                 System.out.println("Type: " + expr.getType().getTypeString());
@@ -250,29 +250,29 @@ public static String getPrecedingCommentBlock(Token firstToken)
                 Token t = firstToken;
 
                 // extract any comment from the previous lines of the file
-                if (t.specialToken != null && !(t.specialToken.kind == PrismParserConstants.WHITESPACE && t.specialToken.image.matches("[\\n\\r]*"))) {
+                if (t.specialToken != null && !(t.specialToken.kind == PrismParserConstants.WHITESPACE && t.specialToken.image.matches("[\u005c\u005cn\u005c\u005cr]*"))) {
                         // trace back thru special tokens that are comments
                         t = t.specialToken;
-                        while (t.specialToken != null && !(t.specialToken.kind == PrismParserConstants.WHITESPACE && t.specialToken.image.matches("[\\n\\r]*")))
+                        while (t.specialToken != null && !(t.specialToken.kind == PrismParserConstants.WHITESPACE && t.specialToken.image.matches("[\u005c\u005cn\u005c\u005cr]*")))
                                 t = t.specialToken;
                         // concatenate comment special tokens
                         while (t != null) {
                                 s = t.image;
                                 // strip any nasty carriage returns
-                                s = s.replaceAll("\r", "");
+                                s = s.replaceAll("\u005cr", "");
                                 // remove "//" and preceding/subsequent spaces/tabs from comments
                                 if (t.kind == PrismParserConstants.COMMENT) {
-                                        while (comment.length() > 0 && (""+comment.charAt(comment.length()-1)).matches("[ \t]"))
+                                        while (comment.length() > 0 && (""+comment.charAt(comment.length()-1)).matches("[ \u005ct]"))
                                                 comment = comment.substring(0,comment.length()-1);
                                         s = s.substring(2);
-                                        s = s.replaceFirst("[ \t]*", "");
+                                        s = s.replaceFirst("[ \u005ct]*", "");
                                 }
                                 comment += s;
                                 t = t.next;
                         }
                 }
                 // remove final new line (if present)
-                if (comment.length() > 0 && (comment.charAt(comment.length()-1) == '\n'))
+                if (comment.length() > 0 && (comment.charAt(comment.length()-1) == '\u005cn'))
                         comment = comment.substring(0,comment.length()-1);
 
                 return comment;
@@ -285,15 +285,15 @@ public static String slashCommentBlock(String comment)
                 int i;
                 String s, res = "";
                 // break into lines
-                while ((i = comment.indexOf("\n")) != -1) {
+                while ((i = comment.indexOf("\u005cn")) != -1) {
                         s = comment.substring(0, i);
                         comment = comment.substring(i+1);
                         // add "//" to non-empty lines
                         if (s.trim().length()>0) res += "// " + s;
-                        res += "\n";
+                        res += "\u005cn";
                 }
                 // deal with any trailing characters (with no new line ending them)
-                if (comment.trim().length()>0) res += "// " + comment + "\n";
+                if (comment.trim().length()>0) res += "// " + comment + "\u005cn";
                 return res;
         }
 
@@ -538,7 +538,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 mf.setPosition(begin != null? begin: getToken(0), getToken(0));
                 {if ("" != null) return mf;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Properties file
   static final public 
@@ -663,7 +663,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(0);
 pf.setPosition(begin, getToken(0)); {if ("" != null) return pf;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Properties file with optional semicolons - beware of potential ambiguities
   static final public 
@@ -788,7 +788,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(0);
 pf.setPosition(begin, getToken(0)); {if ("" != null) return pf;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Property - expression, with optional name/comment
   static final public 
@@ -809,7 +809,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
 prop = new Property(expr, name, getPrecedingCommentBlock(begin));
 prop.setPosition(begin, getToken(0)); {if ("" != null) return prop;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // A single expression
   static final public 
@@ -818,7 +818,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(0);
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // A single LTL formula
   static final public 
@@ -827,7 +827,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(0);
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 //-----------------------------------------------------------------------------------
 // Modules file stuff (a few bits of which are reused for property files)
@@ -941,7 +941,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return modelType;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Formula definition
   static final public 
@@ -953,7 +953,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     expr = Expression(false, false);
     jj_consume_token(SEMICOLON);
 formulaList.addFormula(name, expr);
-}
+  }
 
 // Label definition
   static final public 
@@ -976,7 +976,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       jj_consume_token(-1);
       throw new ParseException();
     }
-}
+  }
 
 // Constant definition
   static final public 
@@ -1057,7 +1057,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
     jj_consume_token(SEMICOLON);
 constantList.addConstant(name, expr, type);
-}
+  }
 
 // Global variable declaration
   static final public 
@@ -1066,7 +1066,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     decl = Declaration();
 {if ("" != null) return decl;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Variable declaration
   static final public 
@@ -1094,7 +1094,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(SEMICOLON);
 decl.setPosition(begin, getToken(0)); {if ("" != null) return decl;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Type part of a declaration
   static final public 
@@ -1134,7 +1134,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 declType.setPosition(begin, getToken(0)); {if ("" != null) return declType;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Module
   static final public 
@@ -1190,7 +1190,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDMODULE);
 module.setPosition(begin, getToken(0)); module.setNameASTElement(name); {if ("" != null) return module;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Command
   static final public 
@@ -1213,7 +1213,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(SEMICOLON);
 comm.setPosition(begin, getToken(0)); {if ("" != null) return comm;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Updates
   static final public 
@@ -1294,7 +1294,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 updates.setPosition(begin, getToken(0)); {if ("" != null) return updates;}
     throw new Error("Missing return statement in function");
-}
+  }
 
   static final public Update Update() throws ParseException {Update update = new Update();
         Token begin = null;
@@ -1329,7 +1329,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 update.setPosition(begin, getToken(0)); {if ("" != null) return update;}
     throw new Error("Missing return statement in function");
-}
+  }
 
   static final public void UpdateElement(Update update) throws ParseException {ExpressionIdent var = null;
         Expression expr = null;
@@ -1340,7 +1340,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     expr = Expression(false, false);
     jj_consume_token(RPARENTH);
 UpdateElement ue = new UpdateElement(var, expr); ue.setPosition(begin, getToken(0)); update.addElement(ue);
-}
+  }
 
 // Module renaming
   static final public 
@@ -1372,7 +1372,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDMODULE);
 rm.setPosition(begin, getToken(0)); rm.setNameASTElement(name); rm.setBaseModuleASTElement(base); {if ("" != null) return rm;}
     throw new Error("Missing return statement in function");
-}
+  }
 
   static final public void Rename(RenamedModule rm) throws ParseException {ExpressionIdent id1 = null, id2 = null;
     // NB: have to explicitly include keywords for functions because they can be renamed
@@ -1380,7 +1380,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(EQ);
     id2 = IdentifierExpressionMinMax();
 rm.addRename(id1.getName(), id2.getName(), id1, id2);
-}
+  }
 
 // Reward structure
   static final public 
@@ -1467,7 +1467,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDREWARDS);
 rs.setPosition(begin, getToken(0)); {if ("" != null) return rs;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Action list (0 or more comma-separated identifiers)
   static final public 
@@ -1500,7 +1500,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return list;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Initial states ("init...endinit" construct)
   static final public 
@@ -1510,7 +1510,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDINIT);
 {if ("" != null) return expr;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Observable variables list (for partially observable models)
   static final public 
@@ -1540,7 +1540,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDOBSERVABLES);
 obsVars.setPosition(begin, getToken(0)); {if ("" != null) return obsVars;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Individual observable (for partially observable models)
   static final public 
@@ -1557,7 +1557,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(SEMICOLON);
 Observable obs = new Observable(name, defn); obs.setPosition(begin, getToken(0)); {if ("" != null) return obs;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition ("system...endsystem" construct)
   static final public 
@@ -1574,7 +1574,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     sysdef = SystemDefn();
     jj_consume_token(ENDSYSTEM);
 mf.addSystemDefn(sysdef, name);
-}
+  }
 
 // System definition component
   static final public 
@@ -1582,7 +1582,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     ret = SystemFullParallel();
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition component (full parallel)
   static final public 
@@ -1612,7 +1612,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                         {if ("" != null) return par;}
                 }
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition component (interleaved parallel)
   static final public 
@@ -1643,7 +1643,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                         {if ("" != null) return par;}
                 }
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition component (parallel over set of actions)
   static final public 
@@ -1689,7 +1689,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                         {if ("" != null) return par;}
                 }
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition component (hiding and renaming)
   static final public 
@@ -1774,7 +1774,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 sys.setPosition(begin, getToken(0)); {if ("" != null) return sys;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // System definition component (bottom level)
   static final public 
@@ -1809,7 +1809,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 sys.setPosition(begin, getToken(0)); {if ("" != null) return sys;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Player definition
   static final public 
@@ -1847,7 +1847,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(ENDPLAYER);
 player.setPosition(begin, getToken(0)); {if ("" != null) return player;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Player definition item (module or [action])
   static final public 
@@ -1870,7 +1870,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       jj_consume_token(-1);
       throw new ParseException();
     }
-}
+  }
 
 //-----------------------------------------------------------------------------------
 // Expressions.
@@ -1886,7 +1886,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     ret = ExpressionTemporalBinary(prop, pathprop);
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: temporal operators, binary (U, W, R) and unary (X, F, G)
 
@@ -1963,7 +1963,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
   static final public Expression ExpressionTemporalUnary(boolean prop, boolean pathprop) throws ParseException {Expression ret, expr;
         ExpressionTemporal exprTemp;
@@ -2056,7 +2056,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Time bound for temporal operators
 // (see ExpressionTemporal production for lookahead explanation)
@@ -2299,7 +2299,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       jj_consume_token(-1);
       throw new ParseException();
     }
-}
+  }
 
 // Expression: if-then-else, i.e. "cond ? then : else"
   static final public 
@@ -2322,7 +2322,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: implies
   static final public 
@@ -2347,7 +2347,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: if-and-only-iff
   static final public 
@@ -2372,7 +2372,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: or
   static final public 
@@ -2397,7 +2397,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: and
   static final public 
@@ -2422,7 +2422,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: not
   static final public 
@@ -2477,7 +2477,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: equality operators: =, !=
   static final public 
@@ -2504,7 +2504,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: relational operators: >, <, >=, <=
   static final public 
@@ -2533,7 +2533,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: plus/minus
 
@@ -2582,7 +2582,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: times/divide
   static final public 
@@ -2624,7 +2624,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: unary minus
   static final public 
@@ -2678,7 +2678,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Basic expression (top of operator precedence ordering)
   static final public 
@@ -2762,7 +2762,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: function or identifier
 
@@ -2807,7 +2807,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 ret.setPosition(begin, getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: min/max function (treated differently because min/max are keywords)
   static final public 
@@ -2836,7 +2836,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(RPARENTH);
 func.setPosition(begin, getToken(0)); {if ("" != null) return func;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: old-style function, i.e. "func(name, ...)"
   static final public 
@@ -2871,7 +2871,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(RPARENTH);
 func.setPosition(begin, getToken(0)); {if ("" != null) return func;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Arguments for a function in an expression
   static final public 
@@ -2893,7 +2893,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       expr = Expression(prop, pathprop);
 func.addOperand(expr);
     }
-}
+  }
 
 // Expression: literal
   static final public 
@@ -2944,7 +2944,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 ret.setPosition(getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Expression: parentheses
   static final public 
@@ -2955,7 +2955,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     jj_consume_token(RPARENTH);
 ret = new ExpressionUnaryOp(ExpressionUnaryOp.PARENTH, expr); ret.setPosition(begin, getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 //-----------------------------------------------------------------------------------
 // Property stuff
@@ -3173,7 +3173,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 }
                 else {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Filter for a P/S/R operator
   static final public 
@@ -3216,7 +3216,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 filter.setPosition(begin, getToken(0)); {if ("" != null) return filter;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: steady-state operator S
   static final public 
@@ -3293,7 +3293,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 }
                 else {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: expected reward operator R
   static final public 
@@ -3516,7 +3516,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 }
                 else {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Reward struct index for R operator
   static final public 
@@ -3663,7 +3663,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 if (discount != null) {
                         exprRew.setDiscount(discount);
                 }
-}
+  }
 
 // Contents of an R operator
 
@@ -3769,7 +3769,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 ret.setPosition(begin, getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: n-player Nash operator
   static final public 
@@ -3780,8 +3780,23 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         String relOp = null;
         boolean isBool;
         int r;
+        int eq = 1; // default NE
+        int crit = 3; // default SW
         int n = 0;
 if (!prop) {if (true) throw generateParseException();}
+    switch ((jj_ntk==-1)?jj_ntk_f():jj_ntk) {
+    case LBRACE:{
+      jj_consume_token(LBRACE);
+      eq = EqType();
+      jj_consume_token(COMMA);
+      crit = EqType();
+      jj_consume_token(RBRACE);
+      break;
+      }
+    default:
+      jj_la1[97] = jj_gen;
+      ;
+    }
     switch ((jj_ntk==-1)?jj_ntk_f():jj_ntk) {
     case MIN:{
       jj_consume_token(MIN);
@@ -3802,7 +3817,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[97] = jj_gen;
+        jj_la1[98] = jj_gen;
         jj_consume_token(-1);
         throw new ParseException();
       }
@@ -3827,14 +3842,14 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[98] = jj_gen;
+        jj_la1[99] = jj_gen;
         jj_consume_token(-1);
         throw new ParseException();
       }
       break;
       }
     default:
-      jj_la1[99] = jj_gen;
+      jj_la1[100] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
@@ -3849,7 +3864,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[100] = jj_gen;
+      jj_la1[101] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
@@ -3867,7 +3882,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[101] = jj_gen;
+        jj_la1[102] = jj_gen;
         jj_consume_token(-1);
         throw new ParseException();
       }
@@ -3878,16 +3893,50 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[102] = jj_gen;
+        jj_la1[103] = jj_gen;
         break label_31;
       }
     }
     jj_consume_token(RPARENTH);
 ret.setBound(bound);
                 ret.setRelOp(relOp);
+                ret.setEqType(eq);
+                ret.setCrit(crit);
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
+
+// Types of Equilibria
+  static final public 
+int EqType() throws ParseException {
+    switch ((jj_ntk==-1)?jj_ntk_f():jj_ntk) {
+    case NASH:{
+      jj_consume_token(NASH);
+{if ("" != null) return ExpressionMultiNash.NASH;}
+      break;
+      }
+    case CORR:{
+      jj_consume_token(CORR);
+{if ("" != null) return ExpressionMultiNash.CORR;}
+      break;
+      }
+    case SWEQ:{
+      jj_consume_token(SWEQ);
+{if ("" != null) return ExpressionMultiNash.SWEQ;}
+      break;
+      }
+    case FAIR:{
+      jj_consume_token(FAIR);
+{if ("" != null) return ExpressionMultiNash.FAIR;}
+      break;
+      }
+    default:
+      jj_la1[104] = jj_gen;
+      jj_consume_token(-1);
+      throw new ParseException();
+    }
+    throw new Error("Missing return statement in function");
+  }
 
 // (Property) expression: probabilistic operator (n-player Nash)
   static final public 
@@ -3903,7 +3952,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 ret.setPosition(begin, getToken(0));
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: reward operator (n-player Nash)
   static final public 
@@ -3920,7 +3969,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 ret.setPosition(begin, getToken(0));
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Reward) structure index for equilibria
   static final public 
@@ -3972,14 +4021,14 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[103] = jj_gen;
+        jj_la1[105] = jj_gen;
         jj_consume_token(-1);
         throw new ParseException();
       }
     }
     jj_consume_token(RBRACE);
 exprMultiNash.setRewardStructIndex(index);
-}
+  }
 
 // (Property) expression: CTL existential operator E
   static final public 
@@ -3995,7 +4044,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 ret.setPosition(begin, getToken(0));
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: CTL universal operator A
   static final public 
@@ -4011,7 +4060,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
                 ret.setPosition(begin, getToken(0));
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: ATL strategy operators <<>> and [[]]
   static final public 
@@ -4036,7 +4085,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[104] = jj_gen;
+      jj_la1[106] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
@@ -4057,7 +4106,8 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     case RMINMAX:
     case RMINMIN:
     case RMIN:
-    case R:{
+    case R:
+    case LBRACE:{
       switch ((jj_ntk==-1)?jj_ntk_f():jj_ntk) {
       case PMAXMAX:
       case PMAXMIN:
@@ -4080,12 +4130,13 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       case MAX:
-      case MIN:{
+      case MIN:
+      case LBRACE:{
         expr = ExpressionMultiNash(prop,pathprop);
         break;
         }
       default:
-        jj_la1[105] = jj_gen;
+        jj_la1[107] = jj_gen;
         jj_consume_token(-1);
         throw new ParseException();
       }
@@ -4098,14 +4149,14 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[106] = jj_gen;
+      jj_la1[108] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
 ret.setPosition(begin, getToken(0));
                 {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // List of coalitions (player lists) for a strategy (<<>> or [[]]) operator
   static final public 
@@ -4121,7 +4172,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[107] = jj_gen;
+        jj_la1[109] = jj_gen;
         break label_32;
       }
       jj_consume_token(COLON);
@@ -4130,7 +4181,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
     }
 {if ("" != null) return coalitions;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Coalition (player list) for a strategy (<<>> or [[]]) operator
   static final public 
@@ -4144,7 +4195,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[110] = jj_gen;
+      jj_la1[112] = jj_gen;
       switch ((jj_ntk==-1)?jj_ntk_f():jj_ntk) {
       case REG_INT:
       case REG_IDENT:{
@@ -4158,7 +4209,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
             break;
             }
           default:
-            jj_la1[108] = jj_gen;
+            jj_la1[110] = jj_gen;
             break label_33;
           }
           jj_consume_token(COMMA);
@@ -4169,13 +4220,13 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
         break;
         }
       default:
-        jj_la1[109] = jj_gen;
+        jj_la1[111] = jj_gen;
         ;
       }
     }
 {if ("" != null) return coalition;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Single player in a coalition for a strategy (<<>> or [[]]) operator
   static final public 
@@ -4190,14 +4241,14 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[111] = jj_gen;
+      jj_la1[113] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
 s = getToken(0).image;
 {if ("" != null) return s;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: label (including "init")
   static final public 
@@ -4217,14 +4268,14 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[112] = jj_gen;
+      jj_la1[114] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
     jj_consume_token(DQUOTE);
 ret = new ExpressionLabel(s); ret.setPosition(begin, getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // (Property) expression: filter (using "filter" keyword)
   static final public 
@@ -4268,7 +4319,7 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[113] = jj_gen;
+      jj_la1[115] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
@@ -4281,13 +4332,13 @@ static class ExpressionPair { public Expression expr1 = null; public Expression
       break;
       }
     default:
-      jj_la1[114] = jj_gen;
+      jj_la1[116] = jj_gen;
       ;
     }
     jj_consume_token(RPARENTH);
 expr = new ExpressionFilter(op, expr2, filter); expr.setPosition(begin, getToken(0)); {if ("" != null) return expr;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 //-----------------------------------------------------------------------------------
 // Miscellaneous stuff
@@ -4299,7 +4350,7 @@ String Identifier() throws ParseException {
     jj_consume_token(REG_IDENT);
 {if ("" != null) return getToken(0).image;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Identifier (returns ExpressionIdent, storing position info)
   static final public 
@@ -4308,7 +4359,7 @@ String Identifier() throws ParseException {
     ident = Identifier();
 ret = new ExpressionIdent(ident); ret.setPosition(getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Identifier or min/max keyword (returns ExpressionIdent, storing position info)
   static final public 
@@ -4330,13 +4381,13 @@ String Identifier() throws ParseException {
       break;
       }
     default:
-      jj_la1[115] = jj_gen;
+      jj_la1[117] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
 ret = new ExpressionIdent(ident); ret.setPosition(getToken(0)); {if ("" != null) return ret;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Primed identifier
   static final public 
@@ -4351,7 +4402,7 @@ ExpressionIdent IdentifierPrime() throws ParseException {
                 expr.setPrime(true);
                 {if ("" != null) return expr;}
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Equality operators: =, !=
   static final public 
@@ -4368,12 +4419,12 @@ int EqNeq() throws ParseException {
       break;
       }
     default:
-      jj_la1[116] = jj_gen;
+      jj_la1[118] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
     throw new Error("Missing return statement in function");
-}
+  }
 
 // Relational operators: >, <, >=, <=
   static final public 
@@ -4400,12 +4451,12 @@ int LtGt() throws ParseException {
       break;
       }
     default:
-      jj_la1[117] = jj_gen;
+      jj_la1[119] = jj_gen;
       jj_consume_token(-1);
       throw new ParseException();
     }
     throw new Error("Missing return statement in function");
-}
+  }
 
 // For loop
   static final public 
@@ -4426,7 +4477,7 @@ int LtGt() throws ParseException {
       break;
       }
     default:
-      jj_la1[118] = jj_gen;
+      jj_la1[120] = jj_gen;
       ;
     }
     jj_consume_token(0);
@@ -4437,12 +4488,12 @@ int LtGt() throws ParseException {
                 fl.setPosition(begin, getToken(0));
                 {if ("" != null) return fl;}
     throw new Error("Missing return statement in function");
-}
+  }
 
   static private boolean jj_2_1(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_1()); }
+    try { return !jj_3_1(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(0, xla); }
   }
@@ -4450,7 +4501,7 @@ static private boolean jj_2_1(int xla)
   static private boolean jj_2_2(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_2()); }
+    try { return !jj_3_2(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(1, xla); }
   }
@@ -4458,7 +4509,7 @@ static private boolean jj_2_2(int xla)
   static private boolean jj_2_3(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_3()); }
+    try { return !jj_3_3(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(2, xla); }
   }
@@ -4466,7 +4517,7 @@ static private boolean jj_2_3(int xla)
   static private boolean jj_2_4(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_4()); }
+    try { return !jj_3_4(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(3, xla); }
   }
@@ -4474,7 +4525,7 @@ static private boolean jj_2_4(int xla)
   static private boolean jj_2_5(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_5()); }
+    try { return !jj_3_5(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(4, xla); }
   }
@@ -4482,7 +4533,7 @@ static private boolean jj_2_5(int xla)
   static private boolean jj_2_6(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_6()); }
+    try { return !jj_3_6(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(5, xla); }
   }
@@ -4490,7 +4541,7 @@ static private boolean jj_2_6(int xla)
   static private boolean jj_2_7(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_7()); }
+    try { return !jj_3_7(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(6, xla); }
   }
@@ -4498,7 +4549,7 @@ static private boolean jj_2_7(int xla)
   static private boolean jj_2_8(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_8()); }
+    try { return !jj_3_8(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(7, xla); }
   }
@@ -4506,7 +4557,7 @@ static private boolean jj_2_8(int xla)
   static private boolean jj_2_9(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_9()); }
+    try { return !jj_3_9(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(8, xla); }
   }
@@ -4514,7 +4565,7 @@ static private boolean jj_2_9(int xla)
   static private boolean jj_2_10(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_10()); }
+    try { return !jj_3_10(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(9, xla); }
   }
@@ -4522,7 +4573,7 @@ static private boolean jj_2_10(int xla)
   static private boolean jj_2_11(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_11()); }
+    try { return !jj_3_11(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(10, xla); }
   }
@@ -4530,7 +4581,7 @@ static private boolean jj_2_11(int xla)
   static private boolean jj_2_12(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_12()); }
+    try { return !jj_3_12(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(11, xla); }
   }
@@ -4538,7 +4589,7 @@ static private boolean jj_2_12(int xla)
   static private boolean jj_2_13(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_13()); }
+    try { return !jj_3_13(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(12, xla); }
   }
@@ -4546,7 +4597,7 @@ static private boolean jj_2_13(int xla)
   static private boolean jj_2_14(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_14()); }
+    try { return !jj_3_14(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(13, xla); }
   }
@@ -4554,7 +4605,7 @@ static private boolean jj_2_14(int xla)
   static private boolean jj_2_15(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_15()); }
+    try { return !jj_3_15(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(14, xla); }
   }
@@ -4562,7 +4613,7 @@ static private boolean jj_2_15(int xla)
   static private boolean jj_2_16(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_16()); }
+    try { return !jj_3_16(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(15, xla); }
   }
@@ -4570,7 +4621,7 @@ static private boolean jj_2_16(int xla)
   static private boolean jj_2_17(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_17()); }
+    try { return !jj_3_17(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(16, xla); }
   }
@@ -4578,7 +4629,7 @@ static private boolean jj_2_17(int xla)
   static private boolean jj_2_18(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_18()); }
+    try { return !jj_3_18(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(17, xla); }
   }
@@ -4586,38 +4637,12 @@ static private boolean jj_2_18(int xla)
   static private boolean jj_2_19(int xla)
  {
     jj_la = xla; jj_lastpos = jj_scanpos = token;
-    try { return (!jj_3_19()); }
+    try { return !jj_3_19(); }
     catch(LookaheadSuccess ls) { return true; }
     finally { jj_save(18, xla); }
   }
 
-  static private boolean jj_3R_ExpressionBasic_1513_17_144()
- {
-    if (jj_3R_ExpressionStrategy_2042_9_156()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionBasic_1511_17_143()
- {
-    if (jj_3R_ExpressionForAll_2022_9_155()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_SystemFullParallel_1073_71_48()
- {
-    if (jj_scan_token(OR)) return true;
-    if (jj_scan_token(OR)) return true;
-    if (jj_3R_SystemParallel_1118_9_54()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionBasic_1509_17_142()
- {
-    if (jj_3R_ExpressionExists_2003_9_154()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionTimesDivide_1461_64_132()
+  static private boolean jj_3R_132()
  {
     if (jj_scan_token(DIVIDE)) return true;
     return false;
@@ -4630,27 +4655,27 @@ static private boolean jj_3_10()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1507_17_141()
+  static private boolean jj_3R_141()
  {
-    if (jj_3R_ExpressionReward_1781_9_153()) return true;
+    if (jj_3R_153()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1505_17_140()
+  static private boolean jj_3R_140()
  {
-    if (jj_3R_ExpressionSS_1737_9_38()) return true;
+    if (jj_3R_38()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1503_17_139()
+  static private boolean jj_3R_139()
  {
-    if (jj_3R_ExpressionProb_1658_9_152()) return true;
+    if (jj_3R_152()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1500_17_138()
+  static private boolean jj_3R_138()
  {
-    if (jj_3R_ExpressionParenth_1634_9_151()) return true;
+    if (jj_3R_151()) return true;
     return false;
   }
 
@@ -4661,104 +4686,104 @@ static private boolean jj_3_18()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1498_17_137()
+  static private boolean jj_3R_137()
  {
-    if (jj_3R_ExpressionFuncOldStyle_1572_9_150()) return true;
+    if (jj_3R_150()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1886_11_229()
+  static private boolean jj_3R_229()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemParallel_1120_11_64()
+  static private boolean jj_3R_64()
  {
     if (jj_scan_token(OR)) return true;
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_SystemParallel_1121_65_75()) { jj_scanpos = xsp; break; }
+      if (jj_3R_75()) { jj_scanpos = xsp; break; }
     }
     if (jj_scan_token(RBRACKET)) return true;
     if (jj_scan_token(OR)) return true;
-    if (jj_3R_SystemHideRename_1146_9_63()) return true;
+    if (jj_3R_63()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1496_17_136()
+  static private boolean jj_3R_136()
  {
-    if (jj_3R_ExpressionFuncMinMax_1558_9_149()) return true;
+    if (jj_3R_149()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1883_11_228()
+  static private boolean jj_3R_228()
  {
     if (jj_scan_token(F0)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1494_17_135()
+  static private boolean jj_3R_135()
  {
-    if (jj_3R_ExpressionFuncOrIdent_1540_9_148()) return true;
+    if (jj_3R_148()) return true;
     return false;
   }
 
   static private boolean jj_3_17()
  {
-    if (jj_3R_ExpressionSS_1737_9_38()) return true;
+    if (jj_3R_38()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1882_11_227()
+  static private boolean jj_3R_227()
  {
     if (jj_scan_token(Fc)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemParallel_1118_9_54()
+  static private boolean jj_3R_54()
  {
-    if (jj_3R_SystemHideRename_1146_9_63()) return true;
+    if (jj_3R_63()) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_SystemParallel_1120_11_64()) jj_scanpos = xsp;
+    if (jj_3R_64()) jj_scanpos = xsp;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1881_11_226()
+  static private boolean jj_3R_226()
  {
     if (jj_scan_token(I)) return true;
     if (jj_scan_token(EQ)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1492_17_134()
+  static private boolean jj_3R_134()
  {
-    if (jj_3R_ExpressionLiteral_1594_9_147()) return true;
+    if (jj_3R_147()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1880_11_225()
+  static private boolean jj_3R_225()
  {
     if (jj_scan_token(C)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1879_11_224()
+  static private boolean jj_3R_224()
  {
     if (jj_scan_token(C)) return true;
     if (jj_scan_token(LE)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionPlusMinus_1444_62_128()
+  static private boolean jj_3R_128()
  {
     if (jj_scan_token(MINUS)) return true;
     return false;
@@ -4770,47 +4795,47 @@ static private boolean jj_3_16()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1876_11_223()
+  static private boolean jj_3R_223()
  {
     if (jj_scan_token(S)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1875_9_222()
+  static private boolean jj_3R_222()
  {
-    if (jj_3R_ExpressionSS_1737_9_38()) return true;
+    if (jj_3R_38()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1491_9_133()
+  static private boolean jj_3R_133()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionBasic_1492_17_134()) {
+    if (jj_3R_134()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1494_17_135()) {
+    if (jj_3R_135()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1496_17_136()) {
+    if (jj_3R_136()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1498_17_137()) {
+    if (jj_3R_137()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1500_17_138()) {
+    if (jj_3R_138()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1503_17_139()) {
+    if (jj_3R_139()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1505_17_140()) {
+    if (jj_3R_140()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1507_17_141()) {
+    if (jj_3R_141()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1509_17_142()) {
+    if (jj_3R_142()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1511_17_143()) {
+    if (jj_3R_143()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1513_17_144()) {
+    if (jj_3R_144()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1515_17_145()) {
+    if (jj_3R_145()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionBasic_1517_17_146()) return true;
+    if (jj_3R_146()) return true;
     }
     }
     }
@@ -4826,25 +4851,25 @@ static private boolean jj_3R_ExpressionBasic_1491_9_133()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRewardContents_1872_9_187()
+  static private boolean jj_3R_187()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionRewardContents_1875_9_222()) {
+    if (jj_3R_222()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1876_11_223()) {
+    if (jj_3R_223()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1879_11_224()) {
+    if (jj_3R_224()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1880_11_225()) {
+    if (jj_3R_225()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1881_11_226()) {
+    if (jj_3R_226()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1882_11_227()) {
+    if (jj_3R_227()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1883_11_228()) {
+    if (jj_3R_228()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionRewardContents_1886_11_229()) return true;
+    if (jj_3R_229()) return true;
     }
     }
     }
@@ -4855,270 +4880,282 @@ static private boolean jj_3R_ExpressionRewardContents_1872_9_187()
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1846_33_262()
+  static private boolean jj_3R_263()
  {
     if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionUnaryMinus_1479_17_130()
+  static private boolean jj_3R_130()
  {
-    if (jj_3R_ExpressionBasic_1491_9_133()) return true;
+    if (jj_3R_133()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1809_69_188()
+  static private boolean jj_3R_188()
  {
-    if (jj_3R_Filter_1713_9_52()) return true;
+    if (jj_3R_52()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionUnaryMinus_1476_17_129()
+  static private boolean jj_3R_129()
  {
     if (jj_scan_token(MINUS)) return true;
-    if (jj_3R_ExpressionUnaryMinus_1475_9_125()) return true;
+    if (jj_3R_125()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemInterleaved_1094_9_47()
+  static private boolean jj_3R_47()
  {
-    if (jj_3R_SystemParallel_1118_9_54()) return true;
+    if (jj_3R_54()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_SystemInterleaved_1096_70_55()) { jj_scanpos = xsp; break; }
-    }
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionUnaryMinus_1475_9_125()
- {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionUnaryMinus_1476_17_129()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionUnaryMinus_1479_17_130()) return true;
+      if (jj_3R_55()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTimesDivide_1461_19_131()
+  static private boolean jj_3R_59()
  {
-    if (jj_scan_token(TIMES)) return true;
+    if (jj_scan_token(LE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTimesDivide_1461_17_126()
+  static private boolean jj_3R_125()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionTimesDivide_1461_19_131()) {
+    if (jj_3R_129()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionTimesDivide_1461_64_132()) return true;
+    if (jj_3R_130()) return true;
     }
-    if (jj_3R_ExpressionUnaryMinus_1475_9_125()) return true;
     return false;
   }
 
-  static private boolean jj_3_15()
+  static private boolean jj_3R_58()
  {
-    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_scan_token(GE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1846_11_254()
+  static private boolean jj_3R_57()
+ {
+    if (jj_scan_token(LT)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_56()
+ {
+    if (jj_scan_token(GT)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_50()
  {
-    if (jj_scan_token(DIVIDE)) return true;
-    if (jj_scan_token(LBRACE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_RewardIndex_1846_33_262()) {
+    if (jj_3R_56()) {
+    jj_scanpos = xsp;
+    if (jj_3R_57()) {
+    jj_scanpos = xsp;
+    if (jj_3R_58()) {
     jj_scanpos = xsp;
-    if (jj_3R_RewardIndex_1846_101_263()) return true;
+    if (jj_3R_59()) return true;
+    }
+    }
     }
-    if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1843_10_253()
+  static private boolean jj_3R_131()
  {
-    if (jj_scan_token(COMMA)) return true;
-    if (jj_scan_token(DISCOUNT)) return true;
-    if (jj_scan_token(EQ)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_scan_token(TIMES)) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1841_10_250()
+  static private boolean jj_3R_126()
  {
-    if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
-    if (jj_scan_token(DQUOTE)) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_131()) {
+    jj_scanpos = xsp;
+    if (jj_3R_132()) return true;
+    }
+    if (jj_3R_125()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTimesDivide_1459_9_121()
+  static private boolean jj_3_15()
  {
-    if (jj_3R_ExpressionUnaryMinus_1475_9_125()) return true;
-    Token xsp;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_ExpressionTimesDivide_1461_17_126()) { jj_scanpos = xsp; break; }
-    }
+    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3_2()
+  static private boolean jj_3R_254()
  {
-    if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
-    if (jj_scan_token(DQUOTE)) return true;
-    if (jj_scan_token(COLON)) return true;
+    if (jj_scan_token(DIVIDE)) return true;
+    if (jj_scan_token(LBRACE)) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_263()) {
+    jj_scanpos = xsp;
+    if (jj_3R_264()) return true;
+    }
+    if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_LtGt_2223_9_59()
+  static private boolean jj_3R_124()
  {
-    if (jj_scan_token(LE)) return true;
+    if (jj_scan_token(NE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1839_9_240()
+  static private boolean jj_3R_120()
  {
-    if (jj_scan_token(LBRACE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_RewardIndex_1841_10_250()) {
-    jj_scanpos = xsp;
-    if (jj_3R_RewardIndex_1841_75_251()) {
+    if (jj_3R_123()) {
     jj_scanpos = xsp;
-    if (jj_3R_RewardIndex_1841_125_252()) return true;
+    if (jj_3R_124()) return true;
     }
-    }
-    xsp = jj_scanpos;
-    if (jj_3R_RewardIndex_1843_10_253()) jj_scanpos = xsp;
-    if (jj_scan_token(RBRACE)) return true;
-    xsp = jj_scanpos;
-    if (jj_3R_RewardIndex_1846_11_254()) jj_scanpos = xsp;
     return false;
   }
 
-  static private boolean jj_3R_LtGt_2222_9_58()
+  static private boolean jj_3R_123()
  {
-    if (jj_scan_token(GE)) return true;
+    if (jj_scan_token(EQ)) return true;
     return false;
   }
 
-  static private boolean jj_3R_LtGt_2221_9_57()
+  static private boolean jj_3R_253()
  {
-    if (jj_scan_token(LT)) return true;
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_scan_token(DISCOUNT)) return true;
+    if (jj_scan_token(EQ)) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemFullParallel_1071_9_40()
+  static private boolean jj_3R_250()
  {
-    if (jj_3R_SystemInterleaved_1094_9_47()) return true;
-    Token xsp;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_SystemFullParallel_1073_71_48()) { jj_scanpos = xsp; break; }
-    }
+    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_3R_34()) return true;
+    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionPlusMinus_1444_19_127()
+  static private boolean jj_3R_121()
  {
-    if (jj_scan_token(PLUS)) return true;
+    if (jj_3R_125()) return true;
+    Token xsp;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_126()) { jj_scanpos = xsp; break; }
+    }
     return false;
   }
 
-  static private boolean jj_3R_LtGt_2220_9_56()
+  static private boolean jj_3_2()
  {
-    if (jj_scan_token(GT)) return true;
+    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_3R_34()) return true;
+    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_scan_token(COLON)) return true;
     return false;
   }
 
-  static private boolean jj_3R_LtGt_2220_9_50()
+  static private boolean jj_3R_240()
  {
+    if (jj_scan_token(LBRACE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_LtGt_2220_9_56()) {
-    jj_scanpos = xsp;
-    if (jj_3R_LtGt_2221_9_57()) {
+    if (jj_3R_250()) {
     jj_scanpos = xsp;
-    if (jj_3R_LtGt_2222_9_58()) {
+    if (jj_3R_251()) {
     jj_scanpos = xsp;
-    if (jj_3R_LtGt_2223_9_59()) return true;
-    }
+    if (jj_3R_252()) return true;
     }
     }
+    xsp = jj_scanpos;
+    if (jj_3R_253()) jj_scanpos = xsp;
+    if (jj_scan_token(RBRACE)) return true;
+    xsp = jj_scanpos;
+    if (jj_3R_254()) jj_scanpos = xsp;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionPlusMinus_1444_17_122()
+  static private boolean jj_3R_40()
  {
+    if (jj_3R_47()) return true;
     Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionPlusMinus_1444_19_127()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionPlusMinus_1444_62_128()) return true;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_48()) { jj_scanpos = xsp; break; }
     }
-    if (jj_3R_ExpressionTimesDivide_1459_9_121()) return true;
     return false;
   }
 
-  static private boolean jj_3R_EqNeq_2211_9_124()
+  static private boolean jj_3R_127()
  {
-    if (jj_scan_token(NE)) return true;
+    if (jj_scan_token(PLUS)) return true;
     return false;
   }
 
-  static private boolean jj_3R_EqNeq_2210_9_120()
+  static private boolean jj_3R_122()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_EqNeq_2210_9_123()) {
+    if (jj_3R_127()) {
     jj_scanpos = xsp;
-    if (jj_3R_EqNeq_2211_9_124()) return true;
+    if (jj_3R_128()) return true;
     }
+    if (jj_3R_121()) return true;
     return false;
   }
 
-  static private boolean jj_3R_EqNeq_2210_9_123()
+  static private boolean jj_3R_53()
  {
-    if (jj_scan_token(EQ)) return true;
+    if (jj_scan_token(REG_IDENTPRIME)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionPlusMinus_1442_9_118()
+  static private boolean jj_3R_118()
  {
-    if (jj_3R_ExpressionTimesDivide_1459_9_121()) return true;
+    if (jj_3R_121()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionPlusMinus_1444_17_122()) { jj_scanpos = xsp; break; }
+      if (jj_3R_122()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_SystemDefn_1058_9_36()
+  static private boolean jj_3R_36()
+ {
+    if (jj_3R_40()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_199()
  {
-    if (jj_3R_SystemFullParallel_1071_9_40()) return true;
+    if (jj_scan_token(OR)) return true;
     return false;
   }
 
   static private boolean jj_3_7()
  {
     if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_SystemDefn_1058_9_36()) return true;
+    if (jj_3R_36()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1794_26_246()
+  static private boolean jj_3R_246()
  {
     if (jj_scan_token(MAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5126,7 +5163,7 @@ static private boolean jj_3R_ExpressionReward_1794_26_246()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1793_26_245()
+  static private boolean jj_3R_245()
  {
     if (jj_scan_token(MIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5134,14 +5171,14 @@ static private boolean jj_3R_ExpressionReward_1793_26_245()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1792_26_244()
+  static private boolean jj_3R_244()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1807_10_186()
+  static private boolean jj_3R_186()
  {
     if (jj_scan_token(RMAXMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5149,13 +5186,7 @@ static private boolean jj_3R_ExpressionReward_1807_10_186()
     return false;
   }
 
-  static private boolean jj_3R_IdentifierPrime_2191_9_53()
- {
-    if (jj_scan_token(REG_IDENTPRIME)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionReward_1790_26_243()
+  static private boolean jj_3R_243()
  {
     if (jj_scan_token(MAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5163,7 +5194,7 @@ static private boolean jj_3R_ExpressionReward_1790_26_243()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1799_17_221()
+  static private boolean jj_3R_221()
  {
     if (jj_scan_token(MAXMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5171,7 +5202,7 @@ static private boolean jj_3R_ExpressionReward_1799_17_221()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1806_10_185()
+  static private boolean jj_3R_185()
  {
     if (jj_scan_token(RMAXMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5179,14 +5210,14 @@ static private boolean jj_3R_ExpressionReward_1806_10_185()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRelop_1422_11_119()
+  static private boolean jj_3R_119()
  {
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_ExpressionPlusMinus_1442_9_118()) return true;
+    if (jj_3R_50()) return true;
+    if (jj_3R_118()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1789_26_242()
+  static private boolean jj_3R_242()
  {
     if (jj_scan_token(MIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5194,7 +5225,7 @@ static private boolean jj_3R_ExpressionReward_1789_26_242()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1798_17_220()
+  static private boolean jj_3R_220()
  {
     if (jj_scan_token(MAXMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5202,7 +5233,7 @@ static private boolean jj_3R_ExpressionReward_1798_17_220()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1805_10_184()
+  static private boolean jj_3R_184()
  {
     if (jj_scan_token(RMINMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5210,14 +5241,14 @@ static private boolean jj_3R_ExpressionReward_1805_10_184()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1788_26_241()
+  static private boolean jj_3R_241()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1797_17_219()
+  static private boolean jj_3R_219()
  {
     if (jj_scan_token(MINMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5225,7 +5256,7 @@ static private boolean jj_3R_ExpressionReward_1797_17_219()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1804_10_183()
+  static private boolean jj_3R_183()
  {
     if (jj_scan_token(RMINMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5233,7 +5264,13 @@ static private boolean jj_3R_ExpressionReward_1804_10_183()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1796_17_218()
+  static private boolean jj_3R_37()
+ {
+    if (jj_3R_34()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_218()
  {
     if (jj_scan_token(MINMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5241,7 +5278,7 @@ static private boolean jj_3R_ExpressionReward_1796_17_218()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1803_10_182()
+  static private boolean jj_3R_182()
  {
     if (jj_scan_token(RMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5249,18 +5286,18 @@ static private boolean jj_3R_ExpressionReward_1803_10_182()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionRelop_1421_9_116()
+  static private boolean jj_3R_116()
  {
-    if (jj_3R_ExpressionPlusMinus_1442_9_118()) return true;
+    if (jj_3R_118()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionRelop_1422_11_119()) { jj_scanpos = xsp; break; }
+      if (jj_3R_119()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1802_10_181()
+  static private boolean jj_3R_181()
  {
     if (jj_scan_token(RMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5268,124 +5305,136 @@ static private boolean jj_3R_ExpressionReward_1802_10_181()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2137_56_199()
- {
-    if (jj_scan_token(OR)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionReward_1792_17_217()
+  static private boolean jj_3R_217()
  {
     if (jj_scan_token(MAX)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1792_26_244()) {
+    if (jj_3R_244()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1793_26_245()) {
+    if (jj_3R_245()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1794_26_246()) return true;
+    if (jj_3R_246()) return true;
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1788_17_216()
+  static private boolean jj_3R_198()
+ {
+    if (jj_scan_token(AND)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_196()
+ {
+    if (jj_scan_token(MAX)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_216()
  {
     if (jj_scan_token(MIN)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1788_26_241()) {
+    if (jj_3R_241()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1789_26_242()) {
+    if (jj_3R_242()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1790_26_243()) return true;
+    if (jj_3R_243()) return true;
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1787_17_215()
+  static private boolean jj_3R_215()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1786_18_214()
+  static private boolean jj_3R_214()
  {
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_50()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1785_18_213()
+  static private boolean jj_3R_213()
  {
-    if (jj_3R_RewardIndex_1839_9_240()) return true;
+    if (jj_3R_240()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1784_19_212()
+  static private boolean jj_3R_212()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionEquality_1408_11_117()
+  static private boolean jj_3R_34()
+ {
+    if (jj_scan_token(REG_IDENT)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_117()
  {
-    if (jj_3R_EqNeq_2210_9_120()) return true;
-    if (jj_3R_ExpressionRelop_1421_9_116()) return true;
+    if (jj_3R_120()) return true;
+    if (jj_3R_116()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionSS_1745_55_44()
+  static private boolean jj_3R_44()
  {
-    if (jj_3R_Filter_1713_9_52()) return true;
+    if (jj_3R_52()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionEquality_1407_9_115()
+  static private boolean jj_3R_115()
  {
-    if (jj_3R_ExpressionRelop_1421_9_116()) return true;
+    if (jj_3R_116()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionEquality_1408_11_117()) { jj_scanpos = xsp; break; }
+      if (jj_3R_117()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_IdentifierExpression_2169_9_37()
+  static private boolean jj_3R_194()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_scan_token(INIT)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1783_10_180()
+  static private boolean jj_3R_180()
  {
     if (jj_scan_token(R)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1784_19_212()) jj_scanpos = xsp;
+    if (jj_3R_212()) jj_scanpos = xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1785_18_213()) jj_scanpos = xsp;
+    if (jj_3R_213()) jj_scanpos = xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1786_18_214()) {
+    if (jj_3R_214()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1787_17_215()) {
+    if (jj_3R_215()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1788_17_216()) {
+    if (jj_3R_216()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1792_17_217()) {
+    if (jj_3R_217()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1796_17_218()) {
+    if (jj_3R_218()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1797_17_219()) {
+    if (jj_3R_219()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1798_17_220()) {
+    if (jj_3R_220()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1799_17_221()) return true;
+    if (jj_3R_221()) return true;
     }
     }
     }
@@ -5396,42 +5445,42 @@ static private boolean jj_3R_ExpressionReward_1783_10_180()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionNot_1393_17_114()
+  static private boolean jj_3R_114()
  {
-    if (jj_3R_ExpressionEquality_1407_9_115()) return true;
+    if (jj_3R_115()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionNot_1391_17_113()
+  static private boolean jj_3R_113()
  {
     if (jj_scan_token(NOT)) return true;
-    if (jj_3R_ExpressionNot_1390_9_111()) return true;
+    if (jj_3R_111()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1308_99_106()
+  static private boolean jj_3R_106()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionReward_1781_9_153()
+  static private boolean jj_3R_153()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1783_10_180()) {
+    if (jj_3R_180()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1802_10_181()) {
+    if (jj_3R_181()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1803_10_182()) {
+    if (jj_3R_182()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1804_10_183()) {
+    if (jj_3R_183()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1805_10_184()) {
+    if (jj_3R_184()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1806_10_185()) {
+    if (jj_3R_185()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionReward_1807_10_186()) return true;
+    if (jj_3R_186()) return true;
     }
     }
     }
@@ -5439,198 +5488,187 @@ static private boolean jj_3R_ExpressionReward_1781_9_153()
     }
     }
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_ExpressionRewardContents_1872_9_187()) return true;
+    if (jj_3R_187()) return true;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionReward_1809_69_188()) jj_scanpos = xsp;
+    if (jj_3R_188()) jj_scanpos = xsp;
     if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1307_99_104()
- {
-    if (jj_3R_Expression_1229_9_43()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionFilter_2137_34_198()
- {
-    if (jj_scan_token(AND)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionFilter_2136_35_196()
- {
-    if (jj_scan_token(MAX)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_TimeBound_1306_99_102()
+  static private boolean jj_3R_201()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1305_99_100()
+  static private boolean jj_3R_104()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_Identifier_2158_9_34()
+  static private boolean jj_3R_102()
  {
-    if (jj_scan_token(REG_IDENT)) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionNot_1390_9_111()
+  static private boolean jj_3R_100()
  {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionNot_1391_17_113()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionNot_1393_17_114()) return true;
-    }
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLabel_2115_47_194()
+  static private boolean jj_3R_200()
  {
-    if (jj_scan_token(INIT)) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionAnd_1378_11_112()
+  static private boolean jj_3R_197()
  {
-    if (jj_scan_token(AND)) return true;
-    if (jj_3R_ExpressionNot_1390_9_111()) return true;
+    if (jj_scan_token(PLUS)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2142_11_201()
+  static private boolean jj_3R_195()
  {
-    if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_scan_token(MIN)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionAnd_1377_9_109()
+  static private boolean jj_3R_111()
  {
-    if (jj_3R_ExpressionNot_1390_9_111()) return true;
     Token xsp;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_ExpressionAnd_1378_11_112()) { jj_scanpos = xsp; break; }
+    xsp = jj_scanpos;
+    if (jj_3R_113()) {
+    jj_scanpos = xsp;
+    if (jj_3R_114()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2138_11_200()
+  static private boolean jj_3R_193()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2137_11_197()
+  static private boolean jj_3R_233()
  {
-    if (jj_scan_token(PLUS)) return true;
+    if (jj_3R_249()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2136_11_195()
+  static private boolean jj_3R_158()
  {
-    if (jj_scan_token(MIN)) return true;
+    if (jj_scan_token(FILTER)) return true;
+    if (jj_scan_token(LPARENTH)) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_195()) {
+    jj_scanpos = xsp;
+    if (jj_3R_196()) {
+    jj_scanpos = xsp;
+    if (jj_3R_197()) {
+    jj_scanpos = xsp;
+    if (jj_3R_198()) {
+    jj_scanpos = xsp;
+    if (jj_3R_199()) {
+    jj_scanpos = xsp;
+    if (jj_3R_200()) return true;
+    }
+    }
+    }
+    }
+    }
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_3R_43()) return true;
+    xsp = jj_scanpos;
+    if (jj_3R_201()) jj_scanpos = xsp;
+    if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLabel_2115_30_193()
+  static private boolean jj_3R_112()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_scan_token(AND)) return true;
+    if (jj_3R_111()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2050_93_233()
+  static private boolean jj_3R_109()
  {
-    if (jj_3R_ExpressionMultiNash_1906_9_249()) return true;
+    if (jj_3R_111()) return true;
+    Token xsp;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_112()) { jj_scanpos = xsp; break; }
+    }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionOr_1365_11_110()
+  static private boolean jj_3R_110()
  {
     if (jj_scan_token(OR)) return true;
-    if (jj_3R_ExpressionAnd_1377_9_109()) return true;
+    if (jj_3R_109()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionSS_1742_17_42()
+  static private boolean jj_3R_42()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionSS_1740_19_49()
+  static private boolean jj_3R_49()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFilter_2131_9_158()
+  static private boolean jj_3R_157()
  {
-    if (jj_scan_token(FILTER)) return true;
-    if (jj_scan_token(LPARENTH)) return true;
+    if (jj_scan_token(DQUOTE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionFilter_2136_11_195()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionFilter_2136_35_196()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionFilter_2137_11_197()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionFilter_2137_34_198()) {
+    if (jj_3R_193()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionFilter_2137_56_199()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionFilter_2138_11_200()) return true;
-    }
-    }
-    }
+    if (jj_3R_194()) return true;
     }
-    }
-    if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionFilter_2142_11_201()) jj_scanpos = xsp;
-    if (jj_scan_token(RPARENTH)) return true;
+    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
   static private boolean jj_3_1()
  {
     if (jj_scan_token(MODULE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     if (jj_scan_token(EQ)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionSS_1740_17_41()
+  static private boolean jj_3R_41()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionSS_1740_19_49()) jj_scanpos = xsp;
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_49()) jj_scanpos = xsp;
+    if (jj_3R_50()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionOr_1364_9_107()
+  static private boolean jj_3R_107()
  {
-    if (jj_3R_ExpressionAnd_1377_9_109()) return true;
+    if (jj_3R_109()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionOr_1365_11_110()) { jj_scanpos = xsp; break; }
+      if (jj_3R_110()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
@@ -5641,340 +5679,350 @@ static private boolean jj_3_6()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionIff_1352_11_108()
+  static private boolean jj_3R_108()
  {
     if (jj_scan_token(IFF)) return true;
-    if (jj_3R_ExpressionOr_1364_9_107()) return true;
+    if (jj_3R_107()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionSS_1737_9_38()
+  static private boolean jj_3R_38()
  {
     if (jj_scan_token(S)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionSS_1740_17_41()) {
+    if (jj_3R_41()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionSS_1742_17_42()) return true;
+    if (jj_3R_42()) return true;
     }
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionSS_1745_55_44()) jj_scanpos = xsp;
+    if (jj_3R_44()) jj_scanpos = xsp;
     if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionIff_1351_9_97()
+  static private boolean jj_3R_275()
  {
-    if (jj_3R_ExpressionOr_1364_9_107()) return true;
     Token xsp;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_ExpressionIff_1352_11_108()) { jj_scanpos = xsp; break; }
+    xsp = jj_scanpos;
+    if (jj_scan_token(117)) {
+    jj_scanpos = xsp;
+    if (jj_scan_token(120)) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLabel_2113_9_157()
+  static private boolean jj_3R_97()
  {
-    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_3R_107()) return true;
     Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionLabel_2115_30_193()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionLabel_2115_47_194()) return true;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_108()) { jj_scanpos = xsp; break; }
     }
-    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1684_51_179()
+  static private boolean jj_3R_232()
+ {
+    if (jj_3R_153()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_276()
+ {
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_3R_275()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_179()
  {
-    if (jj_3R_Filter_1713_9_52()) return true;
+    if (jj_3R_52()) return true;
     return false;
   }
 
-  static private boolean jj_3R_Filter_1716_19_72()
+  static private boolean jj_3R_72()
  {
     if (jj_scan_token(MAX)) return true;
     return false;
   }
 
-  static private boolean jj_3R_Filter_1715_19_71()
+  static private boolean jj_3R_71()
  {
     if (jj_scan_token(MIN)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionImplies_1339_11_98()
+  static private boolean jj_3R_98()
  {
     if (jj_scan_token(IMPLIES)) return true;
-    if (jj_3R_ExpressionIff_1351_9_97()) return true;
+    if (jj_3R_97()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_265()
+ {
+    if (jj_3R_275()) return true;
+    Token xsp;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_276()) { jj_scanpos = xsp; break; }
+    }
+    return false;
+  }
+
+  static private boolean jj_3R_256()
+ {
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_265()) jj_scanpos = xsp;
+    return false;
+  }
+
+  static private boolean jj_3R_255()
+ {
+    if (jj_scan_token(TIMES)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionImplies_1338_9_87()
+  static private boolean jj_3R_87()
  {
-    if (jj_3R_ExpressionIff_1351_9_97()) return true;
+    if (jj_3R_97()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionImplies_1339_11_98()) { jj_scanpos = xsp; break; }
+      if (jj_3R_98()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalitionPlayer_2099_9_273()
+  static private boolean jj_3R_247()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_scan_token(113)) {
+    if (jj_3R_255()) {
     jj_scanpos = xsp;
-    if (jj_scan_token(116)) return true;
+    if (jj_3R_256()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_Filter_1714_11_62()
+  static private boolean jj_3R_62()
  {
     if (jj_scan_token(LBRACE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_Filter_1715_19_71()) {
+    if (jj_3R_71()) {
     jj_scanpos = xsp;
-    if (jj_3R_Filter_1716_19_72()) return true;
+    if (jj_3R_72()) return true;
     }
     if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionITE_1324_17_88()
+  static private boolean jj_3R_88()
  {
     if (jj_scan_token(QMARK)) return true;
-    if (jj_3R_ExpressionImplies_1338_9_87()) return true;
+    if (jj_3R_87()) return true;
     if (jj_scan_token(COLON)) return true;
-    if (jj_3R_ExpressionITE_1322_9_80()) return true;
+    if (jj_3R_80()) return true;
     return false;
   }
 
-  static private boolean jj_3R_Filter_1713_9_52()
+  static private boolean jj_3R_52()
  {
     if (jj_scan_token(LBRACE)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(RBRACE)) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_Filter_1714_11_62()) { jj_scanpos = xsp; break; }
+      if (jj_3R_62()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
   static private boolean jj_3_14()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(LPARENTH)) return true;
     return false;
   }
 
   static private boolean jj_3_13()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(LPARENTH)) return true;
     return false;
   }
 
   static private boolean jj_3_12()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(LPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2050_51_232()
- {
-    if (jj_3R_ExpressionReward_1781_9_153()) return true;
-    return false;
-  }
-
   static private boolean jj_3_11()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(LPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalition_2086_13_274()
- {
-    if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_ExpressionStrategyCoalitionPlayer_2099_9_273()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionITE_1322_9_80()
+  static private boolean jj_3R_248()
  {
-    if (jj_3R_ExpressionImplies_1338_9_87()) return true;
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionITE_1324_17_88()) jj_scanpos = xsp;
+    if (jj_scan_token(COLON)) return true;
+    if (jj_3R_247()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalition_2085_11_264()
+  static private boolean jj_3R_230()
  {
-    if (jj_3R_ExpressionStrategyCoalitionPlayer_2099_9_273()) return true;
+    if (jj_3R_247()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionStrategyCoalition_2086_13_274()) { jj_scanpos = xsp; break; }
+      if (jj_3R_248()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalition_2085_9_256()
+  static private boolean jj_3R_80()
  {
+    if (jj_3R_87()) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionStrategyCoalition_2085_11_264()) jj_scanpos = xsp;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionStrategyCoalition_2083_11_255()
- {
-    if (jj_scan_token(TIMES)) return true;
+    if (jj_3R_88()) jj_scanpos = xsp;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1308_20_105()
+  static private boolean jj_3R_105()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1307_20_103()
+  static private boolean jj_3R_103()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionStrategyCoalition_2083_9_247()
- {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionStrategyCoalition_2083_11_255()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionStrategyCoalition_2085_9_256()) return true;
-    }
+    if (jj_3R_37()) return true;
     return false;
   }
 
-  static private boolean jj_3R_Update_907_36_46()
+  static private boolean jj_3R_46()
  {
     if (jj_scan_token(AND)) return true;
-    if (jj_3R_UpdateElement_920_9_45()) return true;
+    if (jj_3R_45()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1306_20_101()
+  static private boolean jj_3R_101()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1305_20_99()
+  static private boolean jj_3R_99()
  {
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1310_11_94()
+  static private boolean jj_3R_94()
  {
     if (jj_scan_token(EQ)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1309_11_93()
+  static private boolean jj_3R_93()
  {
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1308_11_92()
+  static private boolean jj_3R_92()
  {
     if (jj_scan_token(GT)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_TimeBound_1308_20_105()) {
+    if (jj_3R_105()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1308_99_106()) return true;
+    if (jj_3R_106()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1307_11_91()
+  static private boolean jj_3R_91()
  {
     if (jj_scan_token(GE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_TimeBound_1307_20_103()) {
+    if (jj_3R_103()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1307_99_104()) return true;
+    if (jj_3R_104()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1306_11_90()
+  static private boolean jj_3R_90()
  {
     if (jj_scan_token(LT)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_TimeBound_1306_20_101()) {
+    if (jj_3R_101()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1306_99_102()) return true;
+    if (jj_3R_102()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1305_11_89()
+  static private boolean jj_3R_192()
+ {
+    if (jj_3R_151()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_89()
  {
     if (jj_scan_token(LE)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_TimeBound_1305_20_99()) {
+    if (jj_3R_99()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1305_99_100()) return true;
+    if (jj_3R_100()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalitionList_2070_10_248()
+  static private boolean jj_3R_231()
  {
-    if (jj_scan_token(COLON)) return true;
-    if (jj_3R_ExpressionStrategyCoalition_2083_9_247()) return true;
+    if (jj_3R_152()) return true;
     return false;
   }
 
-  static private boolean jj_3R_TimeBound_1305_9_81()
+  static private boolean jj_3R_81()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_TimeBound_1305_11_89()) {
+    if (jj_3R_89()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1306_11_90()) {
+    if (jj_3R_90()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1307_11_91()) {
+    if (jj_3R_91()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1308_11_92()) {
+    if (jj_3R_92()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1309_11_93()) {
+    if (jj_3R_93()) {
     jj_scanpos = xsp;
-    if (jj_3R_TimeBound_1310_11_94()) return true;
+    if (jj_3R_94()) return true;
     }
     }
     }
@@ -5983,7 +6031,13 @@ static private boolean jj_3R_TimeBound_1305_9_81()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1669_26_239()
+  static private boolean jj_3R_283()
+ {
+    if (jj_3R_43()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_239()
  {
     if (jj_scan_token(MAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -5991,28 +6045,31 @@ static private boolean jj_3R_ExpressionProb_1669_26_239()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategyCoalitionList_2069_9_230()
+  static private boolean jj_3R_191()
  {
-    if (jj_3R_ExpressionStrategyCoalition_2083_9_247()) return true;
     Token xsp;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_ExpressionStrategyCoalitionList_2070_10_248()) { jj_scanpos = xsp; break; }
+    xsp = jj_scanpos;
+    if (jj_3R_231()) {
+    jj_scanpos = xsp;
+    if (jj_3R_232()) {
+    jj_scanpos = xsp;
+    if (jj_3R_233()) return true;
+    }
     }
     return false;
   }
 
-  static private boolean jj_3R_UpdateElement_920_9_45()
+  static private boolean jj_3R_45()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_IdentifierPrime_2191_9_53()) return true;
+    if (jj_3R_53()) return true;
     if (jj_scan_token(EQ)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1668_26_238()
+  static private boolean jj_3R_238()
  {
     if (jj_scan_token(MIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6020,14 +6077,22 @@ static private boolean jj_3R_ExpressionProb_1668_26_238()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1667_26_237()
+  static private boolean jj_3R_237()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1682_10_178()
+  static private boolean jj_3R_190()
+ {
+    if (jj_scan_token(DLBRACKET)) return true;
+    if (jj_3R_230()) return true;
+    if (jj_scan_token(DRBRACKET)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_178()
  {
     if (jj_scan_token(PMAXMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6035,13 +6100,13 @@ static private boolean jj_3R_ExpressionProb_1682_10_178()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1292_17_66()
+  static private boolean jj_3R_66()
  {
-    if (jj_3R_ExpressionITE_1322_9_80()) return true;
+    if (jj_3R_80()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1665_26_236()
+  static private boolean jj_3R_236()
  {
     if (jj_scan_token(MAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6049,7 +6114,7 @@ static private boolean jj_3R_ExpressionProb_1665_26_236()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1674_17_211()
+  static private boolean jj_3R_211()
  {
     if (jj_scan_token(MAXMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6057,7 +6122,15 @@ static private boolean jj_3R_ExpressionProb_1674_17_211()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1681_10_177()
+  static private boolean jj_3R_189()
+ {
+    if (jj_scan_token(DLT)) return true;
+    if (jj_3R_230()) return true;
+    if (jj_scan_token(DGT)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_177()
  {
     if (jj_scan_token(PMAXMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6065,7 +6138,7 @@ static private boolean jj_3R_ExpressionProb_1681_10_177()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1664_26_235()
+  static private boolean jj_3R_235()
  {
     if (jj_scan_token(MIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6073,7 +6146,7 @@ static private boolean jj_3R_ExpressionProb_1664_26_235()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1673_17_210()
+  static private boolean jj_3R_210()
  {
     if (jj_scan_token(MAXMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6081,7 +6154,7 @@ static private boolean jj_3R_ExpressionProb_1673_17_210()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1680_10_176()
+  static private boolean jj_3R_176()
  {
     if (jj_scan_token(PMINMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6089,20 +6162,20 @@ static private boolean jj_3R_ExpressionProb_1680_10_176()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1288_19_79()
+  static private boolean jj_3R_79()
  {
-    if (jj_3R_TimeBound_1305_9_81()) return true;
+    if (jj_3R_81()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1663_26_234()
+  static private boolean jj_3R_234()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1672_17_209()
+  static private boolean jj_3R_209()
  {
     if (jj_scan_token(MINMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6110,7 +6183,7 @@ static private boolean jj_3R_ExpressionProb_1672_17_209()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1679_10_175()
+  static private boolean jj_3R_175()
  {
     if (jj_scan_token(PMINMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6118,13 +6191,13 @@ static private boolean jj_3R_ExpressionProb_1679_10_175()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1287_19_78()
+  static private boolean jj_3R_78()
  {
     if (jj_scan_token(G)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1671_17_208()
+  static private boolean jj_3R_208()
  {
     if (jj_scan_token(MINMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6132,7 +6205,7 @@ static private boolean jj_3R_ExpressionProb_1671_17_208()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1678_10_174()
+  static private boolean jj_3R_174()
  {
     if (jj_scan_token(PMAX)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6140,13 +6213,13 @@ static private boolean jj_3R_ExpressionProb_1678_10_174()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1286_19_77()
+  static private boolean jj_3R_77()
  {
     if (jj_scan_token(F)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1677_10_173()
+  static private boolean jj_3R_173()
  {
     if (jj_scan_token(PMIN)) return true;
     if (jj_scan_token(EQ)) return true;
@@ -6154,190 +6227,158 @@ static private boolean jj_3R_ExpressionProb_1677_10_173()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1285_19_76()
+  static private boolean jj_3R_76()
  {
     if (jj_scan_token(X)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1661_25_204()
+  static private boolean jj_3R_156()
+ {
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_189()) {
+    jj_scanpos = xsp;
+    if (jj_3R_190()) return true;
+    }
+    xsp = jj_scanpos;
+    if (jj_3R_191()) {
+    jj_scanpos = xsp;
+    if (jj_3R_192()) return true;
+    }
+    return false;
+  }
+
+  static private boolean jj_3R_204()
  {
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_50()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1660_26_203()
+  static private boolean jj_3R_203()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_IdentifierExpression_2169_9_37()) return true;
+    if (jj_3R_37()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1667_17_207()
+  static private boolean jj_3R_207()
  {
     if (jj_scan_token(MAX)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1667_26_237()) {
+    if (jj_3R_237()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1668_26_238()) {
+    if (jj_3R_238()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1669_26_239()) return true;
+    if (jj_3R_239()) return true;
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_Update_907_10_39()
+  static private boolean jj_3R_39()
  {
-    if (jj_3R_UpdateElement_920_9_45()) return true;
+    if (jj_3R_45()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_Update_907_36_46()) { jj_scanpos = xsp; break; }
+      if (jj_3R_46()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalUnary_1283_17_65()
+  static private boolean jj_3R_65()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalUnary_1285_19_76()) {
+    if (jj_3R_76()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalUnary_1286_19_77()) {
+    if (jj_3R_77()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalUnary_1287_19_78()) return true;
+    if (jj_3R_78()) return true;
     }
     }
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalUnary_1288_19_79()) jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalUnary_1281_9_60()) return true;
+    if (jj_3R_79()) jj_scanpos = xsp;
+    if (jj_3R_60()) return true;
     return false;
   }
 
   static private boolean jj_3_5()
  {
-    if (jj_3R_Update_905_9_35()) return true;
+    if (jj_3R_35()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1663_17_206()
+  static private boolean jj_3R_206()
  {
     if (jj_scan_token(MIN)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1663_26_234()) {
+    if (jj_3R_234()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1664_26_235()) {
+    if (jj_3R_235()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1665_26_236()) return true;
+    if (jj_3R_236()) return true;
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2052_11_192()
- {
-    if (jj_3R_ExpressionParenth_1634_9_151()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_Update_905_9_35()
+  static private boolean jj_3R_35()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_Update_907_10_39()) {
+    if (jj_3R_39()) {
     jj_scanpos = xsp;
-    if (jj_scan_token(76)) return true;
+    if (jj_scan_token(80)) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1662_17_205()
+  static private boolean jj_3R_205()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2050_11_231()
- {
-    if (jj_3R_ExpressionProb_1658_9_152()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_MultiNashRewardIndexes_1986_73_277()
- {
-    if (jj_3R_Expression_1229_9_43()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionStrategy_2050_9_191()
+  static private boolean jj_3R_60()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionStrategy_2050_11_231()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionStrategy_2050_51_232()) {
+    if (jj_3R_65()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionStrategy_2050_93_233()) return true;
-    }
+    if (jj_3R_66()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2046_11_190()
- {
-    if (jj_scan_token(DLBRACKET)) return true;
-    if (jj_3R_ExpressionStrategyCoalitionList_2069_9_230()) return true;
-    if (jj_scan_token(DRBRACKET)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionTemporalUnary_1281_9_60()
- {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalUnary_1283_17_65()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalUnary_1292_17_66()) return true;
-    }
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionStrategy_2045_10_189()
- {
-    if (jj_scan_token(DLT)) return true;
-    if (jj_3R_ExpressionStrategyCoalitionList_2069_9_230()) return true;
-    if (jj_scan_token(DGT)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionProb_1660_10_172()
+  static private boolean jj_3R_172()
  {
     if (jj_scan_token(P)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1660_26_203()) jj_scanpos = xsp;
+    if (jj_3R_203()) jj_scanpos = xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1661_25_204()) {
+    if (jj_3R_204()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1662_17_205()) {
+    if (jj_3R_205()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1663_17_206()) {
+    if (jj_3R_206()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1667_17_207()) {
+    if (jj_3R_207()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1671_17_208()) {
+    if (jj_3R_208()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1672_17_209()) {
+    if (jj_3R_209()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1673_17_210()) {
+    if (jj_3R_210()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1674_17_211()) return true;
+    if (jj_3R_211()) return true;
     }
     }
     }
@@ -6348,57 +6389,41 @@ static private boolean jj_3R_ExpressionProb_1660_10_172()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalBinary_1267_19_70()
+  static private boolean jj_3R_70()
  {
-    if (jj_3R_TimeBound_1305_9_81()) return true;
+    if (jj_3R_81()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalBinary_1266_19_69()
+  static private boolean jj_3R_69()
  {
     if (jj_scan_token(R)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionStrategy_2042_9_156()
- {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionStrategy_2045_10_189()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionStrategy_2046_11_190()) return true;
-    }
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionStrategy_2050_9_191()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionStrategy_2052_11_192()) return true;
-    }
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionTemporalBinary_1265_19_68()
+  static private boolean jj_3R_68()
  {
     if (jj_scan_token(W)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionProb_1658_9_152()
+  static private boolean jj_3R_152()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1660_10_172()) {
+    if (jj_3R_172()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1677_10_173()) {
+    if (jj_3R_173()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1678_10_174()) {
+    if (jj_3R_174()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1679_10_175()) {
+    if (jj_3R_175()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1680_10_176()) {
+    if (jj_3R_176()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1681_10_177()) {
+    if (jj_3R_177()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionProb_1682_10_178()) return true;
+    if (jj_3R_178()) return true;
     }
     }
     }
@@ -6406,339 +6431,380 @@ static private boolean jj_3R_ExpressionProb_1658_9_152()
     }
     }
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionProb_1684_51_179()) jj_scanpos = xsp;
+    if (jj_3R_179()) jj_scanpos = xsp;
     if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalBinary_1264_19_67()
+  static private boolean jj_3R_155()
+ {
+    if (jj_scan_token(A)) return true;
+    if (jj_scan_token(LBRACKET)) return true;
+    if (jj_3R_43()) return true;
+    if (jj_scan_token(RBRACKET)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_67()
  {
     if (jj_scan_token(U)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalBinary_1262_17_61()
+  static private boolean jj_3R_61()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalBinary_1264_19_67()) {
+    if (jj_3R_67()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalBinary_1265_19_68()) {
+    if (jj_3R_68()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalBinary_1266_19_69()) return true;
+    if (jj_3R_69()) return true;
     }
     }
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalBinary_1267_19_70()) jj_scanpos = xsp;
-    if (jj_3R_ExpressionTemporalUnary_1281_9_60()) return true;
+    if (jj_3R_70()) jj_scanpos = xsp;
+    if (jj_3R_60()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncArgs_1584_72_202()
+  static private boolean jj_3R_202()
  {
     if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOldStyle_1572_83_171()
+  static private boolean jj_3R_171()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionTemporalBinary_1259_9_51()
+  static private boolean jj_3R_270()
  {
-    if (jj_3R_ExpressionTemporalUnary_1281_9_60()) return true;
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionTemporalBinary_1262_17_61()) jj_scanpos = xsp;
+    if (jj_scan_token(EQ)) return true;
+    if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1910_122_268()
+  static private boolean jj_3R_268()
  {
     if (jj_scan_token(EQ)) return true;
     if (jj_scan_token(QMARK)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionForAll_2022_9_155()
+  static private boolean jj_3R_51()
  {
-    if (jj_scan_token(A)) return true;
-    if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
-    if (jj_scan_token(RBRACKET)) return true;
+    if (jj_3R_60()) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_61()) jj_scanpos = xsp;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1908_122_266()
+  static private boolean jj_3R_154()
  {
-    if (jj_scan_token(EQ)) return true;
-    if (jj_scan_token(QMARK)) return true;
+    if (jj_scan_token(E)) return true;
+    if (jj_scan_token(LBRACKET)) return true;
+    if (jj_3R_43()) return true;
+    if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionParenth_1634_9_151()
+  static private boolean jj_3R_151()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOldStyle_1572_60_170()
+  static private boolean jj_3_19()
  {
-    if (jj_scan_token(MAX)) return true;
+    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLiteral_1621_9_162()
+  static private boolean jj_3R_282()
  {
-    if (jj_scan_token(FALSE)) return true;
+    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_3R_34()) return true;
+    if (jj_scan_token(DQUOTE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionExists_2003_9_154()
+  static private boolean jj_3R_170()
  {
-    if (jj_scan_token(E)) return true;
-    if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
-    if (jj_scan_token(RBRACKET)) return true;
+    if (jj_scan_token(MAX)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLiteral_1619_9_161()
+  static private boolean jj_3R_281()
  {
-    if (jj_scan_token(TRUE)) return true;
+    if (jj_scan_token(LBRACE)) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_282()) {
+    jj_scanpos = xsp;
+    if (jj_3R_283()) return true;
+    }
+    if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3_19()
+  static private boolean jj_3R_162()
  {
-    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_scan_token(FALSE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_Expression_1229_9_43()
+  static private boolean jj_3R_161()
  {
-    if (jj_3R_ExpressionTemporalBinary_1259_9_51()) return true;
+    if (jj_scan_token(TRUE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLiteral_1608_9_160()
+  static private boolean jj_3R_43()
  {
-    if (jj_scan_token(REG_DOUBLE)) return true;
+    if (jj_3R_51()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1151_81_95()
+  static private boolean jj_3R_160()
  {
-    if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_scan_token(REG_DOUBLE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_MultiNashRewardIndexes_1986_10_276()
+  static private boolean jj_3R_95()
  {
-    if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
-    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_MultiNashRewardIndexes_1985_9_275()
+  static private boolean jj_3R_272()
  {
-    if (jj_scan_token(LBRACE)) return true;
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_MultiNashRewardIndexes_1986_10_276()) {
-    jj_scanpos = xsp;
-    if (jj_3R_MultiNashRewardIndexes_1986_73_277()) return true;
-    }
-    if (jj_scan_token(RBRACE)) return true;
+    if (jj_scan_token(R)) return true;
+    if (jj_3R_281()) return true;
+    if (jj_scan_token(LBRACKET)) return true;
+    if (jj_3R_187()) return true;
+    if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOldStyle_1572_37_169()
+  static private boolean jj_3R_169()
  {
     if (jj_scan_token(MIN)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLiteral_1595_9_159()
+  static private boolean jj_3R_159()
  {
     if (jj_scan_token(REG_INT)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionLiteral_1594_9_147()
+  static private boolean jj_3R_147()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionLiteral_1595_9_159()) {
+    if (jj_3R_159()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionLiteral_1608_9_160()) {
+    if (jj_3R_160()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionLiteral_1619_9_161()) {
+    if (jj_3R_161()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionLiteral_1621_9_162()) return true;
+    if (jj_3R_162()) return true;
     }
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncMinMax_1558_42_167()
+  static private boolean jj_3R_167()
  {
     if (jj_scan_token(MAX)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncArgs_1584_9_168()
+  static private boolean jj_3R_168()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_ExpressionFuncArgs_1584_72_202()) { jj_scanpos = xsp; break; }
+      if (jj_3R_202()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNashReward_1965_9_270()
+  static private boolean jj_3R_271()
  {
-    if (jj_scan_token(R)) return true;
-    if (jj_3R_MultiNashRewardIndexes_1985_9_275()) return true;
+    if (jj_scan_token(P)) return true;
     if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_ExpressionRewardContents_1872_9_187()) return true;
+    if (jj_3R_43()) return true;
     if (jj_scan_token(RBRACKET)) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1841_125_252()
+  static private boolean jj_3R_252()
  {
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOldStyle_1572_9_150()
+  static private boolean jj_3R_150()
  {
     if (jj_scan_token(FUNC)) return true;
     if (jj_scan_token(LPARENTH)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionFuncOldStyle_1572_37_169()) {
+    if (jj_3R_169()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionFuncOldStyle_1572_60_170()) {
+    if (jj_3R_170()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionFuncOldStyle_1572_83_171()) return true;
+    if (jj_3R_171()) return true;
     }
     }
     if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_ExpressionFuncArgs_1584_9_168()) return true;
+    if (jj_3R_168()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemAtomic_1181_10_84()
+  static private boolean jj_3R_280()
+ {
+    if (jj_scan_token(FAIR)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_279()
+ {
+    if (jj_scan_token(SWEQ)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_84()
  {
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_SystemDefn_1058_9_36()) return true;
+    if (jj_3R_36()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemAtomic_1179_10_83()
+  static private boolean jj_3R_278()
  {
-    if (jj_scan_token(DQUOTE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
-    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_scan_token(CORR)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNashProb_1943_9_269()
+  static private boolean jj_3R_277()
  {
-    if (jj_scan_token(P)) return true;
-    if (jj_scan_token(LBRACKET)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
-    if (jj_scan_token(RBRACKET)) return true;
+    if (jj_scan_token(NASH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncMinMax_1558_11_166()
+  static private boolean jj_3R_266()
+ {
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_277()) {
+    jj_scanpos = xsp;
+    if (jj_3R_278()) {
+    jj_scanpos = xsp;
+    if (jj_3R_279()) {
+    jj_scanpos = xsp;
+    if (jj_3R_280()) return true;
+    }
+    }
+    }
+    return false;
+  }
+
+  static private boolean jj_3R_83()
+ {
+    if (jj_scan_token(DQUOTE)) return true;
+    if (jj_3R_34()) return true;
+    if (jj_scan_token(DQUOTE)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_166()
  {
     if (jj_scan_token(MIN)) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemAtomic_1177_9_82()
+  static private boolean jj_3R_82()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemParallel_1121_65_75()
+  static private boolean jj_3R_75()
  {
     if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_274()
+ {
+    if (jj_3R_272()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncMinMax_1558_9_149()
+  static private boolean jj_3R_273()
+ {
+    if (jj_3R_271()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_149()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionFuncMinMax_1558_11_166()) {
+    if (jj_3R_166()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionFuncMinMax_1558_42_167()) return true;
+    if (jj_3R_167()) return true;
     }
     if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_ExpressionFuncArgs_1584_9_168()) return true;
+    if (jj_3R_168()) return true;
     if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemAtomic_1174_9_73()
+  static private boolean jj_3R_73()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_SystemAtomic_1177_9_82()) {
+    if (jj_3R_82()) {
     jj_scanpos = xsp;
-    if (jj_3R_SystemAtomic_1179_10_83()) {
+    if (jj_3R_83()) {
     jj_scanpos = xsp;
-    if (jj_3R_SystemAtomic_1181_10_84()) return true;
+    if (jj_3R_84()) return true;
     }
     }
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1846_101_263()
- {
-    if (jj_3R_Expression_1229_9_43()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionMultiNash_1921_25_272()
- {
-    if (jj_3R_ExpressionMultiNashReward_1965_9_270()) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionMultiNash_1919_26_271()
+  static private boolean jj_3R_264()
  {
-    if (jj_3R_ExpressionMultiNashProb_1943_9_269()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1158_19_96()
+  static private boolean jj_3R_96()
  {
     if (jj_scan_token(COMMA)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     if (jj_scan_token(RENAME)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
@@ -6750,91 +6816,98 @@ static private boolean jj_3_9()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOrIdent_1545_11_165()
- {
-    if (jj_scan_token(LPARENTH)) return true;
-    if (jj_3R_ExpressionFuncArgs_1584_9_168()) return true;
-    if (jj_scan_token(RPARENTH)) return true;
-    return false;
-  }
-
-  static private boolean jj_3R_ExpressionMultiNash_1918_18_261()
+  static private boolean jj_3R_262()
  {
     if (jj_scan_token(PLUS)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionMultiNash_1919_26_271()) {
+    if (jj_3R_273()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionMultiNash_1921_25_272()) return true;
+    if (jj_3R_274()) return true;
     }
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOrIdent_1542_11_164()
+  static private boolean jj_3R_165()
  {
-    if (jj_3R_IdentifierPrime_2191_9_53()) return true;
+    if (jj_scan_token(LPARENTH)) return true;
+    if (jj_3R_168()) return true;
+    if (jj_scan_token(RPARENTH)) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_261()
+ {
+    if (jj_3R_272()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOrIdent_1541_11_163()
+  static private boolean jj_3R_260()
  {
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_271()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1916_17_260()
+  static private boolean jj_3R_164()
  {
-    if (jj_3R_ExpressionMultiNashReward_1965_9_270()) return true;
+    if (jj_3R_53()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1914_18_259()
+  static private boolean jj_3R_163()
  {
-    if (jj_3R_ExpressionMultiNashProb_1943_9_269()) return true;
+    if (jj_3R_34()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemInterleaved_1096_70_55()
+  static private boolean jj_3R_55()
  {
     if (jj_scan_token(OR)) return true;
     if (jj_scan_token(OR)) return true;
     if (jj_scan_token(OR)) return true;
-    if (jj_3R_SystemFullParallel_1071_9_40()) return true;
+    if (jj_3R_40()) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1155_11_86()
+  static private boolean jj_3R_86()
  {
     if (jj_scan_token(LBRACE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     if (jj_scan_token(RENAME)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_SystemHideRename_1158_19_96()) { jj_scanpos = xsp; break; }
+      if (jj_3R_96()) { jj_scanpos = xsp; break; }
     }
     if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionFuncOrIdent_1540_9_148()
+  static private boolean jj_3R_148()
  {
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionFuncOrIdent_1541_11_163()) {
+    if (jj_3R_163()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionFuncOrIdent_1542_11_164()) return true;
+    if (jj_3R_164()) return true;
     }
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionFuncOrIdent_1545_11_165()) jj_scanpos = xsp;
+    if (jj_3R_165()) jj_scanpos = xsp;
+    return false;
+  }
+
+  static private boolean jj_3R_269()
+ {
+    if (jj_3R_50()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1910_16_267()
+  static private boolean jj_3R_267()
  {
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_50()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
@@ -6844,34 +6917,51 @@ static private boolean jj_3_4()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1908_16_265()
+  static private boolean jj_3R_259()
  {
-    if (jj_3R_LtGt_2220_9_50()) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_scan_token(MAX)) return true;
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_269()) {
+    jj_scanpos = xsp;
+    if (jj_3R_270()) return true;
+    }
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1149_9_85()
+  static private boolean jj_3R_85()
  {
     if (jj_scan_token(DIVIDE)) return true;
     if (jj_scan_token(LBRACE)) return true;
-    if (jj_3R_Identifier_2158_9_34()) return true;
+    if (jj_3R_34()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_SystemHideRename_1151_81_95()) { jj_scanpos = xsp; break; }
+      if (jj_3R_95()) { jj_scanpos = xsp; break; }
     }
     if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1149_9_74()
+  static private boolean jj_3R_74()
+ {
+    Token xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_85()) {
+    jj_scanpos = xsp;
+    if (jj_3R_86()) return true;
+    }
+    return false;
+  }
+
+  static private boolean jj_3R_258()
  {
+    if (jj_scan_token(MIN)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_SystemHideRename_1149_9_85()) {
+    if (jj_3R_267()) {
     jj_scanpos = xsp;
-    if (jj_3R_SystemHideRename_1155_11_86()) return true;
+    if (jj_3R_268()) return true;
     }
     return false;
   }
@@ -6883,13 +6973,13 @@ static private boolean jj_3_3()
     return false;
   }
 
-  static private boolean jj_3R_SystemHideRename_1146_9_63()
+  static private boolean jj_3R_63()
  {
-    if (jj_3R_SystemAtomic_1174_9_73()) return true;
+    if (jj_3R_73()) return true;
     Token xsp;
     while (true) {
       xsp = jj_scanpos;
-      if (jj_3R_SystemHideRename_1149_9_74()) { jj_scanpos = xsp; break; }
+      if (jj_3R_74()) { jj_scanpos = xsp; break; }
     }
     return false;
   }
@@ -6901,70 +6991,84 @@ static private boolean jj_3_8()
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1910_9_258()
+  static private boolean jj_3R_257()
  {
-    if (jj_scan_token(MAX)) return true;
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionMultiNash_1910_16_267()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionMultiNash_1910_122_268()) return true;
-    }
+    if (jj_scan_token(LBRACE)) return true;
+    if (jj_3R_266()) return true;
+    if (jj_scan_token(COMMA)) return true;
+    if (jj_3R_266()) return true;
+    if (jj_scan_token(RBRACE)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1908_9_257()
+  static private boolean jj_3R_249()
  {
-    if (jj_scan_token(MIN)) return true;
     Token xsp;
     xsp = jj_scanpos;
-    if (jj_3R_ExpressionMultiNash_1908_16_265()) {
+    if (jj_3R_257()) jj_scanpos = xsp;
+    xsp = jj_scanpos;
+    if (jj_3R_258()) {
+    jj_scanpos = xsp;
+    if (jj_3R_259()) return true;
+    }
+    if (jj_scan_token(LPARENTH)) return true;
+    xsp = jj_scanpos;
+    if (jj_3R_260()) {
     jj_scanpos = xsp;
-    if (jj_3R_ExpressionMultiNash_1908_122_266()) return true;
+    if (jj_3R_261()) return true;
     }
+    if (jj_3R_262()) return true;
+    while (true) {
+      xsp = jj_scanpos;
+      if (jj_3R_262()) { jj_scanpos = xsp; break; }
+    }
+    if (jj_scan_token(RPARENTH)) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1517_17_146()
+  static private boolean jj_3R_146()
  {
-    if (jj_3R_ExpressionFilter_2131_9_158()) return true;
+    if (jj_3R_158()) return true;
     return false;
   }
 
-  static private boolean jj_3R_RewardIndex_1841_75_251()
+  static private boolean jj_3R_251()
  {
     if (jj_scan_token(DISCOUNT)) return true;
     if (jj_scan_token(EQ)) return true;
-    if (jj_3R_Expression_1229_9_43()) return true;
+    if (jj_3R_43()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionMultiNash_1906_9_249()
+  static private boolean jj_3R_145()
  {
-    Token xsp;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionMultiNash_1908_9_257()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionMultiNash_1910_9_258()) return true;
-    }
-    if (jj_scan_token(LPARENTH)) return true;
-    xsp = jj_scanpos;
-    if (jj_3R_ExpressionMultiNash_1914_18_259()) {
-    jj_scanpos = xsp;
-    if (jj_3R_ExpressionMultiNash_1916_17_260()) return true;
-    }
-    if (jj_3R_ExpressionMultiNash_1918_18_261()) return true;
-    while (true) {
-      xsp = jj_scanpos;
-      if (jj_3R_ExpressionMultiNash_1918_18_261()) { jj_scanpos = xsp; break; }
-    }
-    if (jj_scan_token(RPARENTH)) return true;
+    if (jj_3R_157()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_144()
+ {
+    if (jj_3R_156()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_143()
+ {
+    if (jj_3R_155()) return true;
+    return false;
+  }
+
+  static private boolean jj_3R_48()
+ {
+    if (jj_scan_token(OR)) return true;
+    if (jj_scan_token(OR)) return true;
+    if (jj_3R_54()) return true;
     return false;
   }
 
-  static private boolean jj_3R_ExpressionBasic_1515_17_145()
+  static private boolean jj_3R_142()
  {
-    if (jj_3R_ExpressionLabel_2113_9_157()) return true;
+    if (jj_3R_154()) return true;
     return false;
   }
 
@@ -6980,212 +7084,199 @@ static private boolean jj_3R_ExpressionBasic_1515_17_145()
   static private Token jj_scanpos, jj_lastpos;
   static private int jj_la;
   static private int jj_gen;
-  static final private int[] jj_la1 = new int[119];
+  static final private int[] jj_la1 = new int[121];
   static private int[] jj_la1_0;
   static private int[] jj_la1_1;
   static private int[] jj_la1_2;
   static private int[] jj_la1_3;
   static {
-	   jj_la1_init_0();
-	   jj_la1_init_1();
-	   jj_la1_init_2();
-	   jj_la1_init_3();
-	}
-	private static void jj_la1_init_0() {
-	   jj_la1_0 = new int[] {0xa08023c0,0x208023c0,0x80000000,0x3404048,0x0,0x3404048,0x3404048,0x0,0x3404048,0x2000,0x0,0x100,0x2380,0x1010,0x1010,0x0,0x40,0x0,0x80000000,0x30,0x0,0x0,0x0,0x0,0x47404008,0x0,0x0,0x0,0x47404008,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x44000000,0x0,0x47404008,0x47404008,0x47404008,0x47404008,0x47404008,0x0,0x0,0x0,0x0,0x0,0x0,0x3404008,0x0,0x0,0x0,0x0,0x0,0x0,0x3404008,0x3404008,0x0,0x0,0x0,0x0,0x0,0x400000,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x47404808,0x0,0x47404008,0x0,0x0,0x5f404408,0x0,0x0,0x0,0x0,0x0,0x0,0x47404008,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0,0x0,0x0,0x0,};
-	}
-	private static void jj_la1_init_1() {
-	   jj_la1_1 = new int[] {0x7f80e888,0x3f002088,0x4080c800,0xa87f0448,0x0,0xa87f0448,0xa87f0448,0x0,0xa87f0448,0x4000000,0x2080,0x0,0x17002080,0x4,0x4,0x28000000,0x28000000,0x0,0x0,0x4,0x0,0x1,0x0,0x0,0x807f1440,0x0,0x0,0x0,0x807f1440,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x1000,0x0,0x807f1440,0x807f1440,0x807f1440,0x807f1440,0x807f1440,0x0,0x0,0x0,0x0,0x0,0x0,0x807f0440,0x0,0x0,0x0,0x0,0x0,0x0,0x807f0440,0x807f0440,0x0,0x0,0x440,0x440,0x0,0x0,0x0,0x440,0x440,0x770,0x7f0000,0x0,0x0,0x440,0x0,0x0,0x0,0x0,0x0,0x440,0x440,0x770,0x80000000,0x0,0x807f1440,0x0,0x807f1440,0x0,0x0,0x807f1442,0x0,0x0,0x440,0x400000,0x400000,0x0,0x807f1440,0x0,0x807f0440,0x807f0440,0x0,0x0,0x0,0x0,0x0,0x0,0x440,0x0,0x440,0x0,0x0,0x0,};
-	}
-	private static void jj_la1_init_2() {
-	   jj_la1_2 = new int[] {0xf80,0xb80,0x400,0x2200907f,0x400000,0x2200907f,0x2200907f,0x400000,0x2200907f,0x0,0x0,0x80,0xb80,0x0,0x0,0x0,0x0,0x0,0x0,0x8000000,0x0,0x0,0x8000000,0x0,0x2200907f,0x10000,0x2001000,0x800000,0x2a00907f,0x8000000,0x800000,0x0,0x800000,0x800000,0x80000000,0x800000,0x800000,0x80000000,0x2000000,0x800000,0x8000000,0x8000000,0x6020,0x8000000,0x6020,0x0,0x8000000,0x2200907f,0x2200907f,0x2200907f,0x2200907f,0x2200907f,0x8000000,0x0,0x40000,0x80000,0x20000,0x10000,0x2200907f,0x0,0x0,0x0,0x0,0x0,0x0,0x2200107f,0x2200107f,0x0,0x2000000,0x0,0x0,0x800000,0x1000,0x2000000,0x0,0x0,0x0,0x0,0x80000000,0x80000000,0x0,0x2000000,0x2000000,0x80000000,0x2000000,0x80000000,0x0,0x0,0x0,0x3f,0x80000000,0x2200907f,0x800000,0x2200907f,0x0,0x40,0x2200907f,0x0,0x0,0x0,0x20,0x20,0x0,0x2200907f,0x20000000,0x3f,0x200003f,0x200000,0x800000,0x0,0x0,0x0,0x0,0x30000,0x800000,0x0,0x0,0x0,0x200000,};
-	}
-	private static void jj_la1_init_3() {
-	   jj_la1_3 = new int[] {0x0,0x0,0x0,0x1f0420,0x0,0x1f0420,0x1f0420,0x0,0x1f0420,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x2,0x0,0x0,0x100000,0x0,0x0,0x200,0x1f0420,0x0,0x0,0x0,0x1f0420,0x0,0x0,0x100000,0x0,0x0,0x1000,0x0,0x0,0x1000,0x110000,0x0,0x100000,0x100000,0x0,0x19a,0x0,0x0,0x19a,0x1f0420,0x1f0420,0x1f0420,0x1f0420,0x1f0420,0x19a,0x8000,0x0,0x0,0x0,0x0,0x1f0420,0x6,0x198,0x600,0x600,0x1800,0x1800,0x1f0420,0x1f0020,0x180000,0x0,0x0,0x100000,0x0,0x60000,0x0,0x2,0x2,0x19a,0x0,0x0,0x0,0x0,0x0,0x19a,0x0,0x0,0x0,0x2,0x2,0x19a,0x0,0x0,0x1f0420,0x0,0x1f0420,0x1000,0x0,0x1f0420,0x19a,0x19a,0x0,0x0,0x0,0x200,0x1f0420,0x20,0x0,0x0,0x0,0x0,0x120000,0x800,0x120000,0x100000,0x100200,0x0,0x100000,0x6,0x198,0x0,};
-	}
+      jj_la1_init_0();
+      jj_la1_init_1();
+      jj_la1_init_2();
+      jj_la1_init_3();
+   }
+   private static void jj_la1_init_0() {
+      jj_la1_0 = new int[] {0x8023c00,0x8023c00,0x0,0x34040480,0x0,0x34040480,0x34040480,0x0,0x34040480,0x20000,0x0,0x1000,0x23800,0x10100,0x10100,0x0,0x400,0x0,0x0,0x300,0x0,0x0,0x0,0x0,0x74040080,0x0,0x0,0x0,0x74040080,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x40000000,0x0,0x74040080,0x74040080,0x74040080,0x74040080,0x74040080,0x0,0x0,0x0,0x0,0x0,0x0,0x34040080,0x0,0x0,0x0,0x0,0x0,0x0,0x34040080,0x34040080,0x0,0x0,0x0,0x0,0x0,0x4000000,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x74048080,0x0,0x74040080,0x0,0x0,0xf4044080,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x78,0x74040080,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,};
+   }
+   private static void jj_la1_init_1() {
+      jj_la1_1 = new int[] {0xf80e888a,0xf0020882,0x80c8008,0x87f04480,0x0,0x87f04480,0x87f04480,0x0,0x87f04480,0x40000000,0x20800,0x0,0x70020800,0x40,0x40,0x80000000,0x80000000,0x0,0x8,0x40,0x0,0x10,0x0,0x0,0x7f14404,0x0,0x0,0x0,0x7f14404,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x10004,0x0,0x7f14404,0x7f14404,0x7f14404,0x7f14404,0x7f14404,0x0,0x0,0x0,0x0,0x0,0x0,0x7f04400,0x0,0x0,0x0,0x0,0x0,0x0,0x7f04400,0x7f04400,0x0,0x0,0x4400,0x4400,0x0,0x0,0x0,0x4400,0x4400,0x7700,0x7f00000,0x0,0x0,0x4400,0x0,0x0,0x0,0x0,0x0,0x4400,0x4400,0x7700,0x0,0x0,0x7f14404,0x0,0x7f14404,0x0,0x0,0x7f14425,0x0,0x0,0x0,0x4400,0x4000000,0x4000000,0x0,0x0,0x7f14404,0x0,0x7f04400,0x7f04400,0x0,0x0,0x0,0x0,0x0,0x8,0x4400,0x0,0x4400,0x0,0x0,0x0,};
+   }
+   private static void jj_la1_init_2() {
+      jj_la1_2 = new int[] {0xf807,0xb803,0x4004,0x200907fa,0x4000000,0x200907fa,0x200907fa,0x4000000,0x200907fa,0x0,0x0,0x800,0xb801,0x0,0x0,0x2,0x2,0x0,0x0,0x80000000,0x0,0x0,0x80000000,0x0,0x200907f8,0x100000,0x20010000,0x8000000,0xa00907f8,0x80000000,0x8000000,0x0,0x8000000,0x8000000,0x0,0x8000000,0x8000000,0x0,0x20000000,0x8000000,0x80000000,0x80000000,0x60200,0x80000000,0x60200,0x0,0x80000000,0x200907f8,0x200907f8,0x200907f8,0x200907f8,0x200907f8,0x80000000,0x0,0x400000,0x800000,0x200000,0x100000,0x200907f8,0x0,0x0,0x0,0x0,0x0,0x0,0x200107f8,0x200107f8,0x0,0x20000000,0x0,0x0,0x8000000,0x10000,0x20000000,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x20000000,0x20000000,0x0,0x20000000,0x0,0x0,0x0,0x0,0x3f8,0x0,0x200907f8,0x8000000,0x200907f8,0x0,0x400,0x200907f8,0x0,0x0,0x0,0x0,0x200,0x200,0x0,0x0,0x200907f8,0x0,0x3f8,0x200003f8,0x2000000,0x8000000,0x0,0x0,0x0,0x0,0x300000,0x8000000,0x0,0x0,0x0,0x2000000,};
+   }
+   private static void jj_la1_init_3() {
+      jj_la1_3 = new int[] {0x0,0x0,0x0,0x1f04202,0x0,0x1f04202,0x1f04202,0x0,0x1f04202,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x0,0x20,0x0,0x0,0x1000000,0x0,0x0,0x2000,0x1f04202,0x0,0x0,0x0,0x1f04202,0x0,0x0,0x1000000,0x0,0x0,0x10008,0x0,0x0,0x10008,0x1100000,0x0,0x1000000,0x1000000,0x0,0x19a0,0x0,0x0,0x19a0,0x1f04202,0x1f04202,0x1f04202,0x1f04202,0x1f04202,0x19a0,0x80000,0x0,0x0,0x0,0x0,0x1f04202,0x60,0x1980,0x6000,0x6000,0x18000,0x18000,0x1f04202,0x1f00202,0x1800000,0x0,0x0,0x1000000,0x0,0x600000,0x0,0x20,0x20,0x19a0,0x0,0x8,0x8,0x0,0x0,0x19a0,0x8,0x0,0x8,0x20,0x20,0x19a0,0x0,0x8,0x1f04202,0x0,0x1f04202,0x10000,0x0,0x1f04202,0x8,0x19a0,0x19a0,0x0,0x0,0x0,0x2000,0x0,0x1f04202,0x202,0x8,0x8,0x0,0x0,0x1200000,0x8000,0x1200000,0x1000000,0x1002000,0x0,0x1000000,0x60,0x1980,0x0,};
+   }
   static final private JJCalls[] jj_2_rtns = new JJCalls[19];
   static private boolean jj_rescan = false;
   static private int jj_gc = 0;
 
   /** Constructor with InputStream. */
   public PrismParser(java.io.InputStream stream) {
-	  this(stream, null);
+     this(stream, null);
   }
   /** Constructor with InputStream and supplied encoding */
   public PrismParser(java.io.InputStream stream, String encoding) {
-	 if (jj_initialized_once) {
-	   System.out.println("ERROR: Second call to constructor of static parser.  ");
-	   System.out.println("	   You must either use ReInit() or set the JavaCC option STATIC to false");
-	   System.out.println("	   during parser generation.");
-	   throw new Error();
-	 }
-	 jj_initialized_once = true;
-	 try { jj_input_stream = new SimpleCharStream(stream, encoding, 1, 1); } catch(java.io.UnsupportedEncodingException e) { throw new RuntimeException(e); }
-	 token_source = new PrismParserTokenManager(jj_input_stream);
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    if (jj_initialized_once) {
+      System.out.println("ERROR: Second call to constructor of static parser.  ");
+      System.out.println("       You must either use ReInit() or set the JavaCC option STATIC to false");
+      System.out.println("       during parser generation.");
+      throw new Error();
+    }
+    jj_initialized_once = true;
+    try { jj_input_stream = new SimpleCharStream(stream, encoding, 1, 1); } catch(java.io.UnsupportedEncodingException e) { throw new RuntimeException(e); }
+    token_source = new PrismParserTokenManager(jj_input_stream);
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   /** Reinitialise. */
   static public void ReInit(java.io.InputStream stream) {
-	  ReInit(stream, null);
+     ReInit(stream, null);
   }
   /** Reinitialise. */
   static public void ReInit(java.io.InputStream stream, String encoding) {
-	 try { jj_input_stream.ReInit(stream, encoding, 1, 1); } catch(java.io.UnsupportedEncodingException e) { throw new RuntimeException(e); }
-	 token_source.ReInit(jj_input_stream);
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    try { jj_input_stream.ReInit(stream, encoding, 1, 1); } catch(java.io.UnsupportedEncodingException e) { throw new RuntimeException(e); }
+    token_source.ReInit(jj_input_stream);
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   /** Constructor. */
   public PrismParser(java.io.Reader stream) {
-	 if (jj_initialized_once) {
-	   System.out.println("ERROR: Second call to constructor of static parser. ");
-	   System.out.println("	   You must either use ReInit() or set the JavaCC option STATIC to false");
-	   System.out.println("	   during parser generation.");
-	   throw new Error();
-	 }
-	 jj_initialized_once = true;
-	 jj_input_stream = new SimpleCharStream(stream, 1, 1);
-	 token_source = new PrismParserTokenManager(jj_input_stream);
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    if (jj_initialized_once) {
+      System.out.println("ERROR: Second call to constructor of static parser. ");
+      System.out.println("       You must either use ReInit() or set the JavaCC option STATIC to false");
+      System.out.println("       during parser generation.");
+      throw new Error();
+    }
+    jj_initialized_once = true;
+    jj_input_stream = new SimpleCharStream(stream, 1, 1);
+    token_source = new PrismParserTokenManager(jj_input_stream);
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   /** Reinitialise. */
   static public void ReInit(java.io.Reader stream) {
-	if (jj_input_stream == null) {
-	   jj_input_stream = new SimpleCharStream(stream, 1, 1);
-	} else {
-	   jj_input_stream.ReInit(stream, 1, 1);
-	}
-	if (token_source == null) {
- token_source = new PrismParserTokenManager(jj_input_stream);
-	}
-
-	 token_source.ReInit(jj_input_stream);
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    jj_input_stream.ReInit(stream, 1, 1);
+    token_source.ReInit(jj_input_stream);
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   /** Constructor with generated Token Manager. */
   public PrismParser(PrismParserTokenManager tm) {
-	 if (jj_initialized_once) {
-	   System.out.println("ERROR: Second call to constructor of static parser. ");
-	   System.out.println("	   You must either use ReInit() or set the JavaCC option STATIC to false");
-	   System.out.println("	   during parser generation.");
-	   throw new Error();
-	 }
-	 jj_initialized_once = true;
-	 token_source = tm;
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    if (jj_initialized_once) {
+      System.out.println("ERROR: Second call to constructor of static parser. ");
+      System.out.println("       You must either use ReInit() or set the JavaCC option STATIC to false");
+      System.out.println("       during parser generation.");
+      throw new Error();
+    }
+    jj_initialized_once = true;
+    token_source = tm;
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   /** Reinitialise. */
   public void ReInit(PrismParserTokenManager tm) {
-	 token_source = tm;
-	 token = new Token();
-	 jj_ntk = -1;
-	 jj_gen = 0;
-	 for (int i = 0; i < 119; i++) jj_la1[i] = -1;
-	 for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
+    token_source = tm;
+    token = new Token();
+    jj_ntk = -1;
+    jj_gen = 0;
+    for (int i = 0; i < 121; i++) jj_la1[i] = -1;
+    for (int i = 0; i < jj_2_rtns.length; i++) jj_2_rtns[i] = new JJCalls();
   }
 
   static private Token jj_consume_token(int kind) throws ParseException {
-	 Token oldToken;
-	 if ((oldToken = token).next != null) token = token.next;
-	 else token = token.next = token_source.getNextToken();
-	 jj_ntk = -1;
-	 if (token.kind == kind) {
-	   jj_gen++;
-	   if (++jj_gc > 100) {
-		 jj_gc = 0;
-		 for (int i = 0; i < jj_2_rtns.length; i++) {
-		   JJCalls c = jj_2_rtns[i];
-		   while (c != null) {
-			 if (c.gen < jj_gen) c.first = null;
-			 c = c.next;
-		   }
-		 }
-	   }
-	   return token;
-	 }
-	 token = oldToken;
-	 jj_kind = kind;
-	 throw generateParseException();
+    Token oldToken;
+    if ((oldToken = token).next != null) token = token.next;
+    else token = token.next = token_source.getNextToken();
+    jj_ntk = -1;
+    if (token.kind == kind) {
+      jj_gen++;
+      if (++jj_gc > 100) {
+        jj_gc = 0;
+        for (int i = 0; i < jj_2_rtns.length; i++) {
+          JJCalls c = jj_2_rtns[i];
+          while (c != null) {
+            if (c.gen < jj_gen) c.first = null;
+            c = c.next;
+          }
+        }
+      }
+      return token;
+    }
+    token = oldToken;
+    jj_kind = kind;
+    throw generateParseException();
   }
 
   @SuppressWarnings("serial")
-  static private final class LookaheadSuccess extends java.lang.Error {
-    @Override
-    public Throwable fillInStackTrace() {
-      return this;
-    }
-  }
-  static private final LookaheadSuccess jj_ls = new LookaheadSuccess();
+  static private final class LookaheadSuccess extends java.lang.Error { }
+  static final private LookaheadSuccess jj_ls = new LookaheadSuccess();
   static private boolean jj_scan_token(int kind) {
-	 if (jj_scanpos == jj_lastpos) {
-	   jj_la--;
-	   if (jj_scanpos.next == null) {
-		 jj_lastpos = jj_scanpos = jj_scanpos.next = token_source.getNextToken();
-	   } else {
-		 jj_lastpos = jj_scanpos = jj_scanpos.next;
-	   }
-	 } else {
-	   jj_scanpos = jj_scanpos.next;
-	 }
-	 if (jj_rescan) {
-	   int i = 0; Token tok = token;
-	   while (tok != null && tok != jj_scanpos) { i++; tok = tok.next; }
-	   if (tok != null) jj_add_error_token(kind, i);
-	 }
-	 if (jj_scanpos.kind != kind) return true;
-	 if (jj_la == 0 && jj_scanpos == jj_lastpos) throw jj_ls;
-	 return false;
+    if (jj_scanpos == jj_lastpos) {
+      jj_la--;
+      if (jj_scanpos.next == null) {
+        jj_lastpos = jj_scanpos = jj_scanpos.next = token_source.getNextToken();
+      } else {
+        jj_lastpos = jj_scanpos = jj_scanpos.next;
+      }
+    } else {
+      jj_scanpos = jj_scanpos.next;
+    }
+    if (jj_rescan) {
+      int i = 0; Token tok = token;
+      while (tok != null && tok != jj_scanpos) { i++; tok = tok.next; }
+      if (tok != null) jj_add_error_token(kind, i);
+    }
+    if (jj_scanpos.kind != kind) return true;
+    if (jj_la == 0 && jj_scanpos == jj_lastpos) throw jj_ls;
+    return false;
   }
 
 
 /** Get the next Token. */
   static final public Token getNextToken() {
-	 if (token.next != null) token = token.next;
-	 else token = token.next = token_source.getNextToken();
-	 jj_ntk = -1;
-	 jj_gen++;
-	 return token;
+    if (token.next != null) token = token.next;
+    else token = token.next = token_source.getNextToken();
+    jj_ntk = -1;
+    jj_gen++;
+    return token;
   }
 
 /** Get the specific Token. */
   static final public Token getToken(int index) {
-	 Token t = token;
-	 for (int i = 0; i < index; i++) {
-	   if (t.next != null) t = t.next;
-	   else t = t.next = token_source.getNextToken();
-	 }
-	 return t;
+    Token t = token;
+    for (int i = 0; i < index; i++) {
+      if (t.next != null) t = t.next;
+      else t = t.next = token_source.getNextToken();
+    }
+    return t;
   }
 
   static private int jj_ntk_f() {
-	 if ((jj_nt=token.next) == null)
-	   return (jj_ntk = (token.next=token_source.getNextToken()).kind);
-	 else
-	   return (jj_ntk = jj_nt.kind);
+    if ((jj_nt=token.next) == null)
+      return (jj_ntk = (token.next=token_source.getNextToken()).kind);
+    else
+      return (jj_ntk = jj_nt.kind);
   }
 
   static private java.util.List<int[]> jj_expentries = new java.util.ArrayList<int[]>();
@@ -7195,91 +7286,71 @@ static private int jj_ntk_f() {
   static private int jj_endpos;
 
   static private void jj_add_error_token(int kind, int pos) {
-	 if (pos >= 100) {
-		return;
-	 }
-
-	 if (pos == jj_endpos + 1) {
-	   jj_lasttokens[jj_endpos++] = kind;
-	 } else if (jj_endpos != 0) {
-	   jj_expentry = new int[jj_endpos];
-
-	   for (int i = 0; i < jj_endpos; i++) {
-		 jj_expentry[i] = jj_lasttokens[i];
-	   }
-
-	   for (int[] oldentry : jj_expentries) {
-		 if (oldentry.length == jj_expentry.length) {
-		   boolean isMatched = true;
-
-		   for (int i = 0; i < jj_expentry.length; i++) {
-			 if (oldentry[i] != jj_expentry[i]) {
-			   isMatched = false;
-			   break;
-			 }
-
-		   }
-		   if (isMatched) {
-			 jj_expentries.add(jj_expentry);
-			 break;
-		   }
-		 }
-	   }
-
-	   if (pos != 0) {
-		 jj_lasttokens[(jj_endpos = pos) - 1] = kind;
-	   }
-	 }
+    if (pos >= 100) return;
+    if (pos == jj_endpos + 1) {
+      jj_lasttokens[jj_endpos++] = kind;
+    } else if (jj_endpos != 0) {
+      jj_expentry = new int[jj_endpos];
+      for (int i = 0; i < jj_endpos; i++) {
+        jj_expentry[i] = jj_lasttokens[i];
+      }
+      jj_entries_loop: for (java.util.Iterator<?> it = jj_expentries.iterator(); it.hasNext();) {
+        int[] oldentry = (int[])(it.next());
+        if (oldentry.length == jj_expentry.length) {
+          for (int i = 0; i < jj_expentry.length; i++) {
+            if (oldentry[i] != jj_expentry[i]) {
+              continue jj_entries_loop;
+            }
+          }
+          jj_expentries.add(jj_expentry);
+          break jj_entries_loop;
+        }
+      }
+      if (pos != 0) jj_lasttokens[(jj_endpos = pos) - 1] = kind;
+    }
   }
 
   /** Generate ParseException. */
   static public ParseException generateParseException() {
-	 jj_expentries.clear();
-	 boolean[] la1tokens = new boolean[119];
-	 if (jj_kind >= 0) {
-	   la1tokens[jj_kind] = true;
-	   jj_kind = -1;
-	 }
-	 for (int i = 0; i < 119; i++) {
-	   if (jj_la1[i] == jj_gen) {
-		 for (int j = 0; j < 32; j++) {
-		   if ((jj_la1_0[i] & (1<<j)) != 0) {
-			 la1tokens[j] = true;
-		   }
-		   if ((jj_la1_1[i] & (1<<j)) != 0) {
-			 la1tokens[32+j] = true;
-		   }
-		   if ((jj_la1_2[i] & (1<<j)) != 0) {
-			 la1tokens[64+j] = true;
-		   }
-		   if ((jj_la1_3[i] & (1<<j)) != 0) {
-			 la1tokens[96+j] = true;
-		   }
-		 }
-	   }
-	 }
-	 for (int i = 0; i < 119; i++) {
-	   if (la1tokens[i]) {
-		 jj_expentry = new int[1];
-		 jj_expentry[0] = i;
-		 jj_expentries.add(jj_expentry);
-	   }
-	 }
-	 jj_endpos = 0;
-	 jj_rescan_token();
-	 jj_add_error_token(0, 0);
-	 int[][] exptokseq = new int[jj_expentries.size()][];
-	 for (int i = 0; i < jj_expentries.size(); i++) {
-	   exptokseq[i] = jj_expentries.get(i);
-	 }
-	 return new ParseException(token, exptokseq, tokenImage);
-  }
-
-  static private boolean trace_enabled;
-
-/** Trace enabled. */
-  static final public boolean trace_enabled() {
-	 return trace_enabled;
+    jj_expentries.clear();
+    boolean[] la1tokens = new boolean[123];
+    if (jj_kind >= 0) {
+      la1tokens[jj_kind] = true;
+      jj_kind = -1;
+    }
+    for (int i = 0; i < 121; i++) {
+      if (jj_la1[i] == jj_gen) {
+        for (int j = 0; j < 32; j++) {
+          if ((jj_la1_0[i] & (1<<j)) != 0) {
+            la1tokens[j] = true;
+          }
+          if ((jj_la1_1[i] & (1<<j)) != 0) {
+            la1tokens[32+j] = true;
+          }
+          if ((jj_la1_2[i] & (1<<j)) != 0) {
+            la1tokens[64+j] = true;
+          }
+          if ((jj_la1_3[i] & (1<<j)) != 0) {
+            la1tokens[96+j] = true;
+          }
+        }
+      }
+    }
+    for (int i = 0; i < 123; i++) {
+      if (la1tokens[i]) {
+        jj_expentry = new int[1];
+        jj_expentry[0] = i;
+        jj_expentries.add(jj_expentry);
+      }
+    }
+    jj_endpos = 0;
+    jj_rescan_token();
+    jj_add_error_token(0, 0);
+    int[][] exptokseq = new int[jj_expentries.size()][];
+    for (int i = 0; i < jj_expentries.size(); i++) {
+      exptokseq[i] = jj_expentries.get(i);
+    }
+    return new ParseException(token, exptokseq, tokenImage);
   }
 
   /** Enable tracing. */
@@ -7291,61 +7362,56 @@ static final public void disable_tracing() {
   }
 
   static private void jj_rescan_token() {
-	 jj_rescan = true;
-	 for (int i = 0; i < 19; i++) {
-	   try {
-		 JJCalls p = jj_2_rtns[i];
-
-		 do {
-		   if (p.gen > jj_gen) {
-			 jj_la = p.arg; jj_lastpos = jj_scanpos = p.first;
-			 switch (i) {
-			   case 0: jj_3_1(); break;
-			   case 1: jj_3_2(); break;
-			   case 2: jj_3_3(); break;
-			   case 3: jj_3_4(); break;
-			   case 4: jj_3_5(); break;
-			   case 5: jj_3_6(); break;
-			   case 6: jj_3_7(); break;
-			   case 7: jj_3_8(); break;
-			   case 8: jj_3_9(); break;
-			   case 9: jj_3_10(); break;
-			   case 10: jj_3_11(); break;
-			   case 11: jj_3_12(); break;
-			   case 12: jj_3_13(); break;
-			   case 13: jj_3_14(); break;
-			   case 14: jj_3_15(); break;
-			   case 15: jj_3_16(); break;
-			   case 16: jj_3_17(); break;
-			   case 17: jj_3_18(); break;
-			   case 18: jj_3_19(); break;
-			 }
-		   }
-		   p = p.next;
-		 } while (p != null);
-
-		 } catch(LookaheadSuccess ls) { }
-	 }
-	 jj_rescan = false;
+    jj_rescan = true;
+    for (int i = 0; i < 19; i++) {
+    try {
+      JJCalls p = jj_2_rtns[i];
+      do {
+        if (p.gen > jj_gen) {
+          jj_la = p.arg; jj_lastpos = jj_scanpos = p.first;
+          switch (i) {
+            case 0: jj_3_1(); break;
+            case 1: jj_3_2(); break;
+            case 2: jj_3_3(); break;
+            case 3: jj_3_4(); break;
+            case 4: jj_3_5(); break;
+            case 5: jj_3_6(); break;
+            case 6: jj_3_7(); break;
+            case 7: jj_3_8(); break;
+            case 8: jj_3_9(); break;
+            case 9: jj_3_10(); break;
+            case 10: jj_3_11(); break;
+            case 11: jj_3_12(); break;
+            case 12: jj_3_13(); break;
+            case 13: jj_3_14(); break;
+            case 14: jj_3_15(); break;
+            case 15: jj_3_16(); break;
+            case 16: jj_3_17(); break;
+            case 17: jj_3_18(); break;
+            case 18: jj_3_19(); break;
+          }
+        }
+        p = p.next;
+      } while (p != null);
+      } catch(LookaheadSuccess ls) { }
+    }
+    jj_rescan = false;
   }
 
   static private void jj_save(int index, int xla) {
-	 JJCalls p = jj_2_rtns[index];
-	 while (p.gen > jj_gen) {
-	   if (p.next == null) { p = p.next = new JJCalls(); break; }
-	   p = p.next;
-	 }
-
-	 p.gen = jj_gen + xla - jj_la; 
-	 p.first = token;
-	 p.arg = xla;
+    JJCalls p = jj_2_rtns[index];
+    while (p.gen > jj_gen) {
+      if (p.next == null) { p = p.next = new JJCalls(); break; }
+      p = p.next;
+    }
+    p.gen = jj_gen + xla - jj_la; p.first = token; p.arg = xla;
   }
 
   static final class JJCalls {
-	 int gen;
-	 Token first;
-	 int arg;
-	 JJCalls next;
+    int gen;
+    Token first;
+    int arg;
+    JJCalls next;
   }
 
 }
diff --git a/prism/src/parser/PrismParser.jj b/prism/src/parser/PrismParser.jj
index 591b929e0..91a13b894 100644
--- a/prism/src/parser/PrismParser.jj
+++ b/prism/src/parser/PrismParser.jj
@@ -427,7 +427,13 @@ SPECIAL_TOKEN :
 TOKEN :
 {
 	// Keywords
-	< A:				"A" >
+	// 
+	< NASH: 			"NE">
+|	< CORR:				"CE">
+|	< SWEQ:				"SW">
+|	< FAIR:				"FR">
+  	//	
+|	< A:				"A" >
 //|	< ARRAY:			"array" >
 |	< BOOL:				"bool" >
 |	< CLOCK:			"clock" >
@@ -1899,12 +1905,17 @@ Expression ExpressionMultiNash(boolean prop, boolean pathprop) :
 	String relOp = null;
 	boolean isBool;
 	int r;
+	int eq = 1; // default NE
+	int crit = 3; // default SW
 	int n = 0;
 }
 {
   	// This production is only allowed in expressions if the "prop" parameter is true
 	{ if (!prop) throw generateParseException(); }
 	(
+	<LBRACE> eq = EqType() <COMMA> crit = EqType() <RBRACE>
+	)?
+	(
 	<MIN> (r = LtGt() bound = Expression(false, false) { relOp = ExpressionBinaryOp.opSymbols[r]; isBool = true; } | <EQ> <QMARK> { relOp = "min="; isBool = false; } )
 	|	
 	<MAX> (r = LtGt() bound = Expression(false, false) { relOp = ExpressionBinaryOp.opSymbols[r]; isBool = true; } | <EQ> <QMARK> { relOp = "max="; isBool = false; } )
@@ -1926,10 +1937,24 @@ Expression ExpressionMultiNash(boolean prop, boolean pathprop) :
 	{
 		ret.setBound(bound);
 		ret.setRelOp(relOp);
+		ret.setEqType(eq);
+		ret.setCrit(crit);
 		return ret;
 	}
 }
 
+// Types of Equilibria
+
+int EqType() :
+{
+}
+{
+	<NASH> {return ExpressionMultiNash.NASH; } |
+	<CORR> {return ExpressionMultiNash.CORR; } |
+	<SWEQ> {return ExpressionMultiNash.SWEQ; }|
+	<FAIR> {return ExpressionMultiNash.FAIR; }
+}
+
 // (Property) expression: probabilistic operator (n-player Nash)
 
 ExpressionQuant ExpressionMultiNashProb(boolean prop, boolean pathprop) :
diff --git a/prism/src/parser/PrismParserConstants.java b/prism/src/parser/PrismParserConstants.java
index e92c0edd5..2ae81ed93 100644
--- a/prism/src/parser/PrismParserConstants.java
+++ b/prism/src/parser/PrismParserConstants.java
@@ -15,237 +15,245 @@ public interface PrismParserConstants {
   /** RegularExpression Id. */
   int COMMENT = 2;
   /** RegularExpression Id. */
-  int A = 3;
+  int NASH = 3;
   /** RegularExpression Id. */
-  int BOOL = 4;
+  int CORR = 4;
   /** RegularExpression Id. */
-  int CLOCK = 5;
+  int SWEQ = 5;
   /** RegularExpression Id. */
-  int CONST = 6;
+  int FAIR = 6;
   /** RegularExpression Id. */
-  int CSG = 7;
+  int A = 7;
   /** RegularExpression Id. */
-  int CTMC = 8;
+  int BOOL = 8;
   /** RegularExpression Id. */
-  int CTMDP = 9;
+  int CLOCK = 9;
   /** RegularExpression Id. */
-  int C = 10;
+  int CONST = 10;
   /** RegularExpression Id. */
-  int DISCOUNT = 11;
+  int CSG = 11;
   /** RegularExpression Id. */
-  int DOUBLE = 12;
+  int CTMC = 12;
   /** RegularExpression Id. */
-  int DTMC = 13;
+  int CTMDP = 13;
   /** RegularExpression Id. */
-  int E = 14;
+  int C = 14;
   /** RegularExpression Id. */
-  int ENDINIT = 15;
+  int DISCOUNT = 15;
   /** RegularExpression Id. */
-  int ENDINVARIANT = 16;
+  int DOUBLE = 16;
   /** RegularExpression Id. */
-  int ENDMODULE = 17;
+  int DTMC = 17;
   /** RegularExpression Id. */
-  int ENDOBSERVABLES = 18;
+  int E = 18;
   /** RegularExpression Id. */
-  int ENDPLAYER = 19;
+  int ENDINIT = 19;
   /** RegularExpression Id. */
-  int ENDREWARDS = 20;
+  int ENDINVARIANT = 20;
   /** RegularExpression Id. */
-  int ENDSYSTEM = 21;
+  int ENDMODULE = 21;
   /** RegularExpression Id. */
-  int FALSE = 22;
+  int ENDOBSERVABLES = 22;
   /** RegularExpression Id. */
-  int FORMULA = 23;
+  int ENDPLAYER = 23;
   /** RegularExpression Id. */
-  int FILTER = 24;
+  int ENDREWARDS = 24;
   /** RegularExpression Id. */
-  int FUNC = 25;
+  int ENDSYSTEM = 25;
   /** RegularExpression Id. */
-  int F = 26;
+  int FALSE = 26;
   /** RegularExpression Id. */
-  int Fc = 27;
+  int FORMULA = 27;
   /** RegularExpression Id. */
-  int F0 = 28;
+  int FILTER = 28;
   /** RegularExpression Id. */
-  int GLOBAL = 29;
+  int FUNC = 29;
   /** RegularExpression Id. */
-  int G = 30;
+  int F = 30;
   /** RegularExpression Id. */
-  int INIT = 31;
+  int Fc = 31;
   /** RegularExpression Id. */
-  int INVARIANT = 32;
+  int F0 = 32;
   /** RegularExpression Id. */
-  int I = 33;
+  int GLOBAL = 33;
   /** RegularExpression Id. */
-  int INT = 34;
+  int G = 34;
   /** RegularExpression Id. */
-  int LABEL = 35;
+  int INIT = 35;
   /** RegularExpression Id. */
-  int MAXMAX = 36;
+  int INVARIANT = 36;
   /** RegularExpression Id. */
-  int MAXMIN = 37;
+  int I = 37;
   /** RegularExpression Id. */
-  int MAX = 38;
+  int INT = 38;
   /** RegularExpression Id. */
-  int MDP = 39;
+  int LABEL = 39;
   /** RegularExpression Id. */
-  int MINMAX = 40;
+  int MAXMAX = 40;
   /** RegularExpression Id. */
-  int MINMIN = 41;
+  int MAXMIN = 41;
   /** RegularExpression Id. */
-  int MIN = 42;
+  int MAX = 42;
   /** RegularExpression Id. */
-  int MODULE = 43;
+  int MDP = 43;
   /** RegularExpression Id. */
-  int X = 44;
+  int MINMAX = 44;
   /** RegularExpression Id. */
-  int NONDETERMINISTIC = 45;
+  int MINMIN = 45;
   /** RegularExpression Id. */
-  int OBSERVABLE = 46;
+  int MIN = 46;
   /** RegularExpression Id. */
-  int OBSERVABLES = 47;
+  int MODULE = 47;
   /** RegularExpression Id. */
-  int PMAXMAX = 48;
+  int X = 48;
   /** RegularExpression Id. */
-  int PMAXMIN = 49;
+  int NONDETERMINISTIC = 49;
   /** RegularExpression Id. */
-  int PMAX = 50;
+  int OBSERVABLE = 50;
   /** RegularExpression Id. */
-  int PMINMAX = 51;
+  int OBSERVABLES = 51;
   /** RegularExpression Id. */
-  int PMINMIN = 52;
+  int PMAXMAX = 52;
   /** RegularExpression Id. */
-  int PMIN = 53;
+  int PMAXMIN = 53;
   /** RegularExpression Id. */
-  int P = 54;
+  int PMAX = 54;
   /** RegularExpression Id. */
-  int PLAYER = 55;
+  int PMINMAX = 55;
   /** RegularExpression Id. */
-  int POMDP = 56;
+  int PMINMIN = 56;
   /** RegularExpression Id. */
-  int POPTA = 57;
+  int PMIN = 57;
   /** RegularExpression Id. */
-  int PROBABILISTIC = 58;
+  int P = 58;
   /** RegularExpression Id. */
-  int PROB = 59;
+  int PLAYER = 59;
   /** RegularExpression Id. */
-  int PTA = 60;
+  int POMDP = 60;
   /** RegularExpression Id. */
-  int RATE = 61;
+  int POPTA = 61;
   /** RegularExpression Id. */
-  int REWARDS = 62;
+  int PROBABILISTIC = 62;
   /** RegularExpression Id. */
-  int RMAXMAX = 63;
+  int PROB = 63;
   /** RegularExpression Id. */
-  int RMAXMIN = 64;
+  int PTA = 64;
   /** RegularExpression Id. */
-  int RMAX = 65;
+  int RATE = 65;
   /** RegularExpression Id. */
-  int RMINMAX = 66;
+  int REWARDS = 66;
   /** RegularExpression Id. */
-  int RMINMIN = 67;
+  int RMAXMAX = 67;
   /** RegularExpression Id. */
-  int RMIN = 68;
+  int RMAXMIN = 68;
   /** RegularExpression Id. */
-  int R = 69;
+  int RMAX = 69;
   /** RegularExpression Id. */
-  int S = 70;
+  int RMINMAX = 70;
   /** RegularExpression Id. */
-  int STOCHASTIC = 71;
+  int RMINMIN = 71;
   /** RegularExpression Id. */
-  int STPG = 72;
+  int RMIN = 72;
   /** RegularExpression Id. */
-  int SMG = 73;
+  int R = 73;
   /** RegularExpression Id. */
-  int SYSTEM = 74;
+  int S = 74;
   /** RegularExpression Id. */
-  int TPTG = 75;
+  int STOCHASTIC = 75;
   /** RegularExpression Id. */
-  int TRUE = 76;
+  int STPG = 76;
   /** RegularExpression Id. */
-  int U = 77;
+  int SMG = 77;
   /** RegularExpression Id. */
-  int W = 78;
+  int SYSTEM = 78;
   /** RegularExpression Id. */
-  int NOT = 79;
+  int TPTG = 79;
   /** RegularExpression Id. */
-  int AND = 80;
+  int TRUE = 80;
   /** RegularExpression Id. */
-  int OR = 81;
+  int U = 81;
   /** RegularExpression Id. */
-  int IMPLIES = 82;
+  int W = 82;
   /** RegularExpression Id. */
-  int IFF = 83;
+  int NOT = 83;
   /** RegularExpression Id. */
-  int RARROW = 84;
+  int AND = 84;
   /** RegularExpression Id. */
-  int COLON = 85;
+  int OR = 85;
   /** RegularExpression Id. */
-  int SEMICOLON = 86;
+  int IMPLIES = 86;
   /** RegularExpression Id. */
-  int COMMA = 87;
+  int IFF = 87;
   /** RegularExpression Id. */
-  int DOTS = 88;
+  int RARROW = 88;
   /** RegularExpression Id. */
-  int LPARENTH = 89;
+  int COLON = 89;
   /** RegularExpression Id. */
-  int RPARENTH = 90;
+  int SEMICOLON = 90;
   /** RegularExpression Id. */
-  int LBRACKET = 91;
+  int COMMA = 91;
   /** RegularExpression Id. */
-  int RBRACKET = 92;
+  int DOTS = 92;
   /** RegularExpression Id. */
-  int DLBRACKET = 93;
+  int LPARENTH = 93;
   /** RegularExpression Id. */
-  int DRBRACKET = 94;
+  int RPARENTH = 94;
   /** RegularExpression Id. */
-  int LBRACE = 95;
+  int LBRACKET = 95;
   /** RegularExpression Id. */
-  int RBRACE = 96;
+  int RBRACKET = 96;
   /** RegularExpression Id. */
-  int EQ = 97;
+  int DLBRACKET = 97;
   /** RegularExpression Id. */
-  int NE = 98;
+  int DRBRACKET = 98;
   /** RegularExpression Id. */
-  int LT = 99;
+  int LBRACE = 99;
   /** RegularExpression Id. */
-  int GT = 100;
+  int RBRACE = 100;
   /** RegularExpression Id. */
-  int DLT = 101;
+  int EQ = 101;
   /** RegularExpression Id. */
-  int DGT = 102;
+  int NE = 102;
   /** RegularExpression Id. */
-  int LE = 103;
+  int LT = 103;
   /** RegularExpression Id. */
-  int GE = 104;
+  int GT = 104;
   /** RegularExpression Id. */
-  int PLUS = 105;
+  int DLT = 105;
   /** RegularExpression Id. */
-  int MINUS = 106;
+  int DGT = 106;
   /** RegularExpression Id. */
-  int TIMES = 107;
+  int LE = 107;
   /** RegularExpression Id. */
-  int DIVIDE = 108;
+  int GE = 108;
   /** RegularExpression Id. */
-  int PRIME = 109;
+  int PLUS = 109;
   /** RegularExpression Id. */
-  int RENAME = 110;
+  int MINUS = 110;
   /** RegularExpression Id. */
-  int QMARK = 111;
+  int TIMES = 111;
   /** RegularExpression Id. */
-  int DQUOTE = 112;
+  int DIVIDE = 112;
   /** RegularExpression Id. */
-  int REG_INT = 113;
+  int PRIME = 113;
   /** RegularExpression Id. */
-  int REG_DOUBLE = 114;
+  int RENAME = 114;
   /** RegularExpression Id. */
-  int REG_IDENTPRIME = 115;
+  int QMARK = 115;
   /** RegularExpression Id. */
-  int REG_IDENT = 116;
+  int DQUOTE = 116;
   /** RegularExpression Id. */
-  int PREPROC = 117;
+  int REG_INT = 117;
   /** RegularExpression Id. */
-  int LEXICAL_ERROR = 118;
+  int REG_DOUBLE = 118;
+  /** RegularExpression Id. */
+  int REG_IDENTPRIME = 119;
+  /** RegularExpression Id. */
+  int REG_IDENT = 120;
+  /** RegularExpression Id. */
+  int PREPROC = 121;
+  /** RegularExpression Id. */
+  int LEXICAL_ERROR = 122;
 
   /** Lexical state. */
   int DEFAULT = 0;
@@ -255,6 +263,10 @@ public interface PrismParserConstants {
     "<EOF>",
     "<WHITESPACE>",
     "<COMMENT>",
+    "\"NE\"",
+    "\"CE\"",
+    "\"SW\"",
+    "\"FR\"",
     "\"A\"",
     "\"bool\"",
     "\"clock\"",
diff --git a/prism/src/parser/PrismParserTokenManager.java b/prism/src/parser/PrismParserTokenManager.java
index 0603e9e1b..b1d9e2bb1 100644
--- a/prism/src/parser/PrismParserTokenManager.java
+++ b/prism/src/parser/PrismParserTokenManager.java
@@ -16,8 +16,7 @@
 import prism.PrismLangException;
 
 /** Token Manager. */
-@SuppressWarnings ("unused")
-public class PrismParserTokenManager implements PrismParserConstants {
+@SuppressWarnings("unused")public class PrismParserTokenManager implements PrismParserConstants {
 
   /** Debug output. */
   public static  java.io.PrintStream debugStream = System.out;
@@ -27,162 +26,162 @@ private static final int jjStopStringLiteralDfa_0(int pos, long active0, long ac
    switch (pos)
    {
       case 0:
-         if ((active0 & 0x807f10025c004408L) != 0L || (active1 & 0x607fL) != 0L)
+         if ((active0 & 0x7f10025c00440f0L) != 0L || (active1 & 0x607f8L) != 0L)
             return 23;
-         if ((active1 & 0x100000000000L) != 0L)
+         if ((active1 & 0x1000000000000L) != 0L)
             return 1;
-         if ((active1 & 0x1000000L) != 0L)
+         if ((active1 & 0x10000000L) != 0L)
             return 11;
-         if ((active0 & 0x7f80effda3ffbbf0L) != 0L || (active1 & 0x1f80L) != 0L)
+         if ((active0 & 0xf80effda3ffbbf08L) != 0L || (active1 & 0x1f807L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             return 23;
          }
          return -1;
       case 1:
-         if ((active0 & 0x18000000L) != 0L)
+         if ((active0 & 0x180000078L) != 0L)
             return 23;
-         if ((active0 & 0xffbfeffda3ffbbf0L) != 0L || (active1 & 0x1f9fL) != 0L)
+         if ((active0 & 0xfbfeffda3ffbbf00L) != 0L || (active1 & 0x1f9ffL) != 0L)
          {
             if (jjmatchedPos != 1)
             {
-               jjmatchedKind = 116;
+               jjmatchedKind = 120;
                jjmatchedPos = 1;
             }
             return 23;
          }
          return -1;
       case 2:
-         if ((active0 & 0x100007f400000080L) != 0L || (active1 & 0x200L) != 0L)
+         if ((active0 & 0x7f4000000800L) != 0L || (active1 & 0x2001L) != 0L)
             return 23;
-         if ((active0 & 0xefbfe809a3ffbb70L) != 0L || (active1 & 0x1d9fL) != 0L)
+         if ((active0 & 0xfbfe809a3ffbb700L) != 0L || (active1 & 0x1d9feL) != 0L)
          {
             if (jjmatchedPos != 2)
             {
-               jjmatchedKind = 116;
+               jjmatchedKind = 120;
                jjmatchedPos = 2;
             }
             return 23;
          }
          return -1;
       case 3:
-         if ((active0 & 0xac3f000082002910L) != 0L || (active1 & 0x191fL) != 0L)
+         if ((active0 & 0xc3f0000820029100L) != 0L || (active1 & 0x191faL) != 0L)
             return 23;
-         if ((active0 & 0x4380eb3921ff9260L) != 0L || (active1 & 0x480L) != 0L)
+         if ((active0 & 0x380eb3921ff92600L) != 0L || (active1 & 0x4804L) != 0L)
          {
             if (jjmatchedPos != 3)
             {
-               jjmatchedKind = 116;
+               jjmatchedKind = 120;
                jjmatchedPos = 3;
             }
             return 23;
          }
          return -1;
       case 4:
-         if ((active0 & 0x300000800400260L) != 0L)
+         if ((active0 & 0x3000008004002600L) != 0L)
             return 23;
-         if ((active0 & 0xc49beb3121bf9000L) != 0L || (active1 & 0x48dL) != 0L)
+         if ((active0 & 0x49beb3121bf90000L) != 0L || (active1 & 0x48dcL) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 4;
             return 23;
          }
          return -1;
       case 5:
-         if ((active0 & 0x800b3021001000L) != 0L || (active1 & 0x400L) != 0L)
+         if ((active0 & 0x800b30210010000L) != 0L || (active1 & 0x4000L) != 0L)
             return 23;
-         if ((active0 & 0xc41be00100bf8000L) != 0L || (active1 & 0x8dL) != 0L)
+         if ((active0 & 0x41be00100bf80000L) != 0L || (active1 & 0x8dcL) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 5;
             return 23;
          }
          return -1;
       case 6:
-         if ((active0 & 0xc01b000000808000L) != 0L || (active1 & 0xdL) != 0L)
+         if ((active0 & 0x1b0000008080000L) != 0L || (active1 & 0xdcL) != 0L)
             return 23;
-         if ((active0 & 0x400e001003f0000L) != 0L || (active1 & 0x80L) != 0L)
+         if ((active0 & 0x400e001003f00000L) != 0L || (active1 & 0x800L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 6;
             return 23;
          }
          return -1;
       case 7:
-         if ((active0 & 0x400e001003f0000L) != 0L || (active1 & 0x80L) != 0L)
+         if ((active0 & 0x400e001003f00000L) != 0L || (active1 & 0x800L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 7;
             return 23;
          }
          return -1;
       case 8:
-         if ((active0 & 0x1002a0000L) != 0L)
+         if ((active0 & 0x1002a00000L) != 0L)
             return 23;
-         if ((active0 & 0x400e00000150000L) != 0L || (active1 & 0x80L) != 0L)
+         if ((active0 & 0x400e000001500000L) != 0L || (active1 & 0x800L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 8;
             return 23;
          }
          return -1;
       case 9:
-         if ((active0 & 0xc00000100000L) != 0L || (active1 & 0x80L) != 0L)
-            return 23;
-         if ((active0 & 0x400200000050000L) != 0L)
+         if ((active0 & 0x4002000000500000L) != 0L)
          {
             if (jjmatchedPos != 9)
             {
-               jjmatchedKind = 116;
+               jjmatchedKind = 120;
                jjmatchedPos = 9;
             }
             return 23;
          }
+         if ((active0 & 0xc000001000000L) != 0L || (active1 & 0x800L) != 0L)
+            return 23;
          return -1;
       case 10:
-         if ((active0 & 0x800000000000L) != 0L)
+         if ((active0 & 0x8000000000000L) != 0L)
             return 23;
-         if ((active0 & 0x400200000050000L) != 0L)
+         if ((active0 & 0x4002000000500000L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 10;
             return 23;
          }
          return -1;
       case 11:
-         if ((active0 & 0x10000L) != 0L)
+         if ((active0 & 0x100000L) != 0L)
             return 23;
-         if ((active0 & 0x400200000040000L) != 0L)
+         if ((active0 & 0x4002000000400000L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 11;
             return 23;
          }
          return -1;
       case 12:
-         if ((active0 & 0x400000000000000L) != 0L)
+         if ((active0 & 0x4000000000000000L) != 0L)
             return 23;
-         if ((active0 & 0x200000040000L) != 0L)
+         if ((active0 & 0x2000000400000L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 12;
             return 23;
          }
          return -1;
       case 13:
-         if ((active0 & 0x40000L) != 0L)
-            return 23;
-         if ((active0 & 0x200000000000L) != 0L)
+         if ((active0 & 0x2000000000000L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 13;
             return 23;
          }
+         if ((active0 & 0x400000L) != 0L)
+            return 23;
          return -1;
       case 14:
-         if ((active0 & 0x200000000000L) != 0L)
+         if ((active0 & 0x2000000000000L) != 0L)
          {
-            jjmatchedKind = 116;
+            jjmatchedKind = 120;
             jjmatchedPos = 14;
             return 23;
          }
@@ -204,115 +203,119 @@ static private int jjMoveStringLiteralDfa0_0(){
    switch(curChar)
    {
       case 33:
-         jjmatchedKind = 79;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x400000000L);
+         jjmatchedKind = 83;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x4000000000L);
       case 34:
-         return jjStopAtPos(0, 112);
+         return jjStopAtPos(0, 116);
       case 38:
-         return jjStopAtPos(0, 80);
+         return jjStopAtPos(0, 84);
       case 39:
-         return jjStopAtPos(0, 109);
+         return jjStopAtPos(0, 113);
       case 40:
-         return jjStopAtPos(0, 89);
+         return jjStopAtPos(0, 93);
       case 41:
-         return jjStopAtPos(0, 90);
+         return jjStopAtPos(0, 94);
       case 42:
-         return jjStopAtPos(0, 107);
+         return jjStopAtPos(0, 111);
       case 43:
-         return jjStopAtPos(0, 105);
+         return jjStopAtPos(0, 109);
       case 44:
-         return jjStopAtPos(0, 87);
+         return jjStopAtPos(0, 91);
       case 45:
-         jjmatchedKind = 106;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x100000L);
-      case 46:
+         jjmatchedKind = 110;
          return jjMoveStringLiteralDfa1_0(0x0L, 0x1000000L);
+      case 46:
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x10000000L);
       case 47:
-         return jjStartNfaWithStates_0(0, 108, 1);
+         return jjStartNfaWithStates_0(0, 112, 1);
       case 58:
-         return jjStopAtPos(0, 85);
+         return jjStopAtPos(0, 89);
       case 59:
-         return jjStopAtPos(0, 86);
+         return jjStopAtPos(0, 90);
       case 60:
-         jjmatchedKind = 99;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x40a000080000L);
+         jjmatchedKind = 103;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x40a0000800000L);
       case 61:
-         jjmatchedKind = 97;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x40000L);
+         jjmatchedKind = 101;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x400000L);
       case 62:
-         jjmatchedKind = 100;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x14000000000L);
+         jjmatchedKind = 104;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x140000000000L);
       case 63:
-         return jjStopAtPos(0, 111);
+         return jjStopAtPos(0, 115);
       case 65:
-         return jjStartNfaWithStates_0(0, 3, 23);
+         return jjStartNfaWithStates_0(0, 7, 23);
       case 67:
-         return jjStartNfaWithStates_0(0, 10, 23);
+         jjmatchedKind = 14;
+         return jjMoveStringLiteralDfa1_0(0x10L, 0x0L);
       case 69:
-         return jjStartNfaWithStates_0(0, 14, 23);
+         return jjStartNfaWithStates_0(0, 18, 23);
       case 70:
-         jjmatchedKind = 26;
-         return jjMoveStringLiteralDfa1_0(0x18000000L, 0x0L);
+         jjmatchedKind = 30;
+         return jjMoveStringLiteralDfa1_0(0x180000040L, 0x0L);
       case 71:
-         return jjStartNfaWithStates_0(0, 30, 23);
+         return jjStartNfaWithStates_0(0, 34, 23);
       case 73:
-         return jjStartNfaWithStates_0(0, 33, 23);
+         return jjStartNfaWithStates_0(0, 37, 23);
+      case 78:
+         return jjMoveStringLiteralDfa1_0(0x8L, 0x0L);
       case 80:
-         jjmatchedKind = 54;
-         return jjMoveStringLiteralDfa1_0(0x3f000000000000L, 0x0L);
+         jjmatchedKind = 58;
+         return jjMoveStringLiteralDfa1_0(0x3f0000000000000L, 0x0L);
       case 82:
-         jjmatchedKind = 69;
-         return jjMoveStringLiteralDfa1_0(0x8000000000000000L, 0x1fL);
+         jjmatchedKind = 73;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x1f8L);
       case 83:
-         return jjStartNfaWithStates_0(0, 70, 23);
+         jjmatchedKind = 74;
+         return jjMoveStringLiteralDfa1_0(0x20L, 0x0L);
       case 85:
-         return jjStartNfaWithStates_0(0, 77, 23);
+         return jjStartNfaWithStates_0(0, 81, 23);
       case 87:
-         return jjStartNfaWithStates_0(0, 78, 23);
+         return jjStartNfaWithStates_0(0, 82, 23);
       case 88:
-         return jjStartNfaWithStates_0(0, 44, 23);
+         return jjStartNfaWithStates_0(0, 48, 23);
       case 91:
-         jjmatchedKind = 91;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x20000000L);
+         jjmatchedKind = 95;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x200000000L);
       case 93:
-         jjmatchedKind = 92;
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x40000000L);
+         jjmatchedKind = 96;
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x400000000L);
       case 98:
-         return jjMoveStringLiteralDfa1_0(0x10L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x100L, 0x0L);
       case 99:
-         return jjMoveStringLiteralDfa1_0(0x3e0L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x3e00L, 0x0L);
       case 100:
-         return jjMoveStringLiteralDfa1_0(0x3800L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x38000L, 0x0L);
       case 101:
-         return jjMoveStringLiteralDfa1_0(0x3f8000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x3f80000L, 0x0L);
       case 102:
-         return jjMoveStringLiteralDfa1_0(0x3c00000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x3c000000L, 0x0L);
       case 103:
-         return jjMoveStringLiteralDfa1_0(0x20000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x200000000L, 0x0L);
       case 105:
-         return jjMoveStringLiteralDfa1_0(0x580000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x5800000000L, 0x0L);
       case 108:
-         return jjMoveStringLiteralDfa1_0(0x800000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x8000000000L, 0x0L);
       case 109:
-         return jjMoveStringLiteralDfa1_0(0xff000000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0xff0000000000L, 0x0L);
       case 110:
-         return jjMoveStringLiteralDfa1_0(0x200000000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x2000000000000L, 0x0L);
       case 111:
-         return jjMoveStringLiteralDfa1_0(0xc00000000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0xc000000000000L, 0x0L);
       case 112:
-         return jjMoveStringLiteralDfa1_0(0x1f80000000000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0xf800000000000000L, 0x1L);
       case 114:
-         return jjMoveStringLiteralDfa1_0(0x6000000000000000L, 0x0L);
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x6L);
       case 115:
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x780L);
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x7800L);
       case 116:
-         return jjMoveStringLiteralDfa1_0(0x0L, 0x1800L);
+         return jjMoveStringLiteralDfa1_0(0x0L, 0x18000L);
       case 123:
-         return jjStopAtPos(0, 95);
+         return jjStopAtPos(0, 99);
       case 124:
-         return jjStopAtPos(0, 81);
+         return jjStopAtPos(0, 85);
       case 125:
-         return jjStopAtPos(0, 96);
+         return jjStopAtPos(0, 100);
       default :
          return jjMoveNfa_0(0, 0);
    }
@@ -326,82 +329,96 @@ static private int jjMoveStringLiteralDfa1_0(long active0, long active1){
    switch(curChar)
    {
       case 45:
-         if ((active1 & 0x400000000000L) != 0L)
-            return jjStopAtPos(1, 110);
+         if ((active1 & 0x4000000000000L) != 0L)
+            return jjStopAtPos(1, 114);
          break;
       case 46:
-         if ((active1 & 0x1000000L) != 0L)
-            return jjStopAtPos(1, 88);
+         if ((active1 & 0x10000000L) != 0L)
+            return jjStopAtPos(1, 92);
          break;
       case 48:
-         if ((active0 & 0x10000000L) != 0L)
-            return jjStartNfaWithStates_0(1, 28, 23);
+         if ((active0 & 0x100000000L) != 0L)
+            return jjStartNfaWithStates_0(1, 32, 23);
          break;
       case 60:
-         if ((active1 & 0x2000000000L) != 0L)
-            return jjStopAtPos(1, 101);
+         if ((active1 & 0x20000000000L) != 0L)
+            return jjStopAtPos(1, 105);
          break;
       case 61:
-         if ((active1 & 0x400000000L) != 0L)
-            return jjStopAtPos(1, 98);
-         else if ((active1 & 0x8000000000L) != 0L)
+         if ((active1 & 0x4000000000L) != 0L)
+            return jjStopAtPos(1, 102);
+         else if ((active1 & 0x80000000000L) != 0L)
          {
-            jjmatchedKind = 103;
+            jjmatchedKind = 107;
             jjmatchedPos = 1;
          }
-         else if ((active1 & 0x10000000000L) != 0L)
-            return jjStopAtPos(1, 104);
-         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x80000L);
+         else if ((active1 & 0x100000000000L) != 0L)
+            return jjStopAtPos(1, 108);
+         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x800000L);
       case 62:
-         if ((active1 & 0x40000L) != 0L)
-            return jjStopAtPos(1, 82);
-         else if ((active1 & 0x100000L) != 0L)
-            return jjStopAtPos(1, 84);
-         else if ((active1 & 0x4000000000L) != 0L)
-            return jjStopAtPos(1, 102);
+         if ((active1 & 0x400000L) != 0L)
+            return jjStopAtPos(1, 86);
+         else if ((active1 & 0x1000000L) != 0L)
+            return jjStopAtPos(1, 88);
+         else if ((active1 & 0x40000000000L) != 0L)
+            return jjStopAtPos(1, 106);
+         break;
+      case 69:
+         if ((active0 & 0x8L) != 0L)
+            return jjStartNfaWithStates_0(1, 3, 23);
+         else if ((active0 & 0x10L) != 0L)
+            return jjStartNfaWithStates_0(1, 4, 23);
+         break;
+      case 82:
+         if ((active0 & 0x40L) != 0L)
+            return jjStartNfaWithStates_0(1, 6, 23);
+         break;
+      case 87:
+         if ((active0 & 0x20L) != 0L)
+            return jjStartNfaWithStates_0(1, 5, 23);
          break;
       case 91:
-         if ((active1 & 0x20000000L) != 0L)
-            return jjStopAtPos(1, 93);
+         if ((active1 & 0x200000000L) != 0L)
+            return jjStopAtPos(1, 97);
          break;
       case 93:
-         if ((active1 & 0x40000000L) != 0L)
-            return jjStopAtPos(1, 94);
+         if ((active1 & 0x400000000L) != 0L)
+            return jjStopAtPos(1, 98);
          break;
       case 97:
-         return jjMoveStringLiteralDfa2_0(active0, 0x2000007800400000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x78004000000L, active1, 0x2L);
       case 98:
-         return jjMoveStringLiteralDfa2_0(active0, 0xc00000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0xc000000000000L, active1, 0L);
       case 99:
-         if ((active0 & 0x8000000L) != 0L)
-            return jjStartNfaWithStates_0(1, 27, 23);
+         if ((active0 & 0x80000000L) != 0L)
+            return jjStartNfaWithStates_0(1, 31, 23);
          break;
       case 100:
-         return jjMoveStringLiteralDfa2_0(active0, 0x8000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x80000000000L, active1, 0L);
       case 101:
-         return jjMoveStringLiteralDfa2_0(active0, 0x4000000000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x4L);
       case 105:
-         return jjMoveStringLiteralDfa2_0(active0, 0x70001000800L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x700010008000L, active1, 0L);
       case 108:
-         return jjMoveStringLiteralDfa2_0(active0, 0x80000020000020L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x800000200000200L, active1, 0L);
       case 109:
-         return jjMoveStringLiteralDfa2_0(active0, 0x803f000000000000L, active1, 0x21fL);
+         return jjMoveStringLiteralDfa2_0(active0, 0x3f0000000000000L, active1, 0x21f8L);
       case 110:
-         return jjMoveStringLiteralDfa2_0(active0, 0x5803f8000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x5803f80000L, active1, 0L);
       case 111:
-         return jjMoveStringLiteralDfa2_0(active0, 0x300280000801050L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x3002800008010500L, active1, 0L);
       case 112:
-         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x800L);
+         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x8000L);
       case 114:
-         return jjMoveStringLiteralDfa2_0(active0, 0xc00000000000000L, active1, 0x1000L);
+         return jjMoveStringLiteralDfa2_0(active0, 0xc000000000000000L, active1, 0x10000L);
       case 115:
-         return jjMoveStringLiteralDfa2_0(active0, 0x80L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x800L, active1, 0L);
       case 116:
-         return jjMoveStringLiteralDfa2_0(active0, 0x1000000000002300L, active1, 0x180L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x23000L, active1, 0x1801L);
       case 117:
-         return jjMoveStringLiteralDfa2_0(active0, 0x2000000L, active1, 0L);
+         return jjMoveStringLiteralDfa2_0(active0, 0x20000000L, active1, 0L);
       case 121:
-         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x400L);
+         return jjMoveStringLiteralDfa2_0(active0, 0L, active1, 0x4000L);
       default :
          break;
    }
@@ -418,63 +435,63 @@ static private int jjMoveStringLiteralDfa2_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 62:
-         if ((active1 & 0x80000L) != 0L)
-            return jjStopAtPos(2, 83);
+         if ((active1 & 0x800000L) != 0L)
+            return jjStopAtPos(2, 87);
          break;
       case 97:
-         if ((active0 & 0x1000000000000000L) != 0L)
-            return jjStartNfaWithStates_0(2, 60, 23);
-         return jjMoveStringLiteralDfa3_0(active0, 0x8087000000000000L, active1, 0x3L);
+         if ((active1 & 0x1L) != 0L)
+            return jjStartNfaWithStates_0(2, 64, 23);
+         return jjMoveStringLiteralDfa3_0(active0, 0x870000000000000L, active1, 0x38L);
       case 98:
-         return jjMoveStringLiteralDfa3_0(active0, 0x800000000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x8000000000L, active1, 0L);
       case 100:
-         return jjMoveStringLiteralDfa3_0(active0, 0x800003f8000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x800003f80000L, active1, 0L);
       case 103:
-         if ((active0 & 0x80L) != 0L)
-            return jjStartNfaWithStates_0(2, 7, 23);
-         else if ((active1 & 0x200L) != 0L)
-            return jjStartNfaWithStates_0(2, 73, 23);
+         if ((active0 & 0x800L) != 0L)
+            return jjStartNfaWithStates_0(2, 11, 23);
+         else if ((active1 & 0x2000L) != 0L)
+            return jjStartNfaWithStates_0(2, 77, 23);
          break;
       case 105:
-         return jjMoveStringLiteralDfa3_0(active0, 0x38000080000000L, active1, 0x1cL);
+         return jjMoveStringLiteralDfa3_0(active0, 0x380000800000000L, active1, 0x1c0L);
       case 108:
-         return jjMoveStringLiteralDfa3_0(active0, 0x1400000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x14000000L, active1, 0L);
       case 109:
-         return jjMoveStringLiteralDfa3_0(active0, 0x100000000002300L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x1000000000023000L, active1, 0L);
       case 110:
-         if ((active0 & 0x40000000000L) != 0L)
+         if ((active0 & 0x400000000000L) != 0L)
          {
-            jjmatchedKind = 42;
+            jjmatchedKind = 46;
             jjmatchedPos = 2;
          }
-         return jjMoveStringLiteralDfa3_0(active0, 0x230002000040L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x2300020000400L, active1, 0L);
       case 111:
-         return jjMoveStringLiteralDfa3_0(active0, 0xc00000020000030L, active1, 0x80L);
+         return jjMoveStringLiteralDfa3_0(active0, 0xc000000200000300L, active1, 0x800L);
       case 112:
-         if ((active0 & 0x8000000000L) != 0L)
-            return jjStartNfaWithStates_0(2, 39, 23);
-         return jjMoveStringLiteralDfa3_0(active0, 0x200000000000000L, active1, 0x100L);
+         if ((active0 & 0x80000000000L) != 0L)
+            return jjStartNfaWithStates_0(2, 43, 23);
+         return jjMoveStringLiteralDfa3_0(active0, 0x2000000000000000L, active1, 0x1000L);
       case 114:
-         return jjMoveStringLiteralDfa3_0(active0, 0x800000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x8000000L, active1, 0L);
       case 115:
-         return jjMoveStringLiteralDfa3_0(active0, 0xc00000000800L, active1, 0x400L);
+         return jjMoveStringLiteralDfa3_0(active0, 0xc000000008000L, active1, 0x4000L);
       case 116:
-         if ((active0 & 0x400000000L) != 0L)
-            return jjStartNfaWithStates_0(2, 34, 23);
-         return jjMoveStringLiteralDfa3_0(active0, 0x2000000000000000L, active1, 0x800L);
+         if ((active0 & 0x4000000000L) != 0L)
+            return jjStartNfaWithStates_0(2, 38, 23);
+         return jjMoveStringLiteralDfa3_0(active0, 0L, active1, 0x8002L);
       case 117:
-         return jjMoveStringLiteralDfa3_0(active0, 0x1000L, active1, 0x1000L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x10000L, active1, 0x10000L);
       case 118:
-         return jjMoveStringLiteralDfa3_0(active0, 0x100000000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x1000000000L, active1, 0L);
       case 119:
-         return jjMoveStringLiteralDfa3_0(active0, 0x4000000000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0L, active1, 0x4L);
       case 120:
-         if ((active0 & 0x4000000000L) != 0L)
+         if ((active0 & 0x40000000000L) != 0L)
          {
-            jjmatchedKind = 38;
+            jjmatchedKind = 42;
             jjmatchedPos = 2;
          }
-         return jjMoveStringLiteralDfa3_0(active0, 0x3000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa3_0(active0, 0x30000000000L, active1, 0L);
       default :
          break;
    }
@@ -491,86 +508,86 @@ static private int jjMoveStringLiteralDfa3_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 97:
-         return jjMoveStringLiteralDfa4_0(active0, 0x4000000100000000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x1000000000L, active1, 0x4L);
       case 98:
-         if ((active0 & 0x800000000000000L) != 0L)
+         if ((active0 & 0x8000000000000000L) != 0L)
          {
-            jjmatchedKind = 59;
+            jjmatchedKind = 63;
             jjmatchedPos = 3;
          }
-         return jjMoveStringLiteralDfa4_0(active0, 0x400000020001000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x4000000200010000L, active1, 0L);
       case 99:
-         if ((active0 & 0x100L) != 0L)
-            return jjStartNfaWithStates_0(3, 8, 23);
-         else if ((active0 & 0x800L) != 0L)
-            return jjStartNfaWithStates_0(3, 11, 23);
-         else if ((active0 & 0x2000L) != 0L)
-            return jjStartNfaWithStates_0(3, 13, 23);
-         else if ((active0 & 0x2000000L) != 0L)
-            return jjStartNfaWithStates_0(3, 25, 23);
-         return jjMoveStringLiteralDfa4_0(active0, 0x20L, active1, 0x80L);
+         if ((active0 & 0x1000L) != 0L)
+            return jjStartNfaWithStates_0(3, 12, 23);
+         else if ((active0 & 0x8000L) != 0L)
+            return jjStartNfaWithStates_0(3, 15, 23);
+         else if ((active0 & 0x20000L) != 0L)
+            return jjStartNfaWithStates_0(3, 17, 23);
+         else if ((active0 & 0x20000000L) != 0L)
+            return jjStartNfaWithStates_0(3, 29, 23);
+         return jjMoveStringLiteralDfa4_0(active0, 0x200L, active1, 0x800L);
       case 100:
-         return jjMoveStringLiteralDfa4_0(active0, 0x100200000000200L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x1002000000002000L, active1, 0L);
       case 101:
-         if ((active0 & 0x2000000000000000L) != 0L)
-            return jjStartNfaWithStates_0(3, 61, 23);
-         else if ((active1 & 0x1000L) != 0L)
-            return jjStartNfaWithStates_0(3, 76, 23);
-         return jjMoveStringLiteralDfa4_0(active0, 0xc00800000000L, active1, 0L);
+         if ((active1 & 0x2L) != 0L)
+            return jjStartNfaWithStates_0(3, 65, 23);
+         else if ((active1 & 0x10000L) != 0L)
+            return jjStartNfaWithStates_0(3, 80, 23);
+         return jjMoveStringLiteralDfa4_0(active0, 0xc008000000000L, active1, 0L);
       case 103:
-         if ((active1 & 0x100L) != 0L)
-            return jjStartNfaWithStates_0(3, 72, 23);
-         else if ((active1 & 0x800L) != 0L)
-            return jjStartNfaWithStates_0(3, 75, 23);
+         if ((active1 & 0x1000L) != 0L)
+            return jjStartNfaWithStates_0(3, 76, 23);
+         else if ((active1 & 0x8000L) != 0L)
+            return jjStartNfaWithStates_0(3, 79, 23);
          break;
       case 105:
-         return jjMoveStringLiteralDfa4_0(active0, 0x18000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x180000L, active1, 0L);
       case 108:
-         if ((active0 & 0x10L) != 0L)
-            return jjStartNfaWithStates_0(3, 4, 23);
+         if ((active0 & 0x100L) != 0L)
+            return jjStartNfaWithStates_0(3, 8, 23);
          break;
       case 109:
-         return jjMoveStringLiteralDfa4_0(active0, 0x33000820000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x330008200000L, active1, 0L);
       case 110:
-         if ((active0 & 0x20000000000000L) != 0L)
+         if ((active0 & 0x200000000000000L) != 0L)
          {
-            jjmatchedKind = 53;
+            jjmatchedKind = 57;
             jjmatchedPos = 3;
          }
-         else if ((active1 & 0x10L) != 0L)
+         else if ((active1 & 0x100L) != 0L)
          {
-            jjmatchedKind = 68;
+            jjmatchedKind = 72;
             jjmatchedPos = 3;
          }
-         return jjMoveStringLiteralDfa4_0(active0, 0x18000000000000L, active1, 0xcL);
+         return jjMoveStringLiteralDfa4_0(active0, 0x180000000000000L, active1, 0xc0L);
       case 111:
-         return jjMoveStringLiteralDfa4_0(active0, 0x40000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x400000L, active1, 0L);
       case 112:
-         return jjMoveStringLiteralDfa4_0(active0, 0x80000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x800000L, active1, 0L);
       case 114:
-         return jjMoveStringLiteralDfa4_0(active0, 0x100000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x1000000L, active1, 0L);
       case 115:
-         return jjMoveStringLiteralDfa4_0(active0, 0x600040L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x6000400L, active1, 0L);
       case 116:
-         if ((active0 & 0x80000000L) != 0L)
-            return jjStartNfaWithStates_0(3, 31, 23);
-         return jjMoveStringLiteralDfa4_0(active0, 0x200000001000000L, active1, 0x400L);
+         if ((active0 & 0x800000000L) != 0L)
+            return jjStartNfaWithStates_0(3, 35, 23);
+         return jjMoveStringLiteralDfa4_0(active0, 0x2000000010000000L, active1, 0x4000L);
       case 117:
-         return jjMoveStringLiteralDfa4_0(active0, 0x80000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x800000000000L, active1, 0L);
       case 120:
-         if ((active0 & 0x4000000000000L) != 0L)
+         if ((active0 & 0x40000000000000L) != 0L)
          {
-            jjmatchedKind = 50;
+            jjmatchedKind = 54;
             jjmatchedPos = 3;
          }
-         else if ((active1 & 0x2L) != 0L)
+         else if ((active1 & 0x20L) != 0L)
          {
-            jjmatchedKind = 65;
+            jjmatchedKind = 69;
             jjmatchedPos = 3;
          }
-         return jjMoveStringLiteralDfa4_0(active0, 0x8003000000000000L, active1, 0x1L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x30000000000000L, active1, 0x18L);
       case 121:
-         return jjMoveStringLiteralDfa4_0(active0, 0x80000000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa4_0(active0, 0x800000000000000L, active1, 0L);
       default :
          break;
    }
@@ -587,49 +604,49 @@ static private int jjMoveStringLiteralDfa4_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 97:
-         if ((active0 & 0x200000000000000L) != 0L)
-            return jjStartNfaWithStates_0(4, 57, 23);
-         return jjMoveStringLiteralDfa5_0(active0, 0x400011020000000L, active1, 0L);
+         if ((active0 & 0x2000000000000000L) != 0L)
+            return jjStartNfaWithStates_0(4, 61, 23);
+         return jjMoveStringLiteralDfa5_0(active0, 0x4000110200000000L, active1, 0L);
       case 98:
-         return jjMoveStringLiteralDfa5_0(active0, 0x40000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x400000L, active1, 0L);
       case 101:
-         if ((active0 & 0x400000L) != 0L)
-            return jjStartNfaWithStates_0(4, 22, 23);
-         return jjMoveStringLiteralDfa5_0(active0, 0x80200001100000L, active1, 0x400L);
+         if ((active0 & 0x4000000L) != 0L)
+            return jjStartNfaWithStates_0(4, 26, 23);
+         return jjMoveStringLiteralDfa5_0(active0, 0x802000011000000L, active1, 0x4000L);
       case 104:
-         return jjMoveStringLiteralDfa5_0(active0, 0L, active1, 0x80L);
+         return jjMoveStringLiteralDfa5_0(active0, 0L, active1, 0x800L);
       case 105:
-         return jjMoveStringLiteralDfa5_0(active0, 0x22000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x220000000000L, active1, 0L);
       case 107:
-         if ((active0 & 0x20L) != 0L)
-            return jjStartNfaWithStates_0(4, 5, 23);
+         if ((active0 & 0x200L) != 0L)
+            return jjStartNfaWithStates_0(4, 9, 23);
          break;
       case 108:
-         if ((active0 & 0x800000000L) != 0L)
-            return jjStartNfaWithStates_0(4, 35, 23);
-         return jjMoveStringLiteralDfa5_0(active0, 0x80000081000L, active1, 0L);
+         if ((active0 & 0x8000000000L) != 0L)
+            return jjStartNfaWithStates_0(4, 39, 23);
+         return jjMoveStringLiteralDfa5_0(active0, 0x800000810000L, active1, 0L);
       case 109:
-         return jjMoveStringLiteralDfa5_0(active0, 0x801b000000000000L, active1, 0xdL);
+         return jjMoveStringLiteralDfa5_0(active0, 0x1b0000000000000L, active1, 0xd8L);
       case 110:
-         return jjMoveStringLiteralDfa5_0(active0, 0x18000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x180000L, active1, 0L);
       case 111:
-         return jjMoveStringLiteralDfa5_0(active0, 0x20000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x200000L, active1, 0L);
       case 112:
-         if ((active0 & 0x200L) != 0L)
-            return jjStartNfaWithStates_0(4, 9, 23);
-         else if ((active0 & 0x100000000000000L) != 0L)
-            return jjStartNfaWithStates_0(4, 56, 23);
+         if ((active0 & 0x2000L) != 0L)
+            return jjStartNfaWithStates_0(4, 13, 23);
+         else if ((active0 & 0x1000000000000000L) != 0L)
+            return jjStartNfaWithStates_0(4, 60, 23);
          break;
       case 114:
-         return jjMoveStringLiteralDfa5_0(active0, 0x4000c00100000000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0xc001000000000L, active1, 0x4L);
       case 116:
-         if ((active0 & 0x40L) != 0L)
-            return jjStartNfaWithStates_0(4, 6, 23);
+         if ((active0 & 0x400L) != 0L)
+            return jjStartNfaWithStates_0(4, 10, 23);
          break;
       case 117:
-         return jjMoveStringLiteralDfa5_0(active0, 0x800000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x8000000L, active1, 0L);
       case 121:
-         return jjMoveStringLiteralDfa5_0(active0, 0x200000L, active1, 0L);
+         return jjMoveStringLiteralDfa5_0(active0, 0x2000000L, active1, 0L);
       default :
          break;
    }
@@ -646,52 +663,52 @@ static private int jjMoveStringLiteralDfa5_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 97:
-         return jjMoveStringLiteralDfa6_0(active0, 0x8009000000080000L, active1, 0x84L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x90000000800000L, active1, 0x848L);
       case 98:
-         return jjMoveStringLiteralDfa6_0(active0, 0x400000000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x4000000000000000L, active1, 0L);
       case 100:
-         return jjMoveStringLiteralDfa6_0(active0, 0x4000000000020000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x200000L, active1, 0x4L);
       case 101:
-         if ((active0 & 0x1000L) != 0L)
-            return jjStartNfaWithStates_0(5, 12, 23);
-         else if ((active0 & 0x80000000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 43, 23);
+         if ((active0 & 0x10000L) != 0L)
+            return jjStartNfaWithStates_0(5, 16, 23);
+         else if ((active0 & 0x800000000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 47, 23);
          break;
       case 105:
-         return jjMoveStringLiteralDfa6_0(active0, 0x12000100008000L, active1, 0x9L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x120001000080000L, active1, 0x90L);
       case 108:
-         if ((active0 & 0x20000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 29, 23);
-         return jjMoveStringLiteralDfa6_0(active0, 0x800000L, active1, 0L);
+         if ((active0 & 0x200000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 33, 23);
+         return jjMoveStringLiteralDfa6_0(active0, 0x8000000L, active1, 0L);
       case 109:
-         if ((active1 & 0x400L) != 0L)
-            return jjStartNfaWithStates_0(5, 74, 23);
+         if ((active1 & 0x4000L) != 0L)
+            return jjStartNfaWithStates_0(5, 78, 23);
          break;
       case 110:
-         if ((active0 & 0x2000000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 37, 23);
-         else if ((active0 & 0x20000000000L) != 0L)
+         if ((active0 & 0x20000000000L) != 0L)
             return jjStartNfaWithStates_0(5, 41, 23);
+         else if ((active0 & 0x200000000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 45, 23);
          break;
       case 114:
-         if ((active0 & 0x1000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 24, 23);
-         else if ((active0 & 0x80000000000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 55, 23);
+         if ((active0 & 0x10000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 28, 23);
+         else if ((active0 & 0x800000000000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 59, 23);
          break;
       case 115:
-         return jjMoveStringLiteralDfa6_0(active0, 0x240000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x2400000L, active1, 0L);
       case 116:
-         return jjMoveStringLiteralDfa6_0(active0, 0x200000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x2000000000000L, active1, 0L);
       case 118:
-         return jjMoveStringLiteralDfa6_0(active0, 0xc00000010000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0xc000000100000L, active1, 0L);
       case 119:
-         return jjMoveStringLiteralDfa6_0(active0, 0x100000L, active1, 0L);
+         return jjMoveStringLiteralDfa6_0(active0, 0x1000000L, active1, 0L);
       case 120:
-         if ((active0 & 0x1000000000L) != 0L)
-            return jjStartNfaWithStates_0(5, 36, 23);
-         else if ((active0 & 0x10000000000L) != 0L)
+         if ((active0 & 0x10000000000L) != 0L)
             return jjStartNfaWithStates_0(5, 40, 23);
+         else if ((active0 & 0x100000000000L) != 0L)
+            return jjStartNfaWithStates_0(5, 44, 23);
          break;
       default :
          break;
@@ -709,45 +726,45 @@ static private int jjMoveStringLiteralDfa6_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 97:
-         if ((active0 & 0x800000L) != 0L)
-            return jjStartNfaWithStates_0(6, 23, 23);
-         return jjMoveStringLiteralDfa7_0(active0, 0xc00100110000L, active1, 0L);
+         if ((active0 & 0x8000000L) != 0L)
+            return jjStartNfaWithStates_0(6, 27, 23);
+         return jjMoveStringLiteralDfa7_0(active0, 0xc001001100000L, active1, 0L);
       case 101:
-         return jjMoveStringLiteralDfa7_0(active0, 0x200000040000L, active1, 0L);
+         return jjMoveStringLiteralDfa7_0(active0, 0x2000000400000L, active1, 0L);
       case 105:
-         return jjMoveStringLiteralDfa7_0(active0, 0x400000000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa7_0(active0, 0x4000000000000000L, active1, 0L);
       case 110:
-         if ((active0 & 0x2000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 49, 23);
-         else if ((active0 & 0x10000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 52, 23);
-         else if ((active1 & 0x1L) != 0L)
-            return jjStartNfaWithStates_0(6, 64, 23);
-         else if ((active1 & 0x8L) != 0L)
-            return jjStartNfaWithStates_0(6, 67, 23);
+         if ((active0 & 0x20000000000000L) != 0L)
+            return jjStartNfaWithStates_0(6, 53, 23);
+         else if ((active0 & 0x100000000000000L) != 0L)
+            return jjStartNfaWithStates_0(6, 56, 23);
+         else if ((active1 & 0x10L) != 0L)
+            return jjStartNfaWithStates_0(6, 68, 23);
+         else if ((active1 & 0x80L) != 0L)
+            return jjStartNfaWithStates_0(6, 71, 23);
          break;
       case 115:
-         if ((active0 & 0x4000000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 62, 23);
-         return jjMoveStringLiteralDfa7_0(active0, 0L, active1, 0x80L);
+         if ((active1 & 0x4L) != 0L)
+            return jjStartNfaWithStates_0(6, 66, 23);
+         return jjMoveStringLiteralDfa7_0(active0, 0L, active1, 0x800L);
       case 116:
-         if ((active0 & 0x8000L) != 0L)
-            return jjStartNfaWithStates_0(6, 15, 23);
-         return jjMoveStringLiteralDfa7_0(active0, 0x200000L, active1, 0L);
+         if ((active0 & 0x80000L) != 0L)
+            return jjStartNfaWithStates_0(6, 19, 23);
+         return jjMoveStringLiteralDfa7_0(active0, 0x2000000L, active1, 0L);
       case 117:
-         return jjMoveStringLiteralDfa7_0(active0, 0x20000L, active1, 0L);
+         return jjMoveStringLiteralDfa7_0(active0, 0x200000L, active1, 0L);
       case 120:
-         if ((active0 & 0x1000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 48, 23);
-         else if ((active0 & 0x8000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 51, 23);
-         else if ((active0 & 0x8000000000000000L) != 0L)
-            return jjStartNfaWithStates_0(6, 63, 23);
-         else if ((active1 & 0x4L) != 0L)
-            return jjStartNfaWithStates_0(6, 66, 23);
+         if ((active0 & 0x10000000000000L) != 0L)
+            return jjStartNfaWithStates_0(6, 52, 23);
+         else if ((active0 & 0x80000000000000L) != 0L)
+            return jjStartNfaWithStates_0(6, 55, 23);
+         else if ((active1 & 0x8L) != 0L)
+            return jjStartNfaWithStates_0(6, 67, 23);
+         else if ((active1 & 0x40L) != 0L)
+            return jjStartNfaWithStates_0(6, 70, 23);
          break;
       case 121:
-         return jjMoveStringLiteralDfa7_0(active0, 0x80000L, active1, 0L);
+         return jjMoveStringLiteralDfa7_0(active0, 0x800000L, active1, 0L);
       default :
          break;
    }
@@ -764,17 +781,17 @@ static private int jjMoveStringLiteralDfa7_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 98:
-         return jjMoveStringLiteralDfa8_0(active0, 0xc00000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa8_0(active0, 0xc000000000000L, active1, 0L);
       case 101:
-         return jjMoveStringLiteralDfa8_0(active0, 0x280000L, active1, 0L);
+         return jjMoveStringLiteralDfa8_0(active0, 0x2800000L, active1, 0L);
       case 108:
-         return jjMoveStringLiteralDfa8_0(active0, 0x400000000020000L, active1, 0L);
+         return jjMoveStringLiteralDfa8_0(active0, 0x4000000000200000L, active1, 0L);
       case 110:
-         return jjMoveStringLiteralDfa8_0(active0, 0x100000000L, active1, 0L);
+         return jjMoveStringLiteralDfa8_0(active0, 0x1000000000L, active1, 0L);
       case 114:
-         return jjMoveStringLiteralDfa8_0(active0, 0x200000150000L, active1, 0L);
+         return jjMoveStringLiteralDfa8_0(active0, 0x2000001500000L, active1, 0L);
       case 116:
-         return jjMoveStringLiteralDfa8_0(active0, 0L, active1, 0x80L);
+         return jjMoveStringLiteralDfa8_0(active0, 0L, active1, 0x800L);
       default :
          break;
    }
@@ -791,29 +808,29 @@ static private int jjMoveStringLiteralDfa8_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 100:
-         return jjMoveStringLiteralDfa9_0(active0, 0x100000L, active1, 0L);
+         return jjMoveStringLiteralDfa9_0(active0, 0x1000000L, active1, 0L);
       case 101:
-         if ((active0 & 0x20000L) != 0L)
-            return jjStartNfaWithStates_0(8, 17, 23);
+         if ((active0 & 0x200000L) != 0L)
+            return jjStartNfaWithStates_0(8, 21, 23);
          break;
       case 105:
-         return jjMoveStringLiteralDfa9_0(active0, 0x400000000010000L, active1, 0x80L);
+         return jjMoveStringLiteralDfa9_0(active0, 0x4000000000100000L, active1, 0x800L);
       case 108:
-         return jjMoveStringLiteralDfa9_0(active0, 0xc00000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa9_0(active0, 0xc000000000000L, active1, 0L);
       case 109:
-         if ((active0 & 0x200000L) != 0L)
-            return jjStartNfaWithStates_0(8, 21, 23);
-         return jjMoveStringLiteralDfa9_0(active0, 0x200000000000L, active1, 0L);
+         if ((active0 & 0x2000000L) != 0L)
+            return jjStartNfaWithStates_0(8, 25, 23);
+         return jjMoveStringLiteralDfa9_0(active0, 0x2000000000000L, active1, 0L);
       case 114:
-         if ((active0 & 0x80000L) != 0L)
-            return jjStartNfaWithStates_0(8, 19, 23);
+         if ((active0 & 0x800000L) != 0L)
+            return jjStartNfaWithStates_0(8, 23, 23);
          break;
       case 116:
-         if ((active0 & 0x100000000L) != 0L)
-            return jjStartNfaWithStates_0(8, 32, 23);
+         if ((active0 & 0x1000000000L) != 0L)
+            return jjStartNfaWithStates_0(8, 36, 23);
          break;
       case 118:
-         return jjMoveStringLiteralDfa9_0(active0, 0x40000L, active1, 0L);
+         return jjMoveStringLiteralDfa9_0(active0, 0x400000L, active1, 0L);
       default :
          break;
    }
@@ -830,24 +847,24 @@ static private int jjMoveStringLiteralDfa9_0(long old0, long active0, long old1,
    switch(curChar)
    {
       case 97:
-         return jjMoveStringLiteralDfa10_0(active0, 0x50000L, active1, 0L);
+         return jjMoveStringLiteralDfa10_0(active0, 0x500000L, active1, 0L);
       case 99:
-         if ((active1 & 0x80L) != 0L)
-            return jjStartNfaWithStates_0(9, 71, 23);
+         if ((active1 & 0x800L) != 0L)
+            return jjStartNfaWithStates_0(9, 75, 23);
          break;
       case 101:
-         if ((active0 & 0x400000000000L) != 0L)
+         if ((active0 & 0x4000000000000L) != 0L)
          {
-            jjmatchedKind = 46;
+            jjmatchedKind = 50;
             jjmatchedPos = 9;
          }
-         return jjMoveStringLiteralDfa10_0(active0, 0x800000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa10_0(active0, 0x8000000000000L, active1, 0L);
       case 105:
-         return jjMoveStringLiteralDfa10_0(active0, 0x200000000000L, active1, 0L);
+         return jjMoveStringLiteralDfa10_0(active0, 0x2000000000000L, active1, 0L);
       case 115:
-         if ((active0 & 0x100000L) != 0L)
-            return jjStartNfaWithStates_0(9, 20, 23);
-         return jjMoveStringLiteralDfa10_0(active0, 0x400000000000000L, active1, 0L);
+         if ((active0 & 0x1000000L) != 0L)
+            return jjStartNfaWithStates_0(9, 24, 23);
+         return jjMoveStringLiteralDfa10_0(active0, 0x4000000000000000L, active1, 0L);
       default :
          break;
    }
@@ -864,15 +881,15 @@ static private int jjMoveStringLiteralDfa10_0(long old0, long active0, long old1
    switch(curChar)
    {
       case 98:
-         return jjMoveStringLiteralDfa11_0(active0, 0x40000L);
+         return jjMoveStringLiteralDfa11_0(active0, 0x400000L);
       case 110:
-         return jjMoveStringLiteralDfa11_0(active0, 0x200000010000L);
+         return jjMoveStringLiteralDfa11_0(active0, 0x2000000100000L);
       case 115:
-         if ((active0 & 0x800000000000L) != 0L)
-            return jjStartNfaWithStates_0(10, 47, 23);
+         if ((active0 & 0x8000000000000L) != 0L)
+            return jjStartNfaWithStates_0(10, 51, 23);
          break;
       case 116:
-         return jjMoveStringLiteralDfa11_0(active0, 0x400000000000000L);
+         return jjMoveStringLiteralDfa11_0(active0, 0x4000000000000000L);
       default :
          break;
    }
@@ -889,12 +906,12 @@ static private int jjMoveStringLiteralDfa11_0(long old0, long active0){
    switch(curChar)
    {
       case 105:
-         return jjMoveStringLiteralDfa12_0(active0, 0x400200000000000L);
+         return jjMoveStringLiteralDfa12_0(active0, 0x4002000000000000L);
       case 108:
-         return jjMoveStringLiteralDfa12_0(active0, 0x40000L);
+         return jjMoveStringLiteralDfa12_0(active0, 0x400000L);
       case 116:
-         if ((active0 & 0x10000L) != 0L)
-            return jjStartNfaWithStates_0(11, 16, 23);
+         if ((active0 & 0x100000L) != 0L)
+            return jjStartNfaWithStates_0(11, 20, 23);
          break;
       default :
          break;
@@ -912,13 +929,13 @@ static private int jjMoveStringLiteralDfa12_0(long old0, long active0){
    switch(curChar)
    {
       case 99:
-         if ((active0 & 0x400000000000000L) != 0L)
-            return jjStartNfaWithStates_0(12, 58, 23);
+         if ((active0 & 0x4000000000000000L) != 0L)
+            return jjStartNfaWithStates_0(12, 62, 23);
          break;
       case 101:
-         return jjMoveStringLiteralDfa13_0(active0, 0x40000L);
+         return jjMoveStringLiteralDfa13_0(active0, 0x400000L);
       case 115:
-         return jjMoveStringLiteralDfa13_0(active0, 0x200000000000L);
+         return jjMoveStringLiteralDfa13_0(active0, 0x2000000000000L);
       default :
          break;
    }
@@ -935,11 +952,11 @@ static private int jjMoveStringLiteralDfa13_0(long old0, long active0){
    switch(curChar)
    {
       case 115:
-         if ((active0 & 0x40000L) != 0L)
-            return jjStartNfaWithStates_0(13, 18, 23);
+         if ((active0 & 0x400000L) != 0L)
+            return jjStartNfaWithStates_0(13, 22, 23);
          break;
       case 116:
-         return jjMoveStringLiteralDfa14_0(active0, 0x200000000000L);
+         return jjMoveStringLiteralDfa14_0(active0, 0x2000000000000L);
       default :
          break;
    }
@@ -956,7 +973,7 @@ static private int jjMoveStringLiteralDfa14_0(long old0, long active0){
    switch(curChar)
    {
       case 105:
-         return jjMoveStringLiteralDfa15_0(active0, 0x200000000000L);
+         return jjMoveStringLiteralDfa15_0(active0, 0x2000000000000L);
       default :
          break;
    }
@@ -973,8 +990,8 @@ static private int jjMoveStringLiteralDfa15_0(long old0, long active0){
    switch(curChar)
    {
       case 99:
-         if ((active0 & 0x200000000000L) != 0L)
-            return jjStartNfaWithStates_0(15, 45, 23);
+         if ((active0 & 0x2000000000000L) != 0L)
+            return jjStartNfaWithStates_0(15, 49, 23);
          break;
       default :
          break;
@@ -1016,14 +1033,14 @@ static private int jjMoveNfa_0(int startState, int curPos)
                case 23:
                   if ((0x3ff000000000000L & l) != 0L)
                   {
-                     if (kind > 116)
-                        kind = 116;
+                     if (kind > 120)
+                        kind = 120;
                      { jjCheckNAdd(22); }
                   }
                   else if (curChar == 39)
                   {
-                     if (kind > 115)
-                        kind = 115;
+                     if (kind > 119)
+                        kind = 119;
                   }
                   if ((0x3ff000000000000L & l) != 0L)
                      { jjCheckNAddTwoStates(20, 21); }
@@ -1031,8 +1048,8 @@ else if (curChar == 39)
                case 0:
                   if ((0x3ff000000000000L & l) != 0L)
                   {
-                     if (kind > 114)
-                        kind = 114;
+                     if (kind > 118)
+                        kind = 118;
                      { jjCheckNAddStates(0, 3); }
                   }
                   else if ((0x100002600L & l) != 0L)
@@ -1048,14 +1065,14 @@ else if (curChar == 47)
                      jjstateSet[jjnewStateCnt++] = 1;
                   if ((0x3fe000000000000L & l) != 0L)
                   {
-                     if (kind > 113)
-                        kind = 113;
+                     if (kind > 117)
+                        kind = 117;
                      { jjCheckNAdd(8); }
                   }
                   else if (curChar == 48)
                   {
-                     if (kind > 113)
-                        kind = 113;
+                     if (kind > 117)
+                        kind = 117;
                   }
                   break;
                case 1:
@@ -1091,20 +1108,20 @@ else if (curChar == 48)
                case 7:
                   if ((0x3fe000000000000L & l) == 0L)
                      break;
-                  if (kind > 113)
-                     kind = 113;
+                  if (kind > 117)
+                     kind = 117;
                   { jjCheckNAdd(8); }
                   break;
                case 8:
                   if ((0x3ff000000000000L & l) == 0L)
                      break;
-                  if (kind > 113)
-                     kind = 113;
+                  if (kind > 117)
+                     kind = 117;
                   { jjCheckNAdd(8); }
                   break;
                case 9:
-                  if (curChar == 48 && kind > 113)
-                     kind = 113;
+                  if (curChar == 48 && kind > 117)
+                     kind = 117;
                   break;
                case 10:
                   if (curChar == 46)
@@ -1113,8 +1130,8 @@ else if (curChar == 48)
                case 11:
                   if ((0x3ff000000000000L & l) == 0L)
                      break;
-                  if (kind > 114)
-                     kind = 114;
+                  if (kind > 118)
+                     kind = 118;
                   { jjCheckNAddTwoStates(11, 12); }
                   break;
                case 13:
@@ -1124,8 +1141,8 @@ else if (curChar == 48)
                case 14:
                   if ((0x3ff000000000000L & l) == 0L)
                      break;
-                  if (kind > 114)
-                     kind = 114;
+                  if (kind > 118)
+                     kind = 118;
                   { jjCheckNAdd(14); }
                   break;
                case 15:
@@ -1137,14 +1154,14 @@ else if (curChar == 48)
                      { jjCheckNAddTwoStates(16, 17); }
                   break;
                case 17:
-                  if (curChar == 35 && kind > 117)
-                     kind = 117;
+                  if (curChar == 35 && kind > 121)
+                     kind = 121;
                   break;
                case 18:
                   if ((0x3ff000000000000L & l) == 0L)
                      break;
-                  if (kind > 114)
-                     kind = 114;
+                  if (kind > 118)
+                     kind = 118;
                   { jjCheckNAddStates(0, 3); }
                   break;
                case 20:
@@ -1152,14 +1169,14 @@ else if (curChar == 48)
                      { jjCheckNAddTwoStates(20, 21); }
                   break;
                case 21:
-                  if (curChar == 39 && kind > 115)
-                     kind = 115;
+                  if (curChar == 39 && kind > 119)
+                     kind = 119;
                   break;
                case 22:
                   if ((0x3ff000000000000L & l) == 0L)
                      break;
-                  if (kind > 116)
-                     kind = 116;
+                  if (kind > 120)
+                     kind = 120;
                   { jjCheckNAdd(22); }
                   break;
                default : break;
@@ -1176,8 +1193,8 @@ else if (curChar < 128)
                case 23:
                   if ((0x7fffffe87fffffeL & l) != 0L)
                   {
-                     if (kind > 116)
-                        kind = 116;
+                     if (kind > 120)
+                        kind = 120;
                      { jjCheckNAdd(22); }
                   }
                   if ((0x7fffffe87fffffeL & l) != 0L)
@@ -1186,8 +1203,8 @@ else if (curChar < 128)
                case 0:
                   if ((0x7fffffe87fffffeL & l) == 0L)
                      break;
-                  if (kind > 116)
-                     kind = 116;
+                  if (kind > 120)
+                     kind = 120;
                   { jjCheckNAddStates(7, 9); }
                   break;
                case 2:
@@ -1209,8 +1226,8 @@ else if (curChar < 128)
                case 22:
                   if ((0x7fffffe87fffffeL & l) == 0L)
                      break;
-                  if (kind > 116)
-                     kind = 116;
+                  if (kind > 120)
+                     kind = 120;
                   { jjCheckNAdd(22); }
                   break;
                default : break;
@@ -1239,7 +1256,7 @@ else if (curChar < 128)
                   if (jjCanMove_0(hiByte, i1, i2, l1, l2))
                      { jjAddStates(12, 13); }
                   break;
-               default : if (i1 == 0 || l1 == 0 || i2 == 0 ||  l2 == 0) break; else break;
+               default : if (i1 == 0 || l1 == 0 || i2 == 0 || l2 == 0) break; else break;
             }
          } while(i != startsAt);
       }
@@ -1256,18 +1273,33 @@ else if (curChar < 128)
       catch(java.io.IOException e) { return curPos; }
    }
 }
+static final int[] jjnextStates = {
+   10, 11, 12, 18, 2, 3, 5, 20, 21, 22, 13, 14, 16, 17, 
+};
+private static final boolean jjCanMove_0(int hiByte, int i1, int i2, long l1, long l2)
+{
+   switch(hiByte)
+   {
+      case 0:
+         return ((jjbitVec2[i2] & l2) != 0L);
+      default :
+         if ((jjbitVec0[i1] & l1) != 0L)
+            return true;
+         return false;
+   }
+}
 
 /** Token literal values. */
 public static final String[] jjstrLiteralImages = {
-"", null, null, "\101", "\142\157\157\154", "\143\154\157\143\153", 
-"\143\157\156\163\164", "\143\163\147", "\143\164\155\143", "\143\164\155\144\160", "\103", 
-"\144\151\163\143", "\144\157\165\142\154\145", "\144\164\155\143", "\105", 
-"\145\156\144\151\156\151\164", "\145\156\144\151\156\166\141\162\151\141\156\164", 
-"\145\156\144\155\157\144\165\154\145", "\145\156\144\157\142\163\145\162\166\141\142\154\145\163", 
-"\145\156\144\160\154\141\171\145\162", "\145\156\144\162\145\167\141\162\144\163", 
-"\145\156\144\163\171\163\164\145\155", "\146\141\154\163\145", "\146\157\162\155\165\154\141", 
-"\146\151\154\164\145\162", "\146\165\156\143", "\106", "\106\143", "\106\60", "\147\154\157\142\141\154", 
-"\107", "\151\156\151\164", "\151\156\166\141\162\151\141\156\164", "\111", 
+"", null, null, "\116\105", "\103\105", "\123\127", "\106\122", "\101", 
+"\142\157\157\154", "\143\154\157\143\153", "\143\157\156\163\164", "\143\163\147", 
+"\143\164\155\143", "\143\164\155\144\160", "\103", "\144\151\163\143", 
+"\144\157\165\142\154\145", "\144\164\155\143", "\105", "\145\156\144\151\156\151\164", 
+"\145\156\144\151\156\166\141\162\151\141\156\164", "\145\156\144\155\157\144\165\154\145", 
+"\145\156\144\157\142\163\145\162\166\141\142\154\145\163", "\145\156\144\160\154\141\171\145\162", 
+"\145\156\144\162\145\167\141\162\144\163", "\145\156\144\163\171\163\164\145\155", "\146\141\154\163\145", 
+"\146\157\162\155\165\154\141", "\146\151\154\164\145\162", "\146\165\156\143", "\106", "\106\143", "\106\60", 
+"\147\154\157\142\141\154", "\107", "\151\156\151\164", "\151\156\166\141\162\151\141\156\164", "\111", 
 "\151\156\164", "\154\141\142\145\154", "\155\141\170\155\141\170", 
 "\155\141\170\155\151\156", "\155\141\170", "\155\144\160", "\155\151\156\155\141\170", 
 "\155\151\156\155\151\156", "\155\151\156", "\155\157\144\165\154\145", "\130", 
@@ -1308,21 +1340,6 @@ static protected Token jjFillToken()
 
    return t;
 }
-static final int[] jjnextStates = {
-   10, 11, 12, 18, 2, 3, 5, 20, 21, 22, 13, 14, 16, 17, 
-};
-private static final boolean jjCanMove_0(int hiByte, int i1, int i2, long l1, long l2)
-{
-   switch(hiByte)
-   {
-      case 0:
-         return ((jjbitVec2[i2] & l2) != 0L);
-      default :
-         if ((jjbitVec0[i1] & l1) != 0L)
-            return true;
-         return false;
-   }
-}
 
 static int curLexState = 0;
 static int defaultLexState = 0;
@@ -1345,7 +1362,7 @@ public static Token getNextToken()
    {
       curChar = input_stream.BeginToken();
    }
-   catch(Exception e)
+   catch(java.io.IOException e)
    {
       jjmatchedKind = 0;
       jjmatchedPos = -1;
@@ -1357,9 +1374,9 @@ public static Token getNextToken()
    jjmatchedKind = 0x7fffffff;
    jjmatchedPos = 0;
    curPos = jjMoveStringLiteralDfa0_0();
-   if (jjmatchedPos == 0 && jjmatchedKind > 118)
+   if (jjmatchedPos == 0 && jjmatchedKind > 122)
    {
-      jjmatchedKind = 118;
+      jjmatchedKind = 122;
    }
    if (jjmatchedKind != 0x7fffffff)
    {
@@ -1410,31 +1427,6 @@ public static Token getNextToken()
   }
 }
 
-static void SkipLexicalActions(Token matchedToken)
-{
-   switch(jjmatchedKind)
-   {
-      default :
-         break;
-   }
-}
-static void MoreLexicalActions()
-{
-   jjimageLen += (lengthOfMatch = jjmatchedPos + 1);
-   switch(jjmatchedKind)
-   {
-      default :
-         break;
-   }
-}
-static void TokenLexicalActions(Token matchedToken)
-{
-   switch(jjmatchedKind)
-   {
-      default :
-         break;
-   }
-}
 static private void jjCheckNAdd(int state)
 {
    if (jjrounds[state] != jjround)
@@ -1478,14 +1470,9 @@ public PrismParserTokenManager (SimpleCharStream stream, int lexState){
   }
 
   /** Reinitialise parser. */
-  
   static public void ReInit(SimpleCharStream stream)
   {
-
-
-    jjmatchedPos =
-    jjnewStateCnt =
-    0;
+    jjmatchedPos = jjnewStateCnt = 0;
     curLexState = defaultLexState;
     input_stream = stream;
     ReInitRounds();
@@ -1501,14 +1488,13 @@ static private void ReInitRounds()
 
   /** Reinitialise parser. */
   static public void ReInit(SimpleCharStream stream, int lexState)
-  
   {
     ReInit(stream);
     SwitchTo(lexState);
   }
 
   /** Switch to specified lex state. */
-  public static void SwitchTo(int lexState)
+  static public void SwitchTo(int lexState)
   {
     if (lexState >= 1 || lexState < 0)
       throw new TokenMgrError("Error: Ignoring invalid lexical state : " + lexState + ". State unchanged.", TokenMgrError.INVALID_LEXICAL_STATE);
@@ -1516,39 +1502,24 @@ public static void SwitchTo(int lexState)
       curLexState = lexState;
   }
 
-
 /** Lexer state names. */
 public static final String[] lexStateNames = {
    "DEFAULT",
 };
-
-/** Lex State array. */
-public static final int[] jjnewLexState = {
-   -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-   -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-   -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-   -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-   -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-};
 static final long[] jjtoToken = {
-   0xfffffffffffffff9L, 0x7fffffffffffffL, 
+   0xfffffffffffffff9L, 0x7ffffffffffffffL, 
 };
 static final long[] jjtoSkip = {
    0x6L, 0x0L, 
 };
 static final long[] jjtoSpecial = {
    0x6L, 0x0L, 
-};
-static final long[] jjtoMore = {
-   0x0L, 0x0L, 
 };
     static protected SimpleCharStream  input_stream;
 
     static private final int[] jjrounds = new int[23];
     static private final int[] jjstateSet = new int[2 * 23];
-    private static final StringBuilder jjimage = new StringBuilder();
-    private static StringBuilder image = jjimage;
-    private static int jjimageLen;
-    private static int lengthOfMatch;
-    static protected int curChar;
+
+    
+    static protected char curChar;
 }
diff --git a/prism/src/parser/SimpleCharStream.java b/prism/src/parser/SimpleCharStream.java
index 889869b61..73d4c7f45 100644
--- a/prism/src/parser/SimpleCharStream.java
+++ b/prism/src/parser/SimpleCharStream.java
@@ -1,4 +1,4 @@
-/* Generated By:JavaCC: Do not edit this line. SimpleCharStream.java Version 7.0 */
+/* Generated By:JavaCC: Do not edit this line. SimpleCharStream.java Version 6.0 */
 /* JavaCCOptions:STATIC=true,SUPPORT_CLASS_VISIBILITY_PUBLIC=true */
 package parser;
 
@@ -30,14 +30,13 @@ public class SimpleCharStream
   static protected char[] buffer;
   static protected int maxNextCharInd = 0;
   static protected int inBuf = 0;
-  static protected int tabSize = 1;
-  static protected boolean trackLineColumn = true;
+  static protected int tabSize = 8;
+  static protected boolean trackLineColumn = false;
 
   static public void setTabSize(int i) { tabSize = i; }
   static public int getTabSize() { return tabSize; }
 
 
-
   static protected void ExpandBuff(boolean wrapAround)
   {
     char[] newbuffer = new char[bufsize + 2048];
@@ -472,7 +471,8 @@ static public void adjustBeginLineColumn(int newLine, int newCol)
     line = bufline[j];
     column = bufcolumn[j];
   }
+
   static boolean getTrackLineColumn() { return trackLineColumn; }
-  static void setTrackLineColumn(boolean tlc) { trackLineColumn = tlc; }
+  static void setTrackLineColumn(boolean trackLineColumn) { trackLineColumn = trackLineColumn; }
 }
-/* JavaCC - OriginalChecksum=312d39869f3bfc3a64bf5e66d85fffff (do not edit this line) */
+/* JavaCC - OriginalChecksum=81090b92d191fc568cf66cb10dcab351 (do not edit this line) */
diff --git a/prism/src/parser/Token.java b/prism/src/parser/Token.java
index 49f0d85dc..acc5cc308 100644
--- a/prism/src/parser/Token.java
+++ b/prism/src/parser/Token.java
@@ -1,5 +1,5 @@
-/* Generated By:JavaCC: Do not edit this line. Token.java Version 7.0 */
-/* JavaCCOptions:TOKEN_EXTENDS=,KEEP_LINE_COLUMN=true,SUPPORT_CLASS_VISIBILITY_PUBLIC=true */
+/* Generated By:JavaCC: Do not edit this line. Token.java Version 6.0 */
+/* JavaCCOptions:TOKEN_EXTENDS=,KEEP_LINE_COL=null,SUPPORT_CLASS_VISIBILITY_PUBLIC=true */
 package parser;
 
 /**
@@ -97,7 +97,6 @@ public Token(int kind, String image)
   /**
    * Returns the image.
    */
-  @Override
   public String toString()
   {
     return image;
@@ -129,4 +128,4 @@ public static Token newToken(int ofKind)
   }
 
 }
-/* JavaCC - OriginalChecksum=a6e99fa366f40513e8823da999781b1f (do not edit this line) */
+/* JavaCC - OriginalChecksum=7d751264ae152bf5b6855a5f69a4ab67 (do not edit this line) */
diff --git a/prism/src/parser/TokenMgrError.java b/prism/src/parser/TokenMgrError.java
index 84cacc780..bc8ef8be2 100644
--- a/prism/src/parser/TokenMgrError.java
+++ b/prism/src/parser/TokenMgrError.java
@@ -1,4 +1,4 @@
-/* Generated By:JavaCC: Do not edit this line. TokenMgrError.java Version 7.0 */
+/* Generated By:JavaCC: Do not edit this line. TokenMgrError.java Version 6.0 */
 /* JavaCCOptions: */
 package parser;
 
@@ -20,22 +20,22 @@ public class TokenMgrError extends Error
   /**
    * Lexical error occurred.
    */
-  public static final int LEXICAL_ERROR = 0;
+  static final int LEXICAL_ERROR = 0;
 
   /**
    * An attempt was made to create a second instance of a static token manager.
    */
-  public static final int STATIC_LEXER_ERROR = 1;
+  static final int STATIC_LEXER_ERROR = 1;
 
   /**
    * Tried to change to an invalid lexical state.
    */
-  public static final int INVALID_LEXICAL_STATE = 2;
+  static final int INVALID_LEXICAL_STATE = 2;
 
   /**
    * Detected (and bailed out of) an infinite loop in the token manager.
    */
-  public static final int LOOP_DETECTED = 3;
+  static final int LOOP_DETECTED = 3;
 
   /**
    * Indicates the reason why the exception is thrown. It will have
@@ -48,11 +48,13 @@ public class TokenMgrError extends Error
    * equivalents in the given string
    */
   protected static final String addEscapes(String str) {
-    StringBuilder retval = new StringBuilder();
+    StringBuffer retval = new StringBuffer();
     char ch;
     for (int i = 0; i < str.length(); i++) {
       switch (str.charAt(i))
       {
+        case 0 :
+          continue;
         case '\b':
           retval.append("\\b");
           continue;
@@ -102,12 +104,11 @@ protected static final String addEscapes(String str) {
    *    curchar     : the offending character
    * Note: You can customize the lexical error message by modifying this method.
    */
-  protected static String LexicalErr(boolean EOFSeen, int lexState, int errorLine, int errorColumn, String errorAfter, int curChar) {
-    char curChar1 = (char)curChar;
+  protected static String LexicalError(boolean EOFSeen, int lexState, int errorLine, int errorColumn, String errorAfter, char curChar) {
     return("Lexical error at line " +
           errorLine + ", column " +
           errorColumn + ".  Encountered: " +
-          (EOFSeen ? "<EOF> " : ("\"" + addEscapes(String.valueOf(curChar1)) + "\"") + " (" + curChar + "), ") +
+          (EOFSeen ? "<EOF> " : ("\"" + addEscapes(String.valueOf(curChar)) + "\"") + " (" + (int)curChar + "), ") +
           "after : \"" + addEscapes(errorAfter) + "\"");
   }
 
@@ -120,7 +121,6 @@ protected static String LexicalErr(boolean EOFSeen, int lexState, int errorLine,
    *
    * from this method for such cases in the release version of your parser.
    */
-  @Override
   public String getMessage() {
     return super.getMessage();
   }
@@ -140,8 +140,8 @@ public TokenMgrError(String message, int reason) {
   }
 
   /** Full Constructor. */
-  public TokenMgrError(boolean EOFSeen, int lexState, int errorLine, int errorColumn, String errorAfter, int curChar, int reason) {
-    this(LexicalErr(EOFSeen, lexState, errorLine, errorColumn, errorAfter, curChar), reason);
+  public TokenMgrError(boolean EOFSeen, int lexState, int errorLine, int errorColumn, String errorAfter, char curChar, int reason) {
+    this(LexicalError(EOFSeen, lexState, errorLine, errorColumn, errorAfter, curChar), reason);
   }
 }
-/* JavaCC - OriginalChecksum=247c264b970b850ff3f25ab9073c801d (do not edit this line) */
+/* JavaCC - OriginalChecksum=6c4705c2bebd89492711d8a1e624d837 (do not edit this line) */
diff --git a/prism/src/parser/ast/ExpressionMultiNash.java b/prism/src/parser/ast/ExpressionMultiNash.java
index 7e5423d06..ef78346b1 100644
--- a/prism/src/parser/ast/ExpressionMultiNash.java
+++ b/prism/src/parser/ast/ExpressionMultiNash.java
@@ -19,7 +19,16 @@ public class ExpressionMultiNash extends Expression
 	protected Expression bound = null;
 	// Operands
 	protected ArrayList<ExpressionQuant> operands;
+	// Type of equilibrium
+	protected int eqType;
+	// Criterion
+	protected int crit;
 
+	public static final int NASH = 1;
+	public static final int CORR = 2;
+	public static final int SWEQ = 3;
+	public static final int FAIR = 4;
+	
 	// Constructors
 	
 	public ExpressionMultiNash()
@@ -65,6 +74,16 @@ public void setOperand(int i, ExpressionQuant e)
 		operands.set(i, e);
 	}
 
+	public void setEqType(int eqType) 
+	{
+		this.eqType = eqType;
+	}
+
+	public void setCrit(int crit) 
+	{
+		this.crit = crit;
+	}
+	
 	// Get methods
 	
 	/**
@@ -107,6 +126,16 @@ public OpRelOpBound getRelopBoundInfo(Values constantValues) throws PrismLangExc
 			return new OpRelOpBound("", getRelOp(), null);
 		}
 	}
+	
+	public int getEqType() 
+	{
+		return eqType;
+	}
+
+	public int getCrit() 
+	{
+		return crit;
+	}
 
 	// Methods required for Expression:
 
@@ -168,7 +197,13 @@ public Expression deepCopy()
 	@Override
 	public String toString()
 	{
-		String s = "";
+		String s = "{";
+		if (getEqType() == 1) s+= "NE";
+		if (getEqType() == 2) s+= "CE";						
+		s += ",";
+		if (getCrit() == 3) s+= "SW";
+		if (getCrit() == 4) s+= "FR";
+		s += "}";
 		s += getRelOp();
 		s += (getBound() == null) ? "?" : getBound().toString();
 		s += " (";
@@ -211,6 +246,10 @@ public boolean equals(Object obj)
 				return false;
 		} else if (!bound.equals(other.bound))
 			return false;
+		if (eqType != other.eqType) 
+			return false;
+		if (crit != other.crit)
+			return false;
 		if (operands == null) {
 			if (other.operands != null)
 				return false;
diff --git a/prism/src/prism/PrismSettings.java b/prism/src/prism/PrismSettings.java
index 8beb7ca8e..bde909543 100644
--- a/prism/src/prism/PrismSettings.java
+++ b/prism/src/prism/PrismSettings.java
@@ -133,25 +133,26 @@ public class PrismSettings implements Observer
 	// csg and equilibria
 	public static final String PRISM_ZS_LP_SCALE_FACTOR			= "prism.lpscalefactor";
 	public static final String PRISM_EQ_ASSUMPTION_CHECK 			= "prism.eqassumptioncheck";
+	public static final String PRISM_CSG_LPSOLVER				= "prism.csglpsolver";
 	
     // multi-objective synthesis for games
 	public static final     String PRISM_MULTI_GAUSS_SEIDEL					= "prism.multiGaussSeidel";
-        // iteration control
-        public static final	String PRISM_MULTI_MAX_C_ITER			= "prism.multiMaxCIter";
-        public static final	String PRISM_MULTI_MAX_R_ITER			= "prism.multiMaxRIter";
-        public static final	String PRISM_MULTI_MAX_D_ITER			= "prism.multiMaxDIter";
-        public static final	String PRISM_MULTI_D_ITER_OFFSET       		= "prism.multiDIterOffset";
-        public static final	String PRISM_MULTI_MIN_M         		= "prism.multiMinM";
-        public static final	String PRISM_MULTI_MAX_M         		= "prism.multiMaxM";
-        // rounding
-        public static final String PRISM_MULTI_ROUNDING					= "prism.multiRounding";
-        public static final	String PRISM_MULTI_BASELINE_ACCURACY 		= "prism.baselineAccuracy";
-        public static final	String PRISM_MULTI_INCREASE_FACTOR		= "prism.increaseFactor";
-        // logging
-        public static final	String LOG_MULTI_C_PARETO			= "log.multiCPareto";
-        public static final	String LOG_MULTI_D_PARETO			= "log.multiDPareto";
-        public static final	String LOG_MULTI_R_PARETO			= "log.multiRPareto";
-        public static final	String LOG_MULTI_STRATEGY			= "log.multiStrategy";
+    // iteration control
+    public static final	String PRISM_MULTI_MAX_C_ITER			= "prism.multiMaxCIter";
+    public static final	String PRISM_MULTI_MAX_R_ITER			= "prism.multiMaxRIter";
+    public static final	String PRISM_MULTI_MAX_D_ITER			= "prism.multiMaxDIter";
+    public static final	String PRISM_MULTI_D_ITER_OFFSET       		= "prism.multiDIterOffset";
+    public static final	String PRISM_MULTI_MIN_M         		= "prism.multiMinM";
+    public static final	String PRISM_MULTI_MAX_M         		= "prism.multiMaxM";
+    // rounding
+    public static final String PRISM_MULTI_ROUNDING					= "prism.multiRounding";
+    public static final	String PRISM_MULTI_BASELINE_ACCURACY 		= "prism.baselineAccuracy";
+    public static final	String PRISM_MULTI_INCREASE_FACTOR		= "prism.increaseFactor";
+    // logging
+    public static final	String LOG_MULTI_C_PARETO			= "log.multiCPareto";
+    public static final	String LOG_MULTI_D_PARETO			= "log.multiDPareto";
+    public static final	String LOG_MULTI_R_PARETO			= "log.multiRPareto";
+    public static final	String LOG_MULTI_STRATEGY			= "log.multiStrategy";
 
 	
 	public static final String PRISM_LTL2DA_TOOL					= "prism.ltl2daTool";
@@ -367,7 +368,11 @@ public class PrismSettings implements Observer
 			// CSG ZERO-SUM LP SCALE FACTOR
 			{ DOUBLE_TYPE,		PRISM_ZS_LP_SCALE_FACTOR, 					"Scale factor for LPs",			"4.5", 				Double.valueOf(1.0), 			"1,",
 																			"Scale factor used when building linear programs for solving matrix games"},
-			{ BOOLEAN_TYPE,		PRISM_EQ_ASSUMPTION_CHECK, 					"Assumption check for equilirbia",			"4.5", 				Boolean.valueOf(true), 			"",
+			// CSG SOLVER FOR LPS
+			{ CHOICE_TYPE,		PRISM_CSG_LPSOLVER, 						"LP solver for CSGs",			"4.5", 				"Z3", 			"LpSolve,Z3,Gurobi",
+																			"Solver used when computing solutions for linear programs in CSG model checking"},
+			// CSG ASSUMPTION CHECK
+			{ BOOLEAN_TYPE,		PRISM_EQ_ASSUMPTION_CHECK, 					"Assumption check for equilirbia",			"4.5", 				Boolean.valueOf(false), 			"",
 																			"Assumption check for unbouded equilibria formulae."},
 			// OUTPUT OPTIONS:
 			{ BOOLEAN_TYPE,		PRISM_VERBOSE,							"Verbose output",						"2.1",		Boolean.valueOf(false),															"",																							
@@ -1186,7 +1191,21 @@ else if (sw.equals("lpscalefactor")) {// Scale factor for LPs (zero-sum)
 				throw new PrismException("No value specified for -" + sw + " switch");
 			}
 		}
-		
+		else if (sw.equals("lpsolver")) {
+			if (i < args.length - 1) {
+				s = args[++i];
+				if (s.equals("lpsolve"))
+					set(PRISM_CSG_LPSOLVER, "LpSolve");
+				else if (s.equals("z3"))
+					set(PRISM_CSG_LPSOLVER, "Z3");
+				else if (s.equals("gurobi"))
+					set(PRISM_CSG_LPSOLVER, "Gurobi");
+				else
+					throw new PrismException("Unrecognised option for -" + sw + " switch (options are: lpsolve, z3, gurobi)");
+ 			} else {
+				throw new PrismException("No value specified for -" + sw + " switch");
+			}
+		}
 		else if (sw.equals("eqassumptioncheck")) {
 			set(PRISM_EQ_ASSUMPTION_CHECK, false); 
 		}

From ec09a5f36d40470870b81aeeb61d80cea8a3005f Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabrielhrs@users.noreply.github.com>
Date: Mon, 3 Apr 2023 11:59:48 +0100
Subject: [PATCH 22/30] Disables precomputation for bounded until

---
 prism/src/explicit/CSGModelChecker.java | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index 2b903c004..ee870aa2f 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -3,7 +3,7 @@
 //	Copyright (c) 2002-
 //	Authors:
 //	* Dave Parker <david.parker@cs.ox.ac.uk> (University of Oxford)
-//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//  	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
 //	
 //------------------------------------------------------------------------------
 //	
@@ -282,7 +282,13 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 	public ModelCheckerResult computeBoundedUntilProbs(CSG csg, BitSet remain, BitSet target, int k, boolean min1, boolean min2, Coalition coalition)
 			throws PrismException
 	{
-		return computeUntilProbs(csg, remain, target, k, min1, min2, coalition);
+		ModelCheckerResult res;
+		Boolean tmp;
+		tmp = precomp;
+		precomp = false;
+		res = computeUntilProbs(csg, remain, target, k, min1, min2, coalition);
+		precomp = tmp;
+		return res;	
 	}
 
 	/**

From 8a9eab5ba05b0f378ddae569b33c725e802b6bae Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:06:49 +0100
Subject: [PATCH 23/30] Changes to ProbModelChecker for correlated

---
 prism/src/explicit/ProbModelChecker.java | 48 ++++++++++++++++--------
 1 file changed, 32 insertions(+), 16 deletions(-)

diff --git a/prism/src/explicit/ProbModelChecker.java b/prism/src/explicit/ProbModelChecker.java
index 37c729c28..c8b77f715 100644
--- a/prism/src/explicit/ProbModelChecker.java
+++ b/prism/src/explicit/ProbModelChecker.java
@@ -625,13 +625,16 @@ protected StateValues checkExpressionMultiNash(Model model, ExpressionMultiNash
 		int[] bounds = new int[coalitions.size()];
 		Expression expr1;
 		IntegerBound bound;
-		Arrays.fill(remain, null);
-		Arrays.fill(targets, null);
-		Arrays.fill(bounds, -1);
 		int e, p, r;
 		boolean type = true;
 		boolean rew = false;
 		boolean min = expr.getRelOp().isMin();
+		int eqType = expr.getEqType();
+		int crit = expr.getCrit();
+				
+		Arrays.fill(remain, null);
+		Arrays.fill(targets, null);
+		Arrays.fill(bounds, -1);
 		
 		/*
 		System.out.println("-- RelOp");
@@ -713,10 +716,8 @@ else if (expr1 instanceof ExpressionMultiNashReward) {
 					case ExpressionTemporal.R_I:
 						bounded.set(p);
 						bounds[p] = exprTemp.getUpperBound().evaluateInt(constantValues);
-						//cumul = false;
 						break;
 					case ExpressionTemporal.R_C:
-						//insta = false;
 						if (exprTemp.hasBounds()) {
 							bounded.set(p);
 							bound = IntegerBound.fromExpressionTemporal((ExpressionTemporal) expr1, constantValues, true);
@@ -741,34 +742,49 @@ else if (expr1 instanceof ExpressionMultiNashReward) {
 		else if (coalitions.size() == 2) {
 			if (unbounded.cardinality() == formulae.size()) {
 				if (rew) {
-					res = ((CSGModelChecker) this).computeRewReachEquilibria((CSG) model, coalitions, rewards, targets, min);
+					res = ((CSGModelChecker) this).computeRewReachEquilibria((CSG) model, coalitions, rewards, targets, eqType, crit, min);
 				}
 				else {
-					res = ((CSGModelChecker) this).computeProbReachEquilibria((CSG) model, coalitions, targets, remain, min);
+					res = ((CSGModelChecker) this).computeProbReachEquilibria((CSG) model, coalitions, targets, remain, eqType, crit, min);
 				}
 			}
 			else if (bounded.cardinality() == formulae.size()) {
 				if (rew) {
-					res = ((CSGModelChecker) this).computeRewBoundedEquilibria((CSG) model, coalitions, rewards, exprs, bounds, min);
+					res = ((CSGModelChecker) this).computeRewBoundedEquilibria((CSG) model, coalitions, rewards, exprs, bounds, eqType, crit, min);
 				}
 				else {
-					res = ((CSGModelChecker) this).computeProbBoundedEquilibria((CSG) model, coalitions, exprs, targets, remain, bounds, min);			
+					res = ((CSGModelChecker) this).computeProbBoundedEquilibria((CSG) model, coalitions, exprs, targets, remain, bounds, eqType, crit, min);
 				}
 			}
 			else {
-				res = ((CSGModelChecker) this).computeMixedEquilibria((CSG) model, coalitions, rewards, exprs, bounded, targets, remain, bounds, min);
+				res = ((CSGModelChecker) this).computeMixedEquilibria((CSG) model, coalitions, rewards, exprs, bounded, targets, remain, bounds, eqType, crit, min);
 			}
 		}
 		else if (coalitions.size() > 2) {
-			throw new PrismNotSupportedException("Equilibria-based properties with more than two coalitions are not yet supported");	
-			/*
-			if (rew) {
-				res = ((CSGModelChecker) this).computeMultiRewReachEquilibria((CSG) model, coalitions, rewards, targets, min);
+			if (unbounded.cardinality() == formulae.size()) {
+				if (rew) {
+					res = ((CSGModelChecker) this).computeMultiRewReachEquilibria((CSG) model, coalitions, rewards, targets, eqType, crit, min);
+				}
+				else {
+					res = ((CSGModelChecker) this).computeMultiProbReachEquilibria((CSG) model, coalitions, targets, remain, eqType, crit, min);
+				}
+			}
+			else if (bounded.cardinality() == formulae.size()) {
+				int first_bound = bounds[0];
+				for (int i = 1; i < bounds.length; i++) {
+					if (first_bound != bounds[i])
+						throw new PrismNotSupportedException("Multi-coalitional properties with different bounds are not yet supported");
+				}
+				if (rew) {
+					res = ((CSGModelChecker) this).computeMultiRewBoundedEquilibria((CSG) model, coalitions, rewards, exprs, bounds, eqType, crit, min);
+				}
+				else {
+					res = ((CSGModelChecker) this).computeMultiProbBoundedEquilibria((CSG) model, coalitions, targets, remain, bounds, eqType, crit, min);
+				}
 			}
 			else {
-				res = ((CSGModelChecker) this).computeMultiProbReachEquilibria((CSG) model, coalitions, targets, remain, min);
+				throw new PrismNotSupportedException("Multi-coalitional mixed properties are not yet supported");
 			}
-			*/
 		}
 
 		result.setStrategy(res.strat);

From d86c285c62ab6745340a1b5b8e2e3d0413ba2811 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:15:36 +0100
Subject: [PATCH 24/30] Changes to CSGStrategy to include correlated

---
 prism/src/strat/CSGStrategy.java | 219 ++++++++++++++++++++++++++++++-
 1 file changed, 215 insertions(+), 4 deletions(-)

diff --git a/prism/src/strat/CSGStrategy.java b/prism/src/strat/CSGStrategy.java
index 09729a1c4..1b1aa541c 100644
--- a/prism/src/strat/CSGStrategy.java
+++ b/prism/src/strat/CSGStrategy.java
@@ -43,6 +43,7 @@
 import prism.PrismComponent;
 import prism.PrismException;
 import prism.PrismLog;
+import strat.CSGStrategy.CSGStrategyType;
 
 public class CSGStrategy extends PrismComponent implements Strategy {
 
@@ -58,7 +59,7 @@ public class CSGStrategy extends PrismComponent implements Strategy {
 	protected int numCoalitions;
 	
 	public enum CSGStrategyType {
-		ZERO_SUM, EQUILIBRIA_M, EQUILIBRIA_P, EQUILIBRIA_R;
+		ZERO_SUM, EQUILIBRIA_M, EQUILIBRIA_P, EQUILIBRIA_R, EQUILIBRIA_CE_P, EQUILIBRIA_CE_R, EQUILIBRIA_CE_M;
 	}
 
 	public CSGStrategy(CSG model, List<List<List<Map<BitSet, Double>>>> csgchoices, Map<BitSet, BitSet> subgames, int numCoalitions, CSGStrategyType type) {
@@ -150,6 +151,13 @@ public void exportActions(PrismLog out) {
 				case EQUILIBRIA_R:
 					exportEquilibriaStrategy(out);
 					break;
+				case EQUILIBRIA_CE_M:
+					exportMultiEquilibriaStrategy(out);
+					break;
+				case EQUILIBRIA_CE_P:
+				case EQUILIBRIA_CE_R:
+					exportEquilibriaStrategy(out);
+					break;
 			}
 		}
 		catch (Exception e) {
@@ -226,15 +234,20 @@ public void exportEquilibriaStrategy(PrismLog out) throws PrismException, Invali
 			for (p = 0; p < 2; p++) {
 				reach[p] = new BitSet();
 				for (i = 0; i < model.getNumStates(); i++) {
-					if (type == CSGStrategyType.EQUILIBRIA_P)
+					if (type == CSGStrategyType.EQUILIBRIA_P || type == CSGStrategyType.EQUILIBRIA_CE_P) {
 						if (prechoices[p].soln[i] > 0)
 							reach[p].set(i);
-					if  (type == CSGStrategyType.EQUILIBRIA_R)
+					}
+					if  (type == CSGStrategyType.EQUILIBRIA_R || type == CSGStrategyType.EQUILIBRIA_CE_R) {
 						if (prechoices[p].soln[i] < Double.POSITIVE_INFINITY)
 							reach[p].set(i);
+					}
 				}
 			}
-			generateMDPEquilibria(mdp, onmap, statelist, reach, explored, 0, s); 
+			if (type == CSGStrategyType.EQUILIBRIA_P || type == CSGStrategyType.EQUILIBRIA_R)
+				generateMDPEquilibria(mdp, onmap, statelist, reach, explored, 0, s); 
+			if (type == CSGStrategyType.EQUILIBRIA_CE_P || type == CSGStrategyType.EQUILIBRIA_CE_R)
+				generateMDPCorrelatedEquilibria(mdp, onmap, statelist, reach, explored, 0, s); 
 			addPrecompStrategies(mdp, onmap, statelist, reach);		
 		}
 		mdp.setStatesList(statelist);
@@ -475,6 +488,87 @@ else if (!d.isEmpty()) {
 		}
 	}
 	
+	public void generateMDPMultiCorrelatedEquilibria(MDPSimple mdp, Map<Integer, Integer> onmap, List<State> statelist, BitSet explored, int k, int s) {
+		Distribution d;
+		Map<BitSet, Double> prods = new HashMap<BitSet, Double>();
+		BitSet tmp = new BitSet();
+		BitSet sat = new BitSet();
+		String joint = null;
+		String label = null;
+		String lsubg = "";
+		String prob = "";
+		int c, i, m, n, q, p, t;
+		boolean loop = false;
+		explored.set(s);
+		n = onmap.get(s);
+		for (BitSet subgame : subgames.keySet()) {
+			if (subgames.get(subgame).get(s)) {
+				sat.or(subgame);
+			}
+		}
+		for (p = 0; p < numCoalitions; p++) {
+			if (sat.get(p)) {
+				lsubg += "Sat(" + p + ")";
+			}
+			else {
+				lsubg += "Unsat(" + p + ")";
+			}
+			if (p < numCoalitions - 1)
+				lsubg += " -- ";
+		}
+		if (sat.cardinality() == numCoalitions) {
+			d = new Distribution();
+			d.add(n, 1.0);
+			mdp.addActionLabelledChoice(n, d, lsubg);	
+		}
+		else {
+			prods = csgchoices.get(0).get(k).get(s);
+			d = new Distribution();
+			for (t = 0; t < model.getNumChoices(s); t++) {
+				tmp.clear();
+				for (q = 0; q < model.getIndexes(s, t).length; q++) {
+					i = model.getIndexes(s, t)[q];						
+					tmp.set((i > 0)? i : model.getIdles()[q]);
+				}
+				if (prods.containsKey(tmp)) {						
+					for (int u : model.getChoice(s, t).getSupport()) {
+						if (!onmap.containsKey(u)) {
+							m = mdp.addState();
+							onmap.put(u, m);
+							statelist.add(m, model.getStatesList().get(u));
+							if (!explored.get(u))
+								generateMDPMultiCorrelatedEquilibria(mdp, onmap, statelist, explored, k, u);
+						}
+						else {
+							m = onmap.get(u);
+							if (m == n && model.getChoice(s, t).getSupport().size() == 1 && model.getNumChoices(s) == 1)
+								loop = true;
+						}
+						d.add(m, model.getChoice(s, t).get(u) * prods.get(tmp));
+					}
+				}
+			}
+			if (loop) {
+				mdp.addActionLabelledChoice(n, d, lsubg);	
+			}
+			else if (!d.isEmpty()) {
+				label = "CSG: ";
+				c = csgchoices.get(0).get(k).get(s).keySet().size();
+				for (BitSet act : csgchoices.get(0).get(k).get(s).keySet()) {
+					prob += csgchoices.get(0).get(k).get(s).get(act) +": ";
+					joint = "";
+					for (i = act.nextSetBit(0); i >= 0; i = act.nextSetBit(i + 1)) {
+						joint += "[" + model.getActions().get(i - 1) + "]";
+					}
+					c--;
+					prob += joint + ((c > 0)? " + " : ""); 
+				}
+				label += prob;
+				mdp.addActionLabelledChoice(n, d, label);
+			}
+		}
+	}
+	
 	public void generateMDPEquilibria(MDPSimple mdp, Map<Integer, Integer> onmap, List<State> statelist, BitSet[] reach, BitSet explored, int k, int s) {
 		Distribution d;
 		String[] action = new String[csgchoices.size()];
@@ -557,6 +651,79 @@ else if (!targets[0].get(s) && !targets[1].get(s) && !reach[0].get(s) && !reach[
 		}
 	}
 	
+	public void generateMDPCorrelatedEquilibria(MDPSimple mdp, Map<Integer, Integer> onmap, List<State> statelist, BitSet[] reach, BitSet explored, int k, int s) {
+		Distribution d;
+		String prob = "";
+		String label = null;
+		String joint = null;
+		BitSet tmp = new BitSet();
+		Map<BitSet, Double> prods = new HashMap<BitSet, Double>();
+		int c, i, m, n, q, t;
+		n = onmap.get(s);
+		explored.set(s);
+		if (targets[0].get(s) && targets[1].get(s)) {
+			d = new Distribution();
+			d.add(n, 1.0);
+			mdp.addActionLabelledChoice(n, d, "CSG: Sat(0) -- Sat(1)");
+		}
+		else if (targets[0].get(s) && !targets[1].get(s) && !reach[0].get(s)) {
+			d = new Distribution();
+			d.add(n, 1.0);
+			mdp.addActionLabelledChoice(n, d, "CSG: Sat(0) -- Unsat(1)");
+		}
+		else if (!targets[0].get(s) && targets[1].get(s) && !reach[1].get(s)) {
+			d = new Distribution();
+			d.add(n, 1.0);
+			mdp.addActionLabelledChoice(n, d, "CSG: Unsat(0) -- Sat(1)");
+		}
+		else if (!targets[0].get(s) && !targets[1].get(s) && !reach[0].get(s) && !reach[1].get(s)) {
+			d = new Distribution();
+			d.add(n, 1.0);
+			mdp.addActionLabelledChoice(n, d, "CSG: Unsat(0) -- Unsat(1)");
+		}
+		else if (csgchoices.get(0).get(k).get(s) != null) {
+			prods = csgchoices.get(0).get(k).get(s);
+			d = new Distribution();
+			for (t = 0; t < model.getNumChoices(s); t++) {
+				tmp.clear();
+				for (q = 0; q < model.getIndexes(s, t).length; q++) {
+					i = model.getIndexes(s, t)[q];						
+					tmp.set((i > 0)? i : model.getIdles()[q]);
+				}
+				if (prods.containsKey(tmp)) {
+					for (int u : model.getChoice(s, t).getSupport()) {
+						if (!onmap.containsKey(u)) {
+							m = mdp.addState();
+							onmap.put(u, m);
+							statelist.add(m, model.getStatesList().get(u));
+							if (!explored.get(u))
+								generateMDPCorrelatedEquilibria(mdp, onmap, statelist, reach, explored, k, u);  // should check for explored?
+						}
+						else {
+							m = onmap.get(u);
+						}
+						d.add(m, model.getChoice(s, t).get(u) * prods.get(tmp));
+					}
+				}
+			}
+			if (!d.isEmpty()) {
+				label = "CSG: ";
+				c = csgchoices.get(0).get(k).get(s).keySet().size();
+				for (BitSet act : csgchoices.get(0).get(k).get(s).keySet()) {
+					prob += csgchoices.get(0).get(k).get(s).get(act) +": ";
+					joint = "";
+					for (i = act.nextSetBit(0); i >= 0; i = act.nextSetBit(i + 1)) {
+						joint += "[" + model.getActions().get(i - 1) + "]";
+					}
+					c--;
+					prob += joint + ((c > 0)? " + " : ""); 
+				}
+				label += prob;
+				mdp.addActionLabelledChoice(n, d, label);
+			}
+		}	
+	}
+	
 	public void generateMDPZeroSum(MDPSimple mdp, Map<Integer, Integer> onmap, List<State> statelist, BitSet explored, int k, int p, int s) {
 		Distribution d;
 		BitSet tmp1 = new BitSet();
@@ -633,4 +800,48 @@ public void clear() {
 		// TODO Auto-generated method stub
 		
 	}
+	
+	@Override
+	public String toString() {
+		String[] action;
+		String joint, label;
+		int c, i, k, p, s;
+		boolean chck;
+		label = "CSG:";
+		k = 0;
+		if (csgchoices != null) {
+			/*
+			for (List<List<Map<BitSet, Double>>> entry : csgchoices) {
+				s += entry.toString();
+				s += "\n";
+			}
+			*/
+			for (s = 0; s < model.getNumStates(); s++) {
+				action = new String[csgchoices.size()];
+				chck = true;
+				for (p = 0; p < numCoalitions; p++) {
+					chck = chck && csgchoices.get(p).get(k).get(s) != null;
+					action[p] = "";
+				}
+				label += " $ s:" + s + " -> ";
+				for (p = 0; p < numCoalitions; p++) {
+					if (csgchoices.get(p).get(k).get(s) != null) {
+						c = csgchoices.get(p).get(k).get(s).keySet().size();
+						for (BitSet act : csgchoices.get(p).get(k).get(s).keySet()) {
+							joint = "";
+							for (i = act.nextSetBit(0); i >= 0; i = act.nextSetBit(i + 1)) {
+								joint += "[" + model.getActions().get(i - 1) + "]";
+							}
+							c--;
+							action[p] += csgchoices.get(p).get(k).get(s).get(act) +": " + joint + ((c > 0)? " + " : ""); 
+						}
+						label += (p + 1 < csgchoices.size())? action[p] + " -- " : action[p];
+					}	
+				}
+			}
+			return label;
+		}
+		else 
+			return label;
+	}
 }

From d40d909f68b6a0be6f22ee10d0a485379e3c215e Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:22:33 +0100
Subject: [PATCH 25/30] Minor changes to Nash equilibria computation classes

---
 prism/src/explicit/CSGLabeledPolytopes.java   |  29 ++-
 .../CSGLabeledPolytopesYicesStack.java        |   2 +-
 prism/src/explicit/CSGLabeledPolytopesZ3.java | 245 +++++++++---------
 .../explicit/CSGLabeledPolytopesZ3Stack.java  |  16 +-
 prism/src/explicit/CSGSupportEnumeration.java |   4 +-
 .../src/explicit/CSGSupportEnumerationZ3.java | 202 ++++++++-------
 6 files changed, 273 insertions(+), 225 deletions(-)

diff --git a/prism/src/explicit/CSGLabeledPolytopes.java b/prism/src/explicit/CSGLabeledPolytopes.java
index a94aa6aaf..2ed88e4e2 100644
--- a/prism/src/explicit/CSGLabeledPolytopes.java
+++ b/prism/src/explicit/CSGLabeledPolytopes.java
@@ -1,3 +1,30 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
 package explicit;
 
 import java.util.ArrayList;
@@ -10,7 +37,7 @@ public interface CSGLabeledPolytopes {
     
 	public void update(int nrows, int ncols, double[][] a, double[][] b);
 	
-	public void compEq() throws PrismException;
+	public void computeEquilibria() throws PrismException;
 	
 	public void compPayoffs();
 	
diff --git a/prism/src/explicit/CSGLabeledPolytopesYicesStack.java b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
index ec0c8a36c..f3f010014 100644
--- a/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesYicesStack.java
@@ -257,7 +257,7 @@ private void vMult() {
 		}
 	}
 
-	public void compEq() throws PrismException
+	public void computeEquilibria() throws PrismException
 	{
 		ArrayList<Distribution> dists;
 		Distribution dist1;
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3.java b/prism/src/explicit/CSGLabeledPolytopesZ3.java
index d1dae2b2d..e2baaa973 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3.java
@@ -251,7 +251,7 @@ private void vMult() {
 		}
 	}
 
-	public void compEq() {
+	public void computeEquilibria() {
 		ArrayList<Distribution> dists;
 		Distribution dist1;
 		Distribution dist2;
@@ -270,42 +270,42 @@ public void compEq() {
 
 		//in order to check for indifference
 		BoolExpr xeqrst = ctx.mkTrue();
-				BoolExpr yeqrst = ctx.mkTrue();
+		BoolExpr yeqrst = ctx.mkTrue();
 
-				start = new Date().getTime();
+		start = new Date().getTime();
 
-				vMult();
-				xLabels();
-				yLabels();
+		vMult();
+		xLabels();
+		yLabels();
 
-				eq = ctx.mkTrue();
-				for(i = 0; i < nrows+ncols; i++) {
-					eq = ctx.mkAnd(eq, ctx.mkOr(xlabels[i], ylabels[i]));
-				}
+		eq = ctx.mkTrue();
+		for(i = 0; i < nrows+ncols; i++) {
+			eq = ctx.mkAnd(eq, ctx.mkOr(xlabels[i], ylabels[i]));
+		}
 
-				Expr xctr = zero;
-				Expr yctr = zero;
+		Expr xctr = zero;
+		Expr yctr = zero;
 
-				for(i = 0; i < nrows; i++) {
-					xctr = ctx.mkAdd((ArithExpr) xctr, vars[i]);
-				}
-				xctr = ctx.mkEq(xctr, one);
+		for(i = 0; i < nrows; i++) {
+			xctr = ctx.mkAdd((ArithExpr) xctr, vars[i]);
+		}
+		xctr = ctx.mkEq(xctr, one);
 
-				for(j = i; j < nrows+ncols; j++) {
-					yctr = ctx.mkAdd((ArithExpr) yctr, vars[j]);
-				}
-				yctr = ctx.mkEq(yctr, one);		
+		for(j = i; j < nrows+ncols; j++) {
+			yctr = ctx.mkAdd((ArithExpr) yctr, vars[j]);
+		}
+		yctr = ctx.mkEq(yctr, one);		
 
-				s.add((BoolExpr) xctr); 
-				s.add((BoolExpr) yctr); 
-				s.add(eq);
+		s.add((BoolExpr) xctr); 
+		s.add((BoolExpr) yctr); 
+		s.add(eq);
 
-				j = 0; 
+		j = 0; 
 
-				strat = new ArrayList<ArrayList<Distribution>>();
-				eqs = new HashMap<String,ArrayList<Double>> ();
+		strat = new ArrayList<ArrayList<Distribution>>();
+		eqs = new HashMap<String,ArrayList<Double>> ();
 
-				/*
+		/*
     	System.out.println("-- xlabels");
         for (int l = 0; l < xlabels.length; l++) {
         	System.out.println(l + ": " + xlabels[l]);
@@ -315,9 +315,9 @@ public void compEq() {
         for (int l = 0; l < ylabels.length; l++) {
         	System.out.println(l + ": " + ylabels[l]);        	
         }
-				 */
+		*/
 
-				/*
+		/*
         for(int nv = 0; nv < p1vars.length - 1; nv++) {
         	xeqrst = ctx.mkAnd(xeqrst, ctx.mkEq(p1vars[nv], p1vars[nv+1]));
         }
@@ -325,11 +325,11 @@ public void compEq() {
         for(int nv = 0; nv < p2vars.length - 1; nv++) {
         	yeqrst = ctx.mkAnd(yeqrst, ctx.mkEq(p2vars[nv], p2vars[nv+1]));
         }
-				 */
+		*/
 
-				/*** Too strong? ***/
+		/*** Too strong? ***/
 
-				/* 
+		/* 
         for(int nv = 0; nv < p1vars.length; nv++) {
             for(int nnv = 0; nnv < p1vars.length; nnv++) {
             	xeqrst = ctx.mkAnd(xeqrst, 
@@ -353,34 +353,34 @@ public void compEq() {
             						);
             }
         }
-				 */
+		*/
 
-				/*** Too strong? ***/
+		/*** Too strong? ***/
 
-				xeqrst = ctx.mkNot(xeqrst);
-				yeqrst = ctx.mkNot(yeqrst);
+		xeqrst = ctx.mkNot(xeqrst);
+		yeqrst = ctx.mkNot(yeqrst);
 
-				boolean indif = false;
+		boolean indif = false;
 
-				addPayoffs();
+		addPayoffs();
 
-				/*
+		/*
         Optimize opt = ctx.mkOptimize();
         opt.Add(ctx.mkEq(payoffs[0],  payvars[0]));
         opt.Add(ctx.mkEq(payoffs[1],  payvars[1]));
         opt.MkMaximize(payvars[0]);
         Optimize.Handle mx = opt.MkMaximize(payvars[0]);
         Optimize.Handle my = opt.MkMaximize(payvars[1]);
-				 */
+		*/
 
-				while (Status.SATISFIABLE == s.check()) {
-					model = s.getModel();
-					rstr = ctx.mkFalse();
+		while (Status.SATISFIABLE == s.check()) {
+			model = s.getModel();
+			rstr = ctx.mkFalse();
 
-					c1 = ctx.mkTrue();
-					c2 = ctx.mkTrue();
+			c1 = ctx.mkTrue();
+			c2 = ctx.mkTrue();
 
-					/*
+			/*
             if(j > 0) {          	
             	if(((BoolExpr) model.eval(xeqrst, true)).isFalse()) {
             		System.out.println("## Player 1 is indifferent. ##");
@@ -393,100 +393,100 @@ public void compEq() {
             		//break;	
             	}      	            	
             }
-					 */
-
-					//System.out.println(getDoubleValue(model, payvars[0]));
-					//System.out.println(getDoubleValue(model, payvars[1]));
-					//compPayoffs(model);
-
-					dists = new ArrayList<Distribution>();
-					dist1 = new Distribution();
-					dist2 = new Distribution();
-
-					for(i = 0; i < vars.length; i++) {
-						p = getDoubleValue(model, vars[i]);
-						if(p > 0) {
-							if(i < nrows)
-								dist1.add(i, p);
-							else 
-								dist2.add(i - nrows, p);
-						}
-						if(j == 0) {
-							eqs.put(vars[i].getSExpr(), new ArrayList<Double> ());
-							eqs.get(vars[i].getSExpr()).add(p);
-						}
-						else {
-							//System.out.println((RatNum) model.getConstInterp(vars[i]));
-							eqs.get(vars[i].getSExpr().toString()).add(p);	
-						}
-						//rstr = ctx.mkOr(rstr, ctx.mkNot(ctx.mkEq(vars[i], (RealExpr) model.getConstInterp(vars[i]))));
-					}
+			*/
+
+			//System.out.println(getDoubleValue(model, payvars[0]));
+			//System.out.println(getDoubleValue(model, payvars[1]));
+			//compPayoffs(model);
+
+			dists = new ArrayList<Distribution>();
+			dist1 = new Distribution();
+			dist2 = new Distribution();
+
+			for(i = 0; i < vars.length; i++) {
+				p = getDoubleValue(model, vars[i]);
+				if(p > 0) {
+					if(i < nrows)
+						dist1.add(i, p);
+					else 
+						dist2.add(i - nrows, p);
+				}
+				if(j == 0) {
+					eqs.put(vars[i].getSExpr(), new ArrayList<Double> ());
+					eqs.get(vars[i].getSExpr()).add(p);
+				}
+				else {
+					//System.out.println((RatNum) model.getConstInterp(vars[i]));
+					eqs.get(vars[i].getSExpr().toString()).add(p);	
+				}
+				//rstr = ctx.mkOr(rstr, ctx.mkNot(ctx.mkEq(vars[i], (RealExpr) model.getConstInterp(vars[i]))));
+			}
 
-					for(i = 0; i < p1vars.length; i++) {
-						if(((BoolExpr) model.eval(ctx.mkEq(p1vars[i], zero), true)).isFalse()) {
-							c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(p1vars[i], zero)));
-						}
-						else {
-							c1 = ctx.mkAnd(c1, ctx.mkEq(p1vars[i], zero));
-						}
-					}
+			for(i = 0; i < p1vars.length; i++) {
+				if(((BoolExpr) model.eval(ctx.mkEq(p1vars[i], zero), true)).isFalse()) {
+					c1 = ctx.mkAnd(c1, ctx.mkNot(ctx.mkEq(p1vars[i], zero)));
+				}
+				else {
+					c1 = ctx.mkAnd(c1, ctx.mkEq(p1vars[i], zero));
+				}
+			}
 
-					for(i = 0; i < p2vars.length; i++) {
-						if(((BoolExpr) model.eval(ctx.mkEq(p2vars[i], zero), true)).isFalse()) {
-							c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(p2vars[i], zero)));
-						}
-						else {
-							c2 = ctx.mkAnd(c2, ctx.mkEq(p2vars[i], zero));
-						}
-					}            
+			for(i = 0; i < p2vars.length; i++) {
+				if(((BoolExpr) model.eval(ctx.mkEq(p2vars[i], zero), true)).isFalse()) {
+					c2 = ctx.mkAnd(c2, ctx.mkNot(ctx.mkEq(p2vars[i], zero)));
+				}
+				else {
+					c2 = ctx.mkAnd(c2, ctx.mkEq(p2vars[i], zero));
+				}
+			}            
 
-					/*
+			/*
             p1 = ctx.mkAnd(c2, ctx.mkEq(payvars[0], model.getConstInterp(payvars[0])));
             p2 = ctx.mkAnd(c1, ctx.mkEq(payvars[1], model.getConstInterp(payvars[1])));
-					 */
+			*/
 
-					/*
+			/*
         	prstr = ctx.mkAnd(ctx.mkEq(payvars[0], model.getConstInterp(payvars[0])), ctx.mkEq(payvars[1], model.getConstInterp(payvars[1])));
-					 */
+			*/
 
-					//System.out.println(opt.Check()); 
-					//System.out.println(mx.getValue());
-					//System.out.println(my.getValue());
+			//System.out.println(opt.Check()); 
+			//System.out.println(mx.getValue());
+			//System.out.println(my.getValue());
 
-					/*
+			/*
 			System.out.println("--");
 			for(String v : eqs.keySet()) {
 				System.out.println(v + " " + eqs.get(v).get(j));
 			}
 			System.out.println("--");
-					 */
+			 */
 
-					//System.out.println("$$ dist1 " + dist1);
-					//System.out.println("$$ dist2 " + dist2);
+			//System.out.println("$$ dist1 " + dist1);
+			//System.out.println("$$ dist2 " + dist2);
 
 
-					dists.add(0,dist1);
-					dists.add(1,dist2);
-					strat.add(j,dists);
+			dists.add(0,dist1);
+			dists.add(1,dist2);
+			strat.add(j,dists);
 
-					j++;
-					s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
+			j++;
+			s.add(ctx.mkOr(ctx.mkNot(c1), ctx.mkNot(c2)));
 
-					//s.add(rstr);
-					//s.add(ctx.mkNot(p2));
-					//s.add(ctx.mkNot(p1));
-				}
-				end = new Date().getTime();
-				time = (end - start)/1000.000;
-				//System.out.println("Time: " + time); 
-				if(!indif) {
-					//System.out.println(j + " equilibrium(a)");
-				}
-				else {
-					//System.out.println(j-1 + " equilibrium(a)");
-					//System.out.println("## One of the players is indifferent. ##");
-				}
-				neq = j;
+			//s.add(rstr);
+			//s.add(ctx.mkNot(p2));
+			//s.add(ctx.mkNot(p1));
+		}
+		end = new Date().getTime();
+		time = (end - start)/1000.000;
+		//System.out.println("Time: " + time); 
+		if(!indif) {
+			//System.out.println(j + " equilibrium(a)");
+		}
+		else {
+			//System.out.println(j-1 + " equilibrium(a)");
+			//System.out.println("## One of the players is indifferent. ##");
+		}
+		neq = j;
 	}
 
 	public void addPayoffs() {
@@ -619,8 +619,7 @@ public String[] getLvp2() {
 	}
 
 	@Override
-	public String getSolverName()
-	{
+	public String getSolverName() {
 		return solverName;
 	}
 
diff --git a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
index d07ad5cf4..1b80f9d5d 100644
--- a/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
+++ b/prism/src/explicit/CSGLabeledPolytopesZ3Stack.java
@@ -152,12 +152,6 @@ private void initSolver() throws PrismException
 		}
 	}
 
-	@Override
-	public String getSolverName()
-	{
-		return solverName;
-	}
-
 	public void update(int nrows, int ncols, double[][] a, double[][] b) {
 		this.nrows = nrows;
 		this.ncols = ncols;
@@ -248,7 +242,7 @@ private void vMult() {
 		}
 	}
 
-	public void compEq() {
+	public void computeEquilibria() {
 		ArrayList<Distribution> dists;
 		Distribution dist1;
 		Distribution dist2;
@@ -368,7 +362,7 @@ public void compPayoffs() {
 	public double getDoubleValue(Model model, Expr expr) {
 		RatNum v1;
 		AlgebraicNum v2;
-		if(model.getConstInterp(expr) instanceof RatNum) {
+		if (model.getConstInterp(expr) instanceof RatNum) {
 			v1 = (RatNum) model.getConstInterp(expr);
 			return (Double) (v1.getBigIntNumerator().doubleValue() / v1.getBigIntDenominator().doubleValue());
 		}
@@ -381,6 +375,12 @@ else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 			return Double.NaN;
 	}
 
+	@Override
+	public String getSolverName()
+	{
+		return solverName;
+	}
+	
 	public ArrayList<ArrayList<Distribution>> getStrat() {
 		return strat;
 	}
diff --git a/prism/src/explicit/CSGSupportEnumeration.java b/prism/src/explicit/CSGSupportEnumeration.java
index b45753e8d..d779008ed 100644
--- a/prism/src/explicit/CSGSupportEnumeration.java
+++ b/prism/src/explicit/CSGSupportEnumeration.java
@@ -16,7 +16,7 @@ public interface CSGSupportEnumeration {
 	
 	public void setIndexes(ArrayList<ArrayList<Integer>> a);
 	
-	public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, HashMap<Integer, int[]> map, int s);
+	public EquilibriumResult computeEquilibria(BitSet supp, HashMap<Integer, int[]> map);
 	
 	public void computeConstraints(BitSet supp);
 	
@@ -28,6 +28,8 @@ public interface CSGSupportEnumeration {
 	
 	public void setAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> assertions);
 	
+	public void setMap(HashMap<Integer, int[]> map);
+	
 	public ArrayList<Distribution> getStrat();
 
 }
diff --git a/prism/src/explicit/CSGSupportEnumerationZ3.java b/prism/src/explicit/CSGSupportEnumerationZ3.java
index a9a10c6d8..8aa62395a 100644
--- a/prism/src/explicit/CSGSupportEnumerationZ3.java
+++ b/prism/src/explicit/CSGSupportEnumerationZ3.java
@@ -53,77 +53,64 @@ public class CSGSupportEnumerationZ3 implements CSGSupportEnumeration {
 	private Context ctx;
 	private Solver s;
 
-	private ArrayList<ArithExpr> payoffs;	
-	private ArrayList<ArrayList<ArithExpr>> strategies;
 	private HashMap<Integer, HashMap<Integer, ArithExpr>> assertions;
+	private ArrayList<ArrayList<ArithExpr>> strategies;
 	private ArrayList<ArrayList<Integer>> indexes;
-
+	private ArrayList<ArithExpr> payoffs;	
+	
 	private IntNum zero;
 	private IntNum one;
 
 	private BitSet players;
 	private BoolExpr support;
 
-	private int numPlayers;
+	private int numCoalitions;
 	private Params params;
 
 	private ArrayList<Distribution> strat;
 
-	private int ndigits = 9;
-
 	public CSGSupportEnumerationZ3() {
+		
+	}
+	
+	public CSGSupportEnumerationZ3(int[] maxActions, int numCoalitions) {
 		cfg = new HashMap<String, String>();
 		cfg.put("model", "true");
 		ctx = new Context(cfg);
-		s = ctx.mkSolver();        
-
+		s = ctx.mkSolver();
+		
 		params = ctx.mkParams();
 		params.add("timeout", 20);
 		s.setParameters(params);
-
+		
 		assertions = new HashMap<Integer, HashMap<Integer, ArithExpr>>();
 		strategies = new ArrayList<ArrayList<ArithExpr>>();
 		payoffs = new ArrayList<ArithExpr>();
 		players = new BitSet();
 		strat = new ArrayList<Distribution>();
-	}
-
-	public void init() {
-		s.reset();
-		s.setParameters(params);
-
-		players.clear();
-		players.set(0, numPlayers);
-		strategies.clear();
-		payoffs.clear();
+		
+		players.set(0, numCoalitions);
 		zero = ctx.mkInt(0);
-		one = ctx.mkInt(1);
-		ArithExpr cnstr1;
-		for(int p = 0; p < numPlayers; p++) {
-			cnstr1 = zero;			
-			strategies.add(p, new ArrayList<ArithExpr>());
-			payoffs.add(p, ctx.mkRealConst("v_" + p));
-			for(int a = 0; a < indexes.get(p).size(); a++) {
-				strategies.get(p).add(a, ctx.mkRealConst("p_" + p + "_" + a));
-				s.add(ctx.mkGe(strategies.get(p).get(a), zero));
-				s.add(ctx.mkLe(strategies.get(p).get(a), one));
-				cnstr1 = ctx.mkAdd(cnstr1, strategies.get(p).get(a));
+		one = ctx.mkInt(1);	
+		for (int c = 0; c < numCoalitions; c++) {
+			strategies.add(c, new ArrayList<ArithExpr>());
+			payoffs.add(c, ctx.mkRealConst("v_" + c));
+			for(int a = 0; a < maxActions[c]; a++) {
+				strategies.get(c).add(a, ctx.mkRealConst("p_" + c + "_" + a));
+				s.add(ctx.mkGe(strategies.get(c).get(a), zero));
+				s.add(ctx.mkLe(strategies.get(c).get(a), one));
 			}
-			s.add(ctx.mkEq(cnstr1, one));
-		}
-		//System.out.println(numPlayers);
-		//System.out.println(indexes);
-		//System.out.println(strategies);
+		} 
 	}
 
 	public void computeConstraints(BitSet supp) {
-		for(int p = 0; p < indexes.size(); p++) {
-			for(int a = 0; a < indexes.get(p).size(); a++) {
-				if(supp.get(indexes.get(p).get(a))) {
-					s.add(ctx.mkEq(assertions.get(p).get(a), payoffs.get(p)));
+		for(int c = 0; c < indexes.size(); c++) {
+			for(int a = 0; a < indexes.get(c).size(); a++) {
+				if(supp.get(indexes.get(c).get(a))) {
+					s.add(ctx.mkEq(assertions.get(c).get(a), payoffs.get(c)));
 				}
 				else {
-					s.add(ctx.mkLe(assertions.get(p).get(a), payoffs.get(p)));
+					s.add(ctx.mkLe(assertions.get(c).get(a), payoffs.get(c)));
 				}
 			}
 		}
@@ -131,43 +118,57 @@ public void computeConstraints(BitSet supp) {
 
 	public void computeSupport(BitSet supp, HashMap<Integer, int[]> map) {
 		support = ctx.mkTrue();
-		for(int p = 0; p < indexes.size(); p++) {
-			for(int a = 0; a < indexes.get(p).size(); a++) {
-				if(supp.get(indexes.get(p).get(a))) {
-					support = ctx.mkAnd(support, ctx.mkGt(strategies.get(p).get(a), zero));
+		for(int c = 0; c < indexes.size(); c++) {
+			for(int a = 0; a < indexes.get(c).size(); a++) {
+				if(supp.get(indexes.get(c).get(a))) {
+					support = ctx.mkAnd(support, ctx.mkGt(strategies.get(c).get(a), zero));
 				}
 				else {
-					support = ctx.mkAnd(support, ctx.mkEq(strategies.get(p).get(a), zero));
+					support = ctx.mkAnd(support, ctx.mkEq(strategies.get(c).get(a), zero));
 				}
 			}
 		}
 		s.add(support);
 	}
 
-	public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, HashMap<Integer, int[]> map, int st) {
+	public EquilibriumResult computeEquilibria(BitSet supp, HashMap<Integer, int[]> map) {
+		Model model;
+		EquilibriumResult result = new EquilibriumResult();
+		ArithExpr cnstr1;
+		Distribution d;
+		ArrayList<Double> eq = new ArrayList<>();
+		double v;
+		int a, c;
+		
 		s.push();
 		computeConstraints(supp);
 		computeSupport(supp, map);
+		// Sum variables in the supports to one (for each player)
+		for(c = 0; c < numCoalitions; c++) {
+			cnstr1 = zero;
+			for(a = 0; a < indexes.get(c).size(); a++) {
+				cnstr1 = ctx.mkAdd(cnstr1, strategies.get(c).get(a));
+			}
+			s.add(ctx.mkEq(cnstr1, one));
+		}
 		/*
 		System.out.println("-- to prove");
 		for(int i = 0; i < s.getNumAssertions(); i++) {
 			System.out.println(s.getAssertions()[i]);
 		}
-		 */
-		Model model;
-		ArrayList<Double> eq = new ArrayList<>();
-		Distribution d;
-		double v;
-
-		Status result = s.check();
-		if(result == Status.SATISFIABLE) {
+		*/
+		//System.out.println("\n%% " + supp);
+		Status status = s.check();
+		strat.clear();
+		if(status == Status.SATISFIABLE) {
 			model = s.getModel();
-			strat.clear();
-			for(int p = 0; p < numPlayers; p++) {
+			for(c = 0; c < numCoalitions; c++) {
 				d = new Distribution();
-				eq.add(p, getDoubleValue(model, payoffs.get(p)));
-				for (int a = 0; a < strategies.get(p).size(); a++) {
-					v = getDoubleValue(model, strategies.get(p).get(a));
+				eq.add(c, getDoubleValue(model, payoffs.get(c)));
+				//System.out.println("p" + p + ": " + getDoubleValue(model, payoffs.get(p)));
+				for (a = 0; a < strategies.get(c).size(); a++) {
+					v = getDoubleValue(model, strategies.get(c).get(a));
+					//System.out.println("p" + p + " -> " + a + " " + getDoubleValue(model, strategies.get(p).get(a)));
 					if (v > 0)
 						d.add(a, v);
 				}
@@ -175,9 +176,30 @@ public Pair<CSGResultStatus, ArrayList<Double>> computeEquilibria(BitSet supp, H
 			}
 		}
 		s.pop();
-		return new Pair<CSGResultStatus, ArrayList<Double>>((result == Status.SATISFIABLE)? CSGResultStatus.SAT : 
-			(result == Status.UNKNOWN)? CSGResultStatus.UNKNOWN :
-				CSGResultStatus.UNSAT, new ArrayList<Double>(eq));	
+		result.setStatus((status == Status.SATISFIABLE)? CSGResultStatus.SAT : (status == Status.UNKNOWN)? CSGResultStatus.UNKNOWN : CSGResultStatus.UNSAT);
+		result.setPayoffVector(new ArrayList<Double>(eq));
+		result.setStrategy(new ArrayList<Distribution>(strat));
+		return result;
+	}
+
+	public void translateAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> assertionsIdx, HashMap<Integer, int[]> map) {
+		assertions.clear();
+		ArithExpr sum, prod;
+		int a, c;
+		for(c = 0; c < assertionsIdx.keySet().size(); c++) {
+			assertions.put(c, new HashMap<Integer, ArithExpr>());
+			for(a = 0; a < assertionsIdx.get(c).keySet().size(); a++) {
+				sum = zero;
+				for(Pair<BitSet, Double> product : assertionsIdx.get(c).get(a)) {
+					prod = getRealValue(product.second);
+					for(int id = product.first.nextSetBit(0); id >= 0; id = product.first.nextSetBit(id + 1)) {
+						prod = ctx.mkMul(prod, strategies.get(map.get(id)[0]).get(map.get(id)[1]));
+					}
+					sum = ctx.mkAdd(sum, prod);
+				}
+				assertions.get(c).put(a, sum);
+			}
+		}
 	}
 
 	public double getDoubleValue(Model model, Expr expr) {
@@ -195,46 +217,32 @@ else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
 		else
 			return Double.NaN;
 	}
-
-	public void translateAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> assertionsIdx, HashMap<Integer, int[]> map) {
-		assertions.clear();
-		ArithExpr sum, prod;
-		int a, p;
-		for(p = 0; p < assertionsIdx.keySet().size(); p++) {
-			assertions.put(p, new HashMap<Integer, ArithExpr>());
-			for(a = 0; a < assertionsIdx.get(p).keySet().size(); a++) {
-				sum = zero;
-				for(Pair<BitSet, Double> product : assertionsIdx.get(p).get(a)) {
-					prod = getRealValue(product.second);
-					for(int id = product.first.nextSetBit(0); id >= 0; id = product.first.nextSetBit(id + 1)) {
-						prod = ctx.mkMul(prod, strategies.get(map.get(id)[0]).get(map.get(id)[1]));
-					}
-					sum = ctx.mkAdd(sum, prod);
-				}
-				assertions.get(p).put(a, sum);
-			}
-		}
-	}
-
+	
 	public ArithExpr getRealValue(double v) {
-		ArithExpr result;
-		result = ctx.mkReal((long) (Math.pow(10, ndigits) * v));
-		result = ctx.mkDiv(result, ctx.mkReal((long) (Math.pow(10, ndigits))));
+		ArithExpr result = null;
+		try {
+			result = ctx.mkReal(String.valueOf(v));
+		}
+		catch (Exception e) {
+			System.out.println("Error converting value " + v + " to a real.");
+			System.out.println("assertions: " + assertions);
+			e.printStackTrace();
+		}
 		return result;
 	}
 
+	public ArrayList<Distribution> getStrat() {
+		return new ArrayList<Distribution>(this.strat);
+	}
+	
 	public void setNumPlayers(int n) {
-		this.numPlayers = n;
+		this.numCoalitions = n;
 	}
 
 	public void setIndexes(ArrayList<ArrayList<Integer>> a) {
 		this.indexes = a;
 	}
 
-	public ArrayList<Distribution> getStrat() {
-		return new ArrayList<Distribution>(this.strat);
-	}
-
 	@Override
 	public void setGradient(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> gradient) {
 		// TODO Auto-generated method stub
@@ -247,4 +255,16 @@ public void setAssertions(HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSe
 
 	}
 
+	@Override
+	public void setMap(HashMap<Integer, int[]> map) {
+		// TODO Auto-generated method stub
+		
+	}
+
+	@Override
+	public void init() {
+		// TODO Auto-generated method stub
+		
+	}
+
 }

From 7ecc83397d4bd3d9843ce791032fe839eb144c88 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:25:45 +0100
Subject: [PATCH 26/30] Interface and class for computing correlated
 equilibria, auxiliary classes for results

---
 prism/src/explicit/CSGCorrelated.java         |  59 ++++
 prism/src/explicit/CSGCorrelatedZ3.java       | 284 ++++++++++++++++++
 prism/src/explicit/EquilibriumResult.java     |  63 ++++
 .../src/explicit/ModelCheckerResultMulti.java |  19 ++
 4 files changed, 425 insertions(+)
 create mode 100644 prism/src/explicit/CSGCorrelated.java
 create mode 100644 prism/src/explicit/CSGCorrelatedZ3.java
 create mode 100644 prism/src/explicit/EquilibriumResult.java
 create mode 100644 prism/src/explicit/ModelCheckerResultMulti.java

diff --git a/prism/src/explicit/CSGCorrelated.java b/prism/src/explicit/CSGCorrelated.java
new file mode 100644
index 000000000..efa8554a7
--- /dev/null
+++ b/prism/src/explicit/CSGCorrelated.java
@@ -0,0 +1,59 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
+package explicit;
+
+import java.util.ArrayList;
+import java.util.BitSet;
+import java.util.HashMap;
+
+public interface CSGCorrelated {
+	
+	/**
+	 * Computes correlated equilibria for a normal form game
+	 * 
+	 * @param utilities Utility table as a map from action indexes to utility arrays
+	 * @param ce_constraints An auxiliary mapping of actions to utilities (player i -> action a -> actions of -i -> utility) used to set the constraints for correlated equilibria 
+	 * @param strategies Array with individual actions for each player
+	 * @param ce_var_map Map for joint actions
+	 * @param crit Criterion (social-welfare = 3, fair = 4)
+	 */
+	public EquilibriumResult computeEquilibrium(HashMap<BitSet, ArrayList<Double>> utilities, 
+												ArrayList<ArrayList<HashMap<BitSet, Double>>> ce_constraints,
+												ArrayList<ArrayList<Integer>> strategies,
+												HashMap<BitSet, Integer> ce_var_map, int crit);
+	
+	/**
+	 * Gets the solver's name
+	 */
+	public String getSolverName();
+	
+	public void clear();
+		
+	public void printModel();
+	
+}
diff --git a/prism/src/explicit/CSGCorrelatedZ3.java b/prism/src/explicit/CSGCorrelatedZ3.java
new file mode 100644
index 000000000..5d59e2e29
--- /dev/null
+++ b/prism/src/explicit/CSGCorrelatedZ3.java
@@ -0,0 +1,284 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
+package explicit;
+
+import java.util.ArrayList;
+import java.util.BitSet;
+import java.util.HashMap;
+
+import com.microsoft.z3.AlgebraicNum;
+import com.microsoft.z3.ArithExpr;
+import com.microsoft.z3.BoolExpr;
+import com.microsoft.z3.Context;
+import com.microsoft.z3.Expr;
+import com.microsoft.z3.IntExpr;
+import com.microsoft.z3.Model;
+import com.microsoft.z3.Optimize;
+import com.microsoft.z3.RatNum;
+import com.microsoft.z3.RealExpr;
+import com.microsoft.z3.Status;
+import com.microsoft.z3.Version;
+
+import prism.PrismException;
+
+/**
+ * Z3-based implementation for correlated equilibria computation
+ * @author Gabriel Santos
+ *
+ */
+public class CSGCorrelatedZ3 implements CSGCorrelated {
+
+	private RealExpr[] vars;
+	private RealExpr[] payoff_vars;
+	private RealExpr obj_var;
+	private ArithExpr[] payoffs;
+	
+	private HashMap<String, String> cfg;
+	private Context ctx;
+	private Optimize s;
+	
+	private IntExpr zero;
+	private IntExpr one;
+	
+	private String name;
+	private int n_coalitions;
+	
+	/**
+	 * Creates a new CSGCorrelatedZ3 (without initialisation)
+	 */
+	public CSGCorrelatedZ3() {
+		cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		ctx = new Context(cfg);
+		s = ctx.mkOptimize();
+		name = Version.getFullVersion();
+	}
+	
+	/**
+	 * Creates a new CSGCorrelatedZ3
+	 * @param n_entries Number of entries in the utility table
+	 * @param n_coalitions Number of coalitions
+	 */
+	public CSGCorrelatedZ3(int n_entries, int n_coalitions) {
+		cfg = new HashMap<String, String>();
+		cfg.put("model", "true");
+		cfg.put("auto_config", "true");
+		ctx = new Context(cfg);
+		s = ctx.mkOptimize();
+		name = Version.getFullVersion();
+		zero = ctx.mkInt(0);
+		one = ctx.mkInt(1);
+		vars = new RealExpr[n_entries];
+		payoffs = new ArithExpr[n_coalitions];
+		this.n_coalitions = n_coalitions;
+		for (int i = 0; i < n_entries; i++) {
+			vars[i] = ctx.mkRealConst("v" + i);
+			s.Add(ctx.mkLe(vars[i], one));
+			s.Add(ctx.mkGe(vars[i], zero));
+		}
+		payoff_vars = new RealExpr[n_coalitions];
+		obj_var = ctx.mkRealConst("ob");
+	}
+	
+	public EquilibriumResult computeEquilibrium(HashMap<BitSet, ArrayList<Double>> utilities, 
+												ArrayList<ArrayList<HashMap<BitSet, Double>>> ce_constraints,
+												ArrayList<ArrayList<Integer>> strategies,
+												HashMap<BitSet, Integer> ce_var_map, int type) {
+		EquilibriumResult result = new EquilibriumResult();
+		ArrayList<Double> payoffs_result = new ArrayList<Double>();
+		ArrayList<Distribution> strategy_result = new ArrayList<Distribution>();
+		Distribution d = new Distribution();
+		ArithExpr expr;
+		BitSet is, js;
+		double u;
+		int c, q, r;
+		is = new BitSet();
+		js = new BitSet();
+		
+		s.Push();
+		expr = ctx.mkInt(0);
+		
+		// Builds a payoff expression for each player, and one for the sum of all payoffs
+		for (int i = 0; i < n_coalitions; i++) {
+			payoffs[i] = zero;
+		}
+		for (BitSet e : utilities.keySet()) {
+			u = 0.0;
+			for (c = 0; c < n_coalitions; c++) {
+				u += utilities.get(e).get(c);
+				payoffs[c] = ctx.mkAdd(payoffs[c], ctx.mkMul(vars[ce_var_map.get(e)], ctx.mkReal(String.valueOf(utilities.get(e).get(c)))));
+			}
+			expr = ctx.mkAdd(expr, ctx.mkMul(vars[ce_var_map.get(e)], ctx.mkReal(String.valueOf(u))));
+		}
+		for (c = 0; c < n_coalitions; c++) {
+			payoff_vars[c] = ctx.mkRealConst("p " + c);
+			s.Add(ctx.mkEq(payoff_vars[c], payoffs[c]));
+		}
+	
+		// In case of the fair variant (minimise the difference between the largest and smallest payoffs)
+		// we first need to add auxiliary constraints
+		// The default case is social-welfare, in which we just maximise the sum
+		switch (type) {
+			case CSGModelCheckerEquilibria.FAIR : {
+				RealExpr ph;
+				RealExpr pl;
+				ph = ctx.mkRealConst("ph"); // Highest payoff
+				pl = ctx.mkRealConst("pl"); // Lowest payoff
+				BoolExpr bh;
+				BoolExpr bl;
+				// Additional constraints for fair
+				for (int i = 0; i < n_coalitions; i++) {
+					bh = ctx.mkTrue();
+					bl = ctx.mkTrue();
+					for (int j = 0; j < n_coalitions; j++) {
+						if (i != j) {
+							bh = ctx.mkAnd(bh, ctx.mkGe(payoffs[i], payoffs[j]));
+							bl = ctx.mkAnd(bl, ctx.mkLe(payoffs[i], payoffs[j]));
+						}
+					}
+					s.Add(ctx.mkImplies(bh, ctx.mkEq(ph, payoffs[i])));
+					s.Add(ctx.mkImplies(bl, ctx.mkEq(pl, payoffs[i])));
+				}
+				s.MkMinimize(ctx.mkSub(ph, pl));
+				break;
+			}
+			default : {
+				// Primary objective is maximising the sum
+				s.Add(ctx.mkEq(obj_var, expr));
+				s.MkMaximize(expr);
+			}
+		}
+	
+		// Lower priority objectives of maximising the payoff of each player in decreasing order
+		for (c = 0; c < n_coalitions; c++) {
+			s.MkMaximize(payoffs[(c)]);
+		}
+		
+		// Constraints for correlated equilibria
+		for (c = 0; c < n_coalitions; c++) {
+			for (q = 0; q < strategies.get(c).size(); q++) {
+				expr = zero;
+				is.clear();
+				is.set(strategies.get(c).get(q));
+				for (r = 0; r < strategies.get(c).size(); r++) {
+					js.clear();
+					for (BitSet e : ce_constraints.get(c).get(q).keySet()) {
+						is.or(e);
+						js.or(e);
+						if (q != r) {
+							js.set(strategies.get(c).get(r));
+							expr = ctx.mkAdd(expr, ctx.mkMul(vars[ce_var_map.get(is)], 
+															 ctx.mkSub(ctx.mkReal(String.valueOf(utilities.get(is).get(c))), 
+																	   ctx.mkReal(String.valueOf(utilities.get(js).get(c))))));
+						}
+						is.andNot(e);
+						js.andNot(e);
+					}
+					if (q != r) {
+						s.Add(ctx.mkGe(expr, zero));
+					}
+				}
+			}
+		}
+		
+		// Sets unused variables to zero
+		for (c = utilities.size(); c < vars.length; c++) {
+			s.Add(ctx.mkEq(vars[c], zero));
+		}
+		
+		expr = ctx.mkInt(0);
+		for (c = 0; c < vars.length; c++) {
+			expr = ctx.mkAdd(expr, vars[c]);
+		}
+		s.Add(ctx.mkEq(expr, one));
+				
+		/*
+		for (BoolExpr e : s.getAssertions()) {
+			System.out.println(e);
+		} 
+		*/
+		
+		// If and optimal solution is found, set the values and strategies
+		if (s.Check() == Status.SATISFIABLE) {
+			for (c = 0; c < vars.length; c++) {
+				d.add(c, getDoubleValue(s.getModel(), vars[c]));
+			}
+			for (c = 0; c < payoff_vars.length; c++) {
+				payoffs_result.add(getDoubleValue(s.getModel(), payoff_vars[c]));
+			}
+			result.setStatus(CSGModelCheckerEquilibria.CSGResultStatus.SAT);
+			result.setPayoffVector(payoffs_result);
+			strategy_result.add(d);
+			result.setStrategy(strategy_result);
+		}
+		else {
+			result.setStatus(CSGModelCheckerEquilibria.CSGResultStatus.UNSAT);
+		}
+		
+		s.Pop();
+		return result;
+	}
+	
+	/**
+	 * Return a double value for a given expression (usually variable), converting from BigInt fractions
+	 * @param model The SMT model
+	 * @param expr The SMT expression
+	 * @return
+	 */
+	public double getDoubleValue(Model model, Expr expr) {
+		RatNum v1;
+		AlgebraicNum v2;
+		if(model.getConstInterp(expr) instanceof RatNum) {
+			v1 = (RatNum) model.getConstInterp(expr);
+			return (Double) (v1.getBigIntNumerator().doubleValue() / v1.getBigIntDenominator().doubleValue());
+		}
+		else if (model.getConstInterp(expr) instanceof AlgebraicNum) {
+			v2 = (AlgebraicNum) model.getConstInterp(expr);
+			v1 = v2.toUpper(12);
+			return (Double) (v1.getBigIntNumerator().doubleValue() / v1.getBigIntDenominator().doubleValue());
+		}
+		else
+			return Double.NaN;
+	}
+
+	public String getSolverName() {
+		return name;
+	}
+
+	@Override
+	public void clear() {
+		
+	}
+	
+	@Override
+	public void printModel() {
+		// TODO Auto-generated method stub
+		
+	}
+	
+}
diff --git a/prism/src/explicit/EquilibriumResult.java b/prism/src/explicit/EquilibriumResult.java
new file mode 100644
index 000000000..6d81d5915
--- /dev/null
+++ b/prism/src/explicit/EquilibriumResult.java
@@ -0,0 +1,63 @@
+//==============================================================================
+//	
+//	Copyright (c) 2002-
+//	Authors:
+//	* Dave Parker <david.parker@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//	
+//------------------------------------------------------------------------------
+//	
+//	This file is part of PRISM.
+//	
+//	PRISM is free software; you can redistribute it and/or modify
+//	it under the terms of the GNU General Public License as published by
+//	the Free Software Foundation; either version 2 of the License, or
+//	(at your option) any later version.
+//	
+//	PRISM is distributed in the hope that it will be useful,
+//	but WITHOUT ANY WARRANTY; without even the implied warranty of
+//	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//	GNU General Public License for more details.
+//	
+//	You should have received a copy of the GNU General Public License
+//	along with PRISM; if not, write to the Free Software Foundation,
+//	Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+//	
+//==============================================================================
+
+package explicit;
+
+import java.util.ArrayList;
+import explicit.CSGModelCheckerEquilibria.CSGResultStatus;
+
+public class EquilibriumResult {
+
+	private CSGResultStatus status;
+	private ArrayList<Double> payoffVector;
+	private ArrayList<Distribution> strategy;
+
+	public CSGResultStatus getStatus() {
+		return status;
+	}
+
+	public void setStatus(CSGResultStatus status) {
+		this.status = status;
+	}
+
+	public ArrayList<Double> getPayoffVector() {
+		return payoffVector;
+	}
+
+	public void setPayoffVector(ArrayList<Double> payoffVector) {
+		this.payoffVector = payoffVector;
+	}
+
+	public ArrayList<Distribution> getStrategy() {
+		return strategy;
+	}
+
+	public void setStrategy(ArrayList<Distribution> strategy) {
+		this.strategy = strategy;
+	}
+	
+}
\ No newline at end of file
diff --git a/prism/src/explicit/ModelCheckerResultMulti.java b/prism/src/explicit/ModelCheckerResultMulti.java
new file mode 100644
index 000000000..96a3d11aa
--- /dev/null
+++ b/prism/src/explicit/ModelCheckerResultMulti.java
@@ -0,0 +1,19 @@
+package explicit;
+
+import java.util.BitSet;
+import java.util.Map;
+
+public class ModelCheckerResultMulti extends ModelCheckerResult
+{
+	// Constructor
+	public ModelCheckerResultMulti() 
+	{
+		super();
+	}
+	
+	public Map<BitSet, ModelCheckerResultMulti> subGames = null;
+	public double[][] solnMulti = null;
+	public BitSet D = null;
+	public BitSet E = null;
+	
+}

From 5b3474182c558d3647bc0d838f54cbcdb3cd800a Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:26:58 +0100
Subject: [PATCH 27/30] Changes to CSGModelChecker to handle multi-player
 equilibria

---
 prism/src/explicit/CSGModelChecker.java | 199 ++++++++++++++++--------
 1 file changed, 134 insertions(+), 65 deletions(-)

diff --git a/prism/src/explicit/CSGModelChecker.java b/prism/src/explicit/CSGModelChecker.java
index ee870aa2f..cdab04ebb 100644
--- a/prism/src/explicit/CSGModelChecker.java
+++ b/prism/src/explicit/CSGModelChecker.java
@@ -74,7 +74,6 @@ public class CSGModelChecker extends ProbModelChecker
 
 	protected HashMap<Integer, Distribution> adv; // probably shouldn't be global or be here at all
 
-
 	protected double scaleFactor = getSettings().getDouble(PrismSettings.PRISM_ZS_LP_SCALE_FACTOR);
 
 	// Info about the current coalitions for model checking
@@ -94,6 +93,8 @@ public class CSGModelChecker extends ProbModelChecker
 	protected int maxRows;
 	/** For the current coalition, the max number of columns in the matrix game across all CSG states */
 	protected int maxCols;
+	/** For each coalition, the max number of actions across all CSG states */
+	protected int[] maxNumActions;
 	/** For each coalition, the average number of actions across all CSG states */
 	protected double[] avgNumActions;
 
@@ -117,6 +118,8 @@ public class CSGModelChecker extends ProbModelChecker
 	/** True if all matrix values are equal */
 	protected boolean allEqual;
 
+	/** Which solver to use for linear programming */
+	protected String lpSolver;
 
 	protected long timerVal;
 
@@ -131,6 +134,7 @@ public CSGModelChecker(PrismComponent parent) throws PrismException
 		probabilities = new HashMap<BitSet, ArrayList<Distribution>>();
 		actions = new ArrayList<ArrayList<String>>();
 		strategies = new ArrayList<ArrayList<Integer>>();
+		lpSolver = getSettings().getString(PrismSettings.PRISM_CSG_LPSOLVER);
 	}
 
 	// Numerical computation functions
@@ -138,6 +142,7 @@ public CSGModelChecker(PrismComponent parent) throws PrismException
 	/**
 	 * Compute next-state probabilities.
 	 * i.e. compute the probability of being in a state in {@code target} in the next step.
+	 * 
 	 * @param csg The CSG
 	 * @param target Target states
 	 * @param min1 Min or max probabilities for player 1 (true=min, false=max)
@@ -219,6 +224,7 @@ public ModelCheckerResult computeNextProbs(CSG csg, BitSet target, boolean min1,
 	 * Compute bounded reachability/until probabilities.
 	 * i.e. compute the min/max probability of reaching a state in {@code target},
 	 * within k steps, and while remaining in states in {@code remain}.
+	 * 
 	 * @param csg The CSG
 	 * @param remain Remain in these states (optional: null means "all")
 	 * @param target Target states
@@ -255,6 +261,7 @@ public ModelCheckerResult computeBoundedReachProbs(CSG csg, BitSet remain, BitSe
 	 * Compute until probabilities.
 	 * i.e. compute the min/max probability of reaching a state in {@code target},
 	 * and while remaining in states in {@code remain}.
+	 * 
 	 * @param csg The CSG
 	 * @param remain Remain in these states (optional: null means "all")
 	 * @param target Target states
@@ -271,6 +278,7 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 	 * Compute bounded until probabilities.
 	 * i.e. compute the min/max probability of reaching a state in {@code target},
 	 * within k steps, and while remaining in states in {@code remain}.
+	 * 
 	 * @param csg The CSG
 	 * @param remain Remain in these states (optional: null means "all")
 	 * @param target Target states
@@ -288,12 +296,13 @@ public ModelCheckerResult computeBoundedUntilProbs(CSG csg, BitSet remain, BitSe
 		precomp = false;
 		res = computeUntilProbs(csg, remain, target, k, min1, min2, coalition);
 		precomp = tmp;
-		return res;	
+		return res;
 	}
 
 	/**
 	 * Compute (possibly bounded) reachability probabilities.
 	 * i.e. compute the min/max probability of reaching a state in {@code target}.
+	 * 
 	 * @param csg The CSG
 	 * @param target Target states
 	 * @param k Bound
@@ -371,6 +380,7 @@ public ModelCheckerResult computeReachProbs(CSG csg, BitSet target, boolean min1
 	 * Compute (possibly bounded) reachability/until probabilities.
 	 * i.e. compute the min/max probability of reaching a state in {@code target},
 	 * and while remaining in states in {@code remain}.
+	 * 
 	 * @param csg The CSG
 	 * @param remain Remain in these states (optional: null means "all")
 	 * @param target Target states
@@ -454,6 +464,7 @@ public ModelCheckerResult computeUntilProbs(CSG csg, BitSet remain, BitSet targe
 
 	/**
 	 * Compute reachability probabilities using value iteration.
+	 * 
 	 * @param csg The CSG
 	 * @param no Probability 0 states
 	 * @param yes Probability 1 states
@@ -467,9 +478,8 @@ public ModelCheckerResult computeReachProbsValIter(CSG csg, BitSet no, BitSet ye
 		if ((genStrat || exportAdv) && bounded) {
 			throw new PrismException("Strategy synthesis for bounded properties is not supported yet.");
 		}
-		ModelCheckerResult res = new ModelCheckerResult();
 		LpSolve lp;
-		ArrayList<ArrayList<Double>> mgame = new ArrayList<ArrayList<Double>>();
+		ArrayList<ArrayList<Double>> mgame;
 		List<List<List<Map<BitSet, Double>>>> lstrat = null;
 		List<Map<BitSet, Double>> kstrat = null;
 		Map<Integer, BitSet> mmap = null;
@@ -482,6 +492,7 @@ public ModelCheckerResult computeReachProbsValIter(CSG csg, BitSet no, BitSet ye
 		if (genStrat || exportAdv) {
 			mmap = new HashMap<Integer, BitSet>();
 			kstrat = new ArrayList<Map<BitSet, Double>>();
+			// player -> iteration -> state -> indexes -> value
 			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>();
 			lstrat.add(0, new ArrayList<List<Map<BitSet, Double>>>());
 			lstrat.get(0).add(0, new ArrayList<Map<BitSet, Double>>());
@@ -518,30 +529,11 @@ public ModelCheckerResult computeReachProbsValIter(CSG csg, BitSet no, BitSet ye
 			for (s = 0; s < csg.getNumStates(); s++) {
 				if (!known.get(s)) {
 					mgame = buildMatrixGame(csg, null, mmap, ntmp, s, min);
-					try {
-						if (min)
-							lp.resizeLp(0, maxCols + 1);
-						else
-							lp.resizeLp(0, maxRows + 1);
-
-					} catch (LpSolveException e) {
-						throw new PrismException("Exception raised by lpSolve when resizing linear program for state " + s + " at iteration " + k);
-					}
 					nsol[s] = val(lp, mgame, kstrat, mmap, s, false, min);
 					// player -> iteration -> state -> indexes -> value
-					if (bounded && (genStrat || exportAdv)) {
-						if (lstrat.get(0).get(k).get(s) == null || !lstrat.get(0).get(k - 1).get(s).equals(kstrat.get(s))) {
-							lstrat.get(0).get(k).set(s, kstrat.get(s));
-						} else {
-							lstrat.get(0).get(k).set(s, lstrat.get(0).get(k - 1).get(s));
-						}
-					} else if (genStrat || exportAdv) {
-						if (lstrat.get(0).get(0).get(s) == null) {
-							lstrat.get(0).get(0).set(s, kstrat.get(s));
-						} else if (!lstrat.get(0).get(0).get(s).equals(kstrat.get(s))) {
-							lstrat.get(0).get(0).set(s, kstrat.get(s));
-						}
-					}
+					if (genStrat || exportAdv) {
+						updateStrategy(kstrat, lstrat, k, s, bounded);
+					} 
 				} else if (genStrat || exportAdv) {
 					lstrat.get(0).get(0).add(s, null);
 				}
@@ -558,6 +550,7 @@ public ModelCheckerResult computeReachProbsValIter(CSG csg, BitSet no, BitSet ye
 		}
 		mainLog.println("\nValue iteration converged after " + k + " iterations.");
 		timer = System.currentTimeMillis() - timer;
+		ModelCheckerResult res = new ModelCheckerResult();
 		res.soln = nsol;
 		res.numIters = k;
 		if (genStrat || exportAdv)
@@ -569,6 +562,7 @@ public ModelCheckerResult computeReachProbsValIter(CSG csg, BitSet no, BitSet ye
 	/**
 	 * Compute instantaneous expected rewards,
 	 * i.e. compute the min/max expected reward of the states after {@code k} steps.
+	 * 
 	 * @param csg The CSG
 	 * @param csgRewards The rewards
 	 * @param coalition The coalition of players which define player 1
@@ -635,6 +629,7 @@ public ModelCheckerResult computeInstantaneousRewards(CSG csg, CSGRewards csgRew
 	/**
 	 * Compute expected cumulative rewards,
 	 * i.e. compute the min/max expected reward accumulated within {@code k} steps.
+	 * 
 	 * @param csg The CSG
 	 * @param csgRewards The rewards
 	 * @param coalition The coalition of players which define player 1
@@ -662,6 +657,7 @@ public ModelCheckerResult computeCumulativeRewards(CSG csg, CSGRewards csgReward
 	/**
 	 * Compute expected total rewards,
 	 * i.e. compute the min/max expected reward accumulated.
+	 * 
 	 * @param csg The CSG
 	 * @param rewards The rewards
 	 * @param coalition The coalition of players which define player 1
@@ -745,6 +741,7 @@ public ModelCheckerResult computeTotalRewards(CSG csg, CSGRewards rewards, Coali
 	/**
 	 * Compute expected reachability rewards.
 	 * i.e. compute the min/max reward accumulated to reach a state in {@code target}.
+	 * 
 	 * @param csg The CSG
 	 * @param coalition The coalition of players which define player 1
 	 * @param rewards The rewards
@@ -772,6 +769,7 @@ public ModelCheckerResult computeReachRewards(CSG csg, CSGRewards rewards, BitSe
 	/**
 	 * Compute expected reachability rewards (infinite if not reaching target).
 	 * i.e. compute the min/max reward accumulated to reach a state in {@code target}.
+	 * 
 	 * @param csg The CSG
 	 * @param coalition The coalition of players which define player 1
 	 * @param rewards The rewards
@@ -915,6 +913,7 @@ public ModelCheckerResult computeReachRewardsInfinity(CSG csg, Coalition coaliti
 	/**
 	 * Compute expected reachability rewards (cumnulated value if not reaching target).
 	 * i.e. compute the min/max reward accumulated to reach a state in {@code target}.
+	 * 
 	 * @param csg The CSG
 	 * @param coalition The coalition of players which define player 1
 	 * @param rewards The rewards
@@ -1007,6 +1006,7 @@ public ModelCheckerResult computeReachRewardsCumulative(CSG csg, Coalition coali
 
 	/**
 	 * Compute expected reachability rewards using value iteration.
+	 * 
 	 * @param csg The CSG
 	 * @param rewards The rewards
 	 * @param target Target states
@@ -1037,7 +1037,8 @@ public ModelCheckerResult computeReachRewardsValIter(CSG csg, CSGRewards rewards
 		if (genStrat || exportAdv) {
 			mmap = new HashMap<Integer, BitSet>();
 			kstrat = new ArrayList<Map<BitSet, Double>>();
-			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>(1);
+			// player -> iteration -> state -> indexes -> value
+			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>();
 			lstrat.add(0, new ArrayList<List<Map<BitSet, Double>>>());
 			lstrat.get(0).add(0, new ArrayList<Map<BitSet, Double>>());
 			for (i = 0; i < csg.getNumStates(); i++) {
@@ -1083,29 +1084,11 @@ public ModelCheckerResult computeReachRewardsValIter(CSG csg, CSGRewards rewards
 			for (s = 0; s < csg.getNumStates(); s++) {
 				if (unknown.get(s)) {
 					mgame = buildMatrixGame(csg, rewards, mmap, ntmp, s, min);
-					try {
-						if (min)
-							lp.resizeLp(0, maxCols + 1);
-						else
-							lp.resizeLp(0, maxRows + 1);
-					} catch (LpSolveException e) {
-						throw new PrismException("Exception raised by lpSolve when resizing linear program for state " + s + " at iteration " + k);
-					}
 					nsol[s] = val(lp, mgame, kstrat, mmap, s, true, min);
 					nsol[s] += rewards.getStateReward(s);
-					if (bounded && (genStrat || exportAdv)) {
+					if (genStrat || exportAdv) {
 						// player -> iteration -> state -> indexes -> value
-						if (lstrat.get(0).get(k).get(s) == null || !lstrat.get(0).get(k - 1).get(s).equals(kstrat.get(s))) {
-							lstrat.get(0).get(k).set(s, kstrat.get(s));
-						} else {
-							lstrat.get(0).get(k).set(s, lstrat.get(0).get(k - 1).get(s));
-						}
-					} else if (genStrat || exportAdv) {
-						if (lstrat.get(0).get(0).get(s) == null) {
-							lstrat.get(0).get(0).set(s, kstrat.get(s));
-						} else if (!lstrat.get(0).get(0).get(s).equals(kstrat.get(s))) {
-							lstrat.get(0).get(0).set(s, kstrat.get(s));
-						}
+						updateStrategy(kstrat, lstrat, k, s, bounded);
 					}
 				}
 			}
@@ -1131,6 +1114,7 @@ public ModelCheckerResult computeReachRewardsValIter(CSG csg, CSGRewards rewards
 	
 	/**
 	 * Deal with two-player bounded probabilistic reachability formulae
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions A list of two coalitions
 	 * @param exprs The list of objectives
@@ -1142,16 +1126,17 @@ public ModelCheckerResult computeReachRewardsValIter(CSG csg, CSGRewards rewards
 	 * @throws PrismException
 	 */
 	public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<ExpressionTemporal> exprs, BitSet[] targets,
-			BitSet[] remain, int[] bounds, boolean min) throws PrismException
+			BitSet[] remain, int[] bounds, int eqType, int crit, boolean min) throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeBoundedEquilibria(csg, coalitions, null, exprs, targets, remain, bounds, min);
+		res = csgeq.computeBoundedEquilibria(csg, coalitions, null, exprs, targets, remain, bounds, eqType, crit, min);
 		return res;
 	}
 
 	/**
 	 * Deal with two-player probabilistic reachability formulae
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions A list of two coalitions
 	 * @param targets The list of sets of target states
@@ -1160,17 +1145,18 @@ public ModelCheckerResult computeProbBoundedEquilibria(CSG csg, List<Coalition>
 	 * @return
 	 * @throws PrismException
 	 */
-	public ModelCheckerResult computeProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, boolean min)
-			throws PrismException
+	public ModelCheckerResult computeProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, 
+			int eqType, int crit, boolean min) throws PrismException 
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeReachEquilibria(csg, coalitions, null, targets, remain, min);
+		res = csgeq.computeReachEquilibria(csg, coalitions, null, targets, remain, eqType, crit, min);
 		return res;
 	}
 
 	/**
 	 * Deal with two-player bounded reachability rewards
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions A list of two coalitions
 	 * @param rewards The list of reward structures
@@ -1181,16 +1167,17 @@ public ModelCheckerResult computeProbReachEquilibria(CSG csg, List<Coalition> co
 	 * @throws PrismException
 	 */
 	public ModelCheckerResult computeRewBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs,
-			int[] bounds, boolean min) throws PrismException
+			int[] bounds, int eqType, int crit, boolean min) throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeBoundedEquilibria(csg, coalitions, rewards, exprs, null, null, bounds, min);
+		res = csgeq.computeBoundedEquilibria(csg, coalitions, rewards, exprs, null, null, bounds, eqType, crit, min);
 		return res;
 	}
 
 	/**
 	 * Deal with two-player reachability rewards formulae
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions A list of two coalitions
 	 * @param rewards The list of reward structures
@@ -1199,17 +1186,63 @@ public ModelCheckerResult computeRewBoundedEquilibria(CSG csg, List<Coalition> c
 	 * @return
 	 * @throws PrismException
 	 */
-	public ModelCheckerResult computeRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, boolean min)
+	public ModelCheckerResult computeRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, 
+			int eqType, int crit, boolean min)
 			throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeReachEquilibria(csg, coalitions, rewards, targets, null, min);
+		res = csgeq.computeReachEquilibria(csg, coalitions, rewards, targets, null, eqType, crit, min);
 		return res;
 	}
 
+	/**
+	 * Deal with multi-player bounded probabilistic formulae
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param targets
+	 * @param remain
+	 * @param bounds
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeMultiProbBoundedEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, 
+			int [] bounds, int eqType, int crit, boolean min) throws PrismException {
+		ModelCheckerResult res = new ModelCheckerResult();
+		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
+		res = csgeq.computeMultiBoundedEquilibria(csg, coalitions, null, null, null, null, bounds, eqType, crit, min);
+		return res;
+	}
+	
+	/**
+	 * Deal with multi-player bounded reward formulae
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param exprs
+	 * @param bounds
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeMultiRewBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs, 
+			int[] bounds, int eqType, int crit, boolean min) throws PrismException {
+		ModelCheckerResult res = new ModelCheckerResult();
+		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
+		res = csgeq.computeMultiBoundedEquilibria(csg, coalitions, rewards, exprs, null, null, bounds, eqType, crit, min);
+		return res;
+	}
+	
 	/**
 	 * Deal with multi-player probabilistic reachability formulae
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions The list of coalitions
 	 * @param targets The list of sets of target states
@@ -1218,17 +1251,19 @@ public ModelCheckerResult computeRewReachEquilibria(CSG csg, List<Coalition> coa
 	 * @return
 	 * @throws PrismException
 	 */
-	public ModelCheckerResult computeMultiProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, boolean min)
+	public ModelCheckerResult computeMultiProbReachEquilibria(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, 
+			int eqType, int crit, boolean min)
 			throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeMultiReachEquilibria(csg, coalitions, null, targets, remain, min);
+		res = csgeq.computeMultiReachEquilibria(csg, coalitions, null, targets, remain, eqType, crit, min);
 		return res;
 	}
 
 	/**
 	 * Deal with multi-player reachability rewards formulae
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions The list of coalitions
 	 * @param rewards The list of reward structures
@@ -1237,17 +1272,19 @@ public ModelCheckerResult computeMultiProbReachEquilibria(CSG csg, List<Coalitio
 	 * @return
 	 * @throws PrismException
 	 */
-	public ModelCheckerResult computeMultiRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, boolean min)
+	public ModelCheckerResult computeMultiRewReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, 
+			int eqType, int crit, boolean min)
 			throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
-		res = csgeq.computeMultiReachEquilibria(csg, coalitions, rewards, targets, null, min);
+		res = csgeq.computeMultiReachEquilibria(csg, coalitions, rewards, targets, null, eqType, crit, min);
 		return res;
 	}
 
 	/**
 	 * Deal with computing mixed bounded and unbounded equilibria.
+	 * 
 	 * @param csg The CSG
 	 * @param coalitions The list of coalitions
 	 * @param rewards The list of reward structures
@@ -1261,7 +1298,7 @@ public ModelCheckerResult computeMultiRewReachEquilibria(CSG csg, List<Coalition
 	 * @throws PrismException
 	 */
 	public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs,
-			BitSet bounded, BitSet[] targets, BitSet[] remain, int[] bounds, boolean min) throws PrismException
+			BitSet bounded, BitSet[] targets, BitSet[] remain, int[] bounds, int eqType, int crit, boolean min) throws PrismException
 	{
 		ModelCheckerResult res = new ModelCheckerResult();
 		CSGModelCheckerEquilibria csgeq = new CSGModelCheckerEquilibria(this);
@@ -1459,9 +1496,9 @@ public ModelCheckerResult computeMixedEquilibria(CSG csg, List<Coalition> coalit
 			}
 			res = csgeq.computeReachEquilibria(csg_rm, coalitions, csg_rew_rm, filtered_targets, null);			
 			*/
-			res = csgeq.computeReachEquilibria(product.productModel, coalitions, newrewards, newtargets, null, min);
+			res = csgeq.computeReachEquilibria(product.productModel, coalitions, newrewards, newtargets, null, eqType, crit, min);
 		} else {
-			res = csgeq.computeReachEquilibria(product.productModel, coalitions, null, newtargets, newremain, min);
+			res = csgeq.computeReachEquilibria(product.productModel, coalitions, null, newtargets, newremain, eqType, crit, min);
 		}
 		return res;
 	}
@@ -1526,7 +1563,7 @@ public BitSet apreXY(CSG csg, BitSet x, BitSet y) throws PrismException
 	}
 
 	/*
-	 * Eventually B
+	 * Eventually b
 	 */
 	public BitSet AF(CSG csg, BitSet b) throws PrismException
 	{
@@ -1721,6 +1758,32 @@ public BitSet G(CSG csg, BitSet b) throws PrismException
 
 	// Utility methods for CSG solving
 	
+	/**
+	 * Update the strategy
+	 * 
+	 * @param kstrat The strategies for all states computed in iteration k 
+	 * @param lstrat The overall strategy
+	 * @param k Iteration k, if bounded
+	 * @param s The index of the state
+	 * @param bounded
+	 */
+	public void updateStrategy(List<Map<BitSet, Double>> kstrat, List<List<List<Map<BitSet, Double>>>> lstrat, int k, int s, boolean bounded) {
+		// player -> iteration -> state -> indexes -> value
+		if (bounded) {
+			if (lstrat.get(0).get(k).get(s) == null || !lstrat.get(0).get(k - 1).get(s).equals(kstrat.get(s))) {
+				lstrat.get(0).get(k).set(s, kstrat.get(s));
+			} else {
+				lstrat.get(0).get(k).set(s, lstrat.get(0).get(k - 1).get(s));
+			}
+		} else {
+			if (lstrat.get(0).get(0).get(s) == null) {
+				lstrat.get(0).get(0).set(s, kstrat.get(s));
+			} else if (!lstrat.get(0).get(0).get(s).equals(kstrat.get(s))) {
+				lstrat.get(0).get(0).set(s, kstrat.get(s));
+			}
+		}
+	}
+	
 	/**
 	 * Compute and store information about coalitions (for a zero-sum problem):
 	 * - numPlayers and numCoalitions
@@ -1782,6 +1845,7 @@ public void buildCoalitions(CSG csg, Coalition coalition, boolean min) throws Pr
 	 * Find the max size of the matrix game needed across any CSG state,
 	 * for the current coalition (as stored in coalitionIndexes).
 	 * Also compute/report the average number of actions for each coalition across all CSG states.
+	 * 
 	 * @param csg The CSG
 	 */
 	public void findMaxRowsCols(CSG csg)
@@ -1813,6 +1877,7 @@ public void findMaxRowsCols(CSG csg)
 
 	/**
 	 * Build a matrix game with the transition distributions for state s. 
+	 * 
 	 * @param csg The CSG
 	 * @param s Index of state to build matrix game for 
 	 * @return
@@ -2089,6 +2154,10 @@ public double val(LpSolve lp, ArrayList<ArrayList<Double>> mgame, List<Map<BitSe
 				return res;
 			} else {
 				try {
+					if (min)
+						lp.resizeLp(0, maxCols + 1);
+					else
+						lp.resizeLp(0, maxRows + 1);
 					buildLPLpsolve(lp, mgame, rew, min);
 				} catch (LpSolveException e1) {
 					throw new PrismException("Exception raised by lpSolve when building linear program for state  " + s);
@@ -2366,7 +2435,7 @@ public void filterStates(CSG csg, CSGSimple csg_rm, List<CSGRewards> rewards, Li
 		for (int c = 0; c < csg.getNumChoices(s); c++) { // gets all choices
 			Distribution d = new Distribution();
 			csg.forEachTransition(s, c, (__, t, pr) -> { // gets all targets
-				if (!map_state.keySet().contains(t)) { //if not yet explored
+				if (!map_state.keySet().contains(t)) { // if not yet explored
 					map_state.put(t, csg_rm.addState());
 					filterStates(csg, csg_rm, rewards, rew_rm, t);
 				}

From 2524dacbcc02e692f7a72a1d929e4f31671c6e48 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:28:32 +0100
Subject: [PATCH 28/30] Changes to CSGModelCheckerEquilibria to include
 correlated, fair and (many) other things

---
 .../explicit/CSGModelCheckerEquilibria.java   | 2218 ++++++++++++-----
 1 file changed, 1591 insertions(+), 627 deletions(-)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index db293b10e..12c6c7e85 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -3,7 +3,7 @@
 //	Copyright (c) 2002-
 //	Authors:
 //	* Dave Parker <david.parker@comlab.ox.ac.uk> (University of Oxford)
-//  	* Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
+//  * Gabriel Santos <gabriel.santos@cs.ox.ac.uk> (University of Oxford)
 //	
 //------------------------------------------------------------------------------
 //	
@@ -28,8 +28,6 @@
 package explicit;
 
 import java.math.BigDecimal;
-import java.nio.file.Path;
-import java.nio.file.Paths;
 import java.util.ArrayList;
 import java.util.Arrays;
 import java.util.BitSet;
@@ -39,23 +37,20 @@
 import java.util.Iterator;
 import java.util.List;
 import java.util.Map;
+import java.util.Map.Entry;
 import java.util.Set;
+import java.util.concurrent.Callable;
+import java.util.concurrent.ExecutorService;
+import java.util.concurrent.Executors;
+import java.util.concurrent.Future;
 import java.util.stream.Collectors;
 
 import org.apache.commons.math3.util.Precision;
 
 import explicit.CSGModelCheckerEquilibria.CSGResultStatus;
-import explicit.ProbModelChecker.TermCrit;
 import explicit.rewards.CSGRewards;
-import explicit.rewards.CSGRewardsSimple;
 import explicit.rewards.MDPRewards;
-import parser.State;
-import parser.VarList;
 import parser.ast.Coalition;
-import parser.ast.Declaration;
-import parser.ast.DeclarationBool;
-import parser.ast.DeclarationInt;
-import parser.ast.Expression;
 import parser.ast.ExpressionTemporal;
 import prism.Pair;
 import prism.PrismComponent;
@@ -79,49 +74,73 @@ public class CSGModelCheckerEquilibria extends CSGModelChecker {
 	private ArrayList<ArrayList<ArrayList<Pair<BitSet, Double>>>> products;
 	//[id payoff player i]
 	private ArrayList<Integer> payoffs;	
-	
+	/** Gradient of the objective function (multi-player Nash) */
 	private HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>> gradient;
 	//{action j -> [player i, action j (index)]}
 	private HashMap<Integer, int[]> mapActionIndex;
 	
+	/** Supports for a normal form game (indexed by coalition) */
 	private ArrayList<ArrayList<BitSet>> supports;
+	/** Pure supports for a normal form game (indexed by coalition) */
+	private ArrayList<BitSet> psupports;
+	/** All (joint-action) supports for a given normal form game */
 	private ArrayList<BitSet> allSupports;
 	
+	
+	/** Exclusive to correlated equilibria */
+	private ArrayList<ArrayList<HashMap<BitSet, Double>>> ceConstraints;
+	private HashMap<BitSet, Integer> ceVarMap;
+	
+	/** Dominated actions */
 	protected BitSet[] dominated;
+	/** Dominating actions */
 	protected BitSet[] dominating;
+	/** Set with all the players */
 	protected BitSet players;
 	
-	//smt solver for labelled polytopes 
-	protected CSGLabeledPolytopes eqslps;
-	//smt solver for support enumeration
-	protected CSGSupportEnumeration eqssmt;
-	
+	/** SMT solver for labelled polytopes */
+	protected CSGLabeledPolytopes smtLabeleldPolytopes;
+	/** SMT solver for support enumeration */
+	protected CSGSupportEnumeration smtSupportEnumeration;
+	/** Numerical solver for support enumeration */
+	protected CSGSupportEnumeration nlpSupportEnumeration;
+	/** Solver for correlated equilibria */
+	protected CSGCorrelated ceSolver;
+	/** Name of the SMT solver */
 	protected String smtSolver;
-		
+	/** Whether to check for the assumption for equilibria model checking */	
 	protected boolean assumptionCheck = true;
+	/** Types and criteria for equilibria */
+	public static final int NASH = 1;
+	public static final int CORR = 2;
+	public static final int SWEQ = 3;
+	public static final int FAIR = 4;
 	
+	/** Different status for SMT equilibria computation */
 	public enum CSGResultStatus {
 		SAT, UNKNOWN, UNSAT;
 	}
 	
+	/**
+	 * Create a new CSGModelCheckerEquilibria, inherit basic state from parent (unless null).
+	 */
 	public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		super(parent);
 		players = new BitSet();
+		psupports = new ArrayList<BitSet>();
 		supports = new ArrayList<ArrayList<BitSet>>();
-		allSupports =  new ArrayList<BitSet>();
-				
+		allSupports =  new ArrayList<BitSet>();			
 		mapActionIndex = new HashMap<Integer, int[]>();
 		products = new ArrayList<ArrayList<ArrayList<Pair<BitSet, Double>>>>();
 		assertions = new HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>>();
+		ceConstraints = new ArrayList<ArrayList<HashMap<BitSet, Double>>>();
+		ceVarMap = new HashMap<BitSet, Integer>();
 		gradient = new HashMap<Integer, HashMap<Integer, ArrayList<Pair<BitSet, Double>>>>();
 		payoffs = new ArrayList<Integer>();
-		
 		mdpmc = new MDPModelChecker(parent);
 		mdpmc.setVerbosity(0);
-		mdpmc.setSilentPrecomputations(true);
-		
+		mdpmc.setSilentPrecomputations(true);		
 		assumptionCheck = getSettings().getBoolean(PrismSettings.PRISM_EQ_ASSUMPTION_CHECK);
-
 		smtSolver = getSettings().getString(PrismSettings.PRISM_SMT_SOLVER);
 		switch (smtSolver) {
 			case "Z3":
@@ -133,16 +152,48 @@ public CSGModelCheckerEquilibria(PrismComponent parent) throws PrismException {
 		}
 	}
 	
-	public void setSolver() throws PrismException {
-		switch (smtSolver) {
-			case "Z3":
-				eqslps = new CSGLabeledPolytopesZ3Stack(maxRows, maxCols);
+
+	/**
+	 * Sets the solver according to the settings and the equilibrium type. 
+	 * 
+	 * @param eqType Correlated/Nash
+	 * @return Name
+	 * @throws PrismException
+	 */
+	public String setSolver(int eqType) throws PrismException {
+		String name = null;
+		switch (eqType) {
+			case CORR:
+				switch (lpSolver) {
+					case "Z3":
+						ceSolver = new CSGCorrelatedZ3(maxRows * maxCols, numCoalitions);
+						name = ceSolver.getSolverName();
+						break;
+					default: throw new PrismException("Unsupported solver for correlated equilibria computation");
+				}
 				break;
-			case "Yices":
-				eqslps = new CSGLabeledPolytopesYicesStack();
+			default: {
+				switch (smtSolver) {
+					case "Z3":
+						smtLabeleldPolytopes = new CSGLabeledPolytopesZ3Stack(maxRows, maxCols);
+						name = smtLabeleldPolytopes.getSolverName();
+						break;
+					case "Yices":
+						smtLabeleldPolytopes = new CSGLabeledPolytopesYicesStack();
+						name = smtLabeleldPolytopes.getSolverName();
+				}
+			}
 		}
+		return name;
 	}
 
+	/**
+	 * Compute and store information about coalitions (for a nonzero-sum problem):
+	 * 
+	 * @param csg The CSG
+	 * @param coalitions The list of coalitions
+	 * @throws PrismException
+	 */
 	public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismException {
 		if (coalitions == null || coalitions.isEmpty())
 			throw new PrismException("Coalitions must not be empty");
@@ -179,6 +230,9 @@ public void buildCoalitions(CSG csg, List<Coalition> coalitions) throws PrismExc
 		players.set(0, numCoalitions);
 	}
 	
+	/*
+	 * Builds and stores all supports as BitSets of action indexes. 
+	 */
 	public void buildAllSupports() {
 		BitSet support;
 		for (int p = 0; p < numCoalitions; p++) {
@@ -196,6 +250,12 @@ public void buildAllSupports() {
 		}
 	}
 	
+	/**
+	 * Auxiliary method for building the set of supports. 
+	 * 
+	 * @param supp Current support
+	 * @param p Player index
+	 */
 	public void buildAllSupportsAux(BitSet supp, int p) {
 		for (BitSet s : supports.get(p)) {
 			BitSet curr = (BitSet) supp.clone();
@@ -210,6 +270,13 @@ public void buildAllSupportsAux(BitSet supp, int p) {
 		}		
 	}
 
+	/**
+	 * Builds all supports for a specific player.
+	 * 
+	 * @param supp Current support
+	 * @param p Player index
+	 * @param a Action index
+	 */
 	public void buildSupportsPlayer(BitSet supp, int p, int a) {
 		BitSet gt0 = (BitSet) supp.clone(); 
 		if (!dominated[p].get(strategies.get(p).get(a))) {
@@ -230,6 +297,46 @@ public void buildSupportsPlayer(BitSet supp, int p, int a) {
 		}	
 	}
 	
+	/**
+	 * Finds maximum and average number of actions for all coalitions.
+	 * 
+	 * @param csg The CSG
+	 */
+	public void findMaxAvgAct(CSG csg) {
+		String max = "(";
+		String avg = "(";
+		int c, p, n, s;
+		maxRows = 0;
+		maxCols = 0;
+		avgNumActions = new double[numCoalitions];
+		Arrays.fill(avgNumActions, 0.0);
+		maxNumActions  = new int[numCoalitions];
+		Arrays.fill(maxNumActions, 0);
+		for (s = 0; s < csg.getNumStates(); s++) {
+			for (c = 0; c < numCoalitions; c++) {
+				n = 1;
+				for (p = coalitionIndexes[c].nextSetBit(0); p >= 0; p = coalitionIndexes[c].nextSetBit(p + 1)) {
+					n *= csg.getIndexesForPlayer(s, p).cardinality();
+				}
+				maxNumActions[c] = (maxNumActions[c] < n)? n : maxNumActions[c];
+				avgNumActions[c] += n;
+			}
+		}
+		for (c = 0; c < numCoalitions; c++) {
+			avgNumActions[c] /= csg.getNumStates();
+			max += (c < numCoalitions -1)? maxNumActions[c] + "," : maxNumActions[c] + ")";
+			avg += (c < numCoalitions -1)? PrismUtils.formatDouble2dp(avgNumActions[c]) + "," : PrismUtils.formatDouble2dp(avgNumActions[c]) + ")";
+		}
+		mainLog.println("Max/avg (actions): " + max + "/" + avg);
+	}
+	
+	/**
+	 * Finds dominated actions for a specific player.
+	 * 
+	 * @param p Player index
+	 * @return
+	 * @throws PrismException
+	 */
 	public BitSet findDominated(int p) throws PrismException {
 		Pair<BitSet, Double> pair1, pair2;
 		BitSet domi = new BitSet();
@@ -263,6 +370,13 @@ public BitSet findDominated(int p) throws PrismException {
 		return domi;
 	}
 	
+	/**
+	 * Finds dominating actions for a specific player.
+	 * 
+	 * @param p Player index
+	 * @return
+	 * @throws PrismException
+	 */
 	public BitSet findDominating(int p) throws PrismException {
 		Pair<BitSet, Double> pair1, pair2;
 		BitSet domi = new BitSet();
@@ -295,6 +409,12 @@ public BitSet findDominating(int p) throws PrismException {
 		return domi;
 	}
 	
+	/**
+	 * Finds row and column indexes for the maximum entry in a matrix.
+	 * 
+	 * @param a Matrix
+	 * @return
+	 */
 	public int[] findMaxIndexes(double[][] a) {
 		int result[] = new int[2];
 		result[0] = 0;
@@ -312,6 +432,150 @@ public int[] findMaxIndexes(double[][] a) {
 		return result;
 	}
 	
+	/**
+	 * Checks whether all entries in the utility table are zero.
+	 * 
+	 * @return
+	 */
+	public boolean checkAllZeroEntries() {
+		boolean allzero = true;
+		for (BitSet entry : utilities.keySet()) {
+			for (int p = 0; p < numCoalitions; p++) {
+				allzero = allzero && Double.compare(utilities.get(entry).get(p), 0.0) == 0;
+				if (!allzero)
+					break;
+			}
+			if (!allzero)
+				break;
+		}
+		return allzero;
+	}
+	
+	/**
+	 * Finds the SWNE for when just one player has choices. 
+	 * 
+	 * @param mmap Index map
+	 * @param strats Overall strategy
+	 * @param eqstrat Strategy for the current state
+	 * @param active Active player
+	 * @return
+	 */
+	public double[][] findSWNEOnePlayer(List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats, List<Map<BitSet, Double>> eqstrat, BitSet active) {
+		BitSet support = null;
+		double[][] result;
+		double sumt, sumv, v;
+		int p1, p2;
+		result = new double[1][numCoalitions];
+		p1 = active.nextSetBit(0);
+		v = Double.NEGATIVE_INFINITY;
+		sumv = Double.NEGATIVE_INFINITY;
+		sumt = Double.NEGATIVE_INFINITY;
+		for (BitSet entry : utilities.keySet()) {
+			sumv = 0.0;
+			for (p2 = 0; p2 < numCoalitions; p2++) {
+				sumv += utilities.get(entry).get(p2); // computes sum of utilities
+			}
+			if (Double.compare(utilities.get(entry).get(p1), v) > 0) { // maximizes for player who has a choice
+				support = entry;
+				sumt = 0.0;
+				v = utilities.get(entry).get(p1);
+				for (p2 = 0; p2 < numCoalitions; p2++) {
+					result[0][p2] = utilities.get(entry).get(p2);
+					sumt += utilities.get(entry).get(p2); // sum of the utilities for the selected entry
+				}
+			}
+			else if (Double.compare(utilities.get(entry).get(p1), v) == 0 && Double.compare(sumv, sumt) > 0) { // case utility for player is the same but sum is higher
+				support = entry;
+				sumt = 0.0;
+				for (p2 = 0; p2 < numCoalitions; p2++) {
+					result[0][p2] = utilities.get(entry).get(p2);
+					sumt += utilities.get(entry).get(p2);
+				}
+			}
+		}
+		if (genStrat || exportAdv) {
+			eqstrat = new ArrayList<Map<BitSet, Double>>();
+			extractStrategyFromSupport(mmap, eqstrat, support);
+			strats.add(eqstrat);
+		}
+		return result;
+	}
+	
+	/**
+	 * Extracts the SWNE for when there is only one support.
+	 * 
+	 * @param mmap Index map
+	 * @param strats Overall strategy
+	 * @param eqstrat 
+	 * @return
+	 */
+	public double[][] findSWNEUniqueSupport(List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats, List<Map<BitSet, Double>> eqstrat) {
+		double[][] result;
+		result = new double[1][numCoalitions];
+		for (BitSet entry : allSupports) {
+			for (int p = 0; p < numCoalitions; p++) {
+				result[0][p] = utilities.get(entry).get(p);
+			}
+			if (genStrat || exportAdv) {
+				eqstrat = new ArrayList<Map<BitSet, Double>>();
+				extractStrategyFromSupport(mmap, eqstrat, entry);
+				strats.add(eqstrat);
+			}
+		}
+		return result;
+	}
+	
+	/**
+	 * Extracts the strategy for a given support.
+	 * 
+	 * @param mmap Index map
+	 * @param eqstrat Strategy for the current state
+	 * @param support Support
+	 */
+	public void extractStrategyFromSupport(List<Map<Integer, BitSet>> mmap, List<Map<BitSet, Double>> eqstrat, BitSet support) {
+		BitSet indx = new BitSet();
+		int a, i, p;
+		for (p = 0; p < numCoalitions; p++) {
+			indx.clear();
+			for (a = 0; a < strategies.get(p).size(); a++) {
+				indx.set(strategies.get(p).get(a));
+			}
+			indx.and(support);
+			i = indx.nextSetBit(0);
+			eqstrat.add(p, new HashMap<BitSet, Double>());
+			eqstrat.get(p).put(mmap.get(p).get(strategies.get(p).indexOf(i)), 1.0); // indexOf should be changed
+		}
+	}
+	
+	/**
+	 * Extract the strategy for the case of an unique equilibrium.
+	 * 
+	 * @param eq Equilibria
+	 * @param mmap Index map
+	 * @return
+	 */
+	public ArrayList<Map<BitSet, Double>> extractStrategyFromEquilibrium(EquilibriumResult eq, List<Map<Integer, BitSet>> mmap) {
+		ArrayList<Map<BitSet, Double>> eqstrat = new ArrayList<Map<BitSet, Double>>();
+		for (int p = 0; p < numCoalitions; p++) {
+			eqstrat.add(p, new HashMap<BitSet, Double>());
+			for (int t : eq.getStrategy().get(p).getSupport()) {
+				eqstrat.get(p).put(mmap.get(p).get(t), eq.getStrategy().get(p).get(t));
+			}
+		}
+		return eqstrat;
+	}
+	
+	/**
+	 * Build info needed for the utility table to solve a CSG state s. 
+	 * 
+	 * @param csg The CSG
+	 * @param rewards List of rewards
+	 * @param mmap Index map
+	 * @param val Current values for each state
+	 * @param s State index
+	 * @param min Whether minimising/maximising
+	 * @throws PrismException
+	 */
 	public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, double[][] val, int s, boolean min) throws PrismException {
 		Map<BitSet, Integer> imap = new HashMap<BitSet, Integer>();
 		BitSet jidx;
@@ -322,13 +586,16 @@ public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, B
 		int c, i, p, t;
 		int[] joint;
 		int[] idle = new int[numPlayers];
+		ceVarMap.clear();
 		actions.clear();
+		psupports.clear();
 		strategies.clear();
 		utilities.clear();
 		varIndex = 0;
 		Arrays.fill(idle, -1);
 		for (c = 0; c < numCoalitions; c++) {
 			actions.add(c, new ArrayList<String>());
+			psupports.add(c, new BitSet());
 			strategies.add(c, new ArrayList<Integer>());
 		}
 		for (t = 0; t < csg.getNumChoices(s); t++) {
@@ -353,6 +620,7 @@ public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, B
 					if(!imap.keySet().contains(tmp)) {
 						act = "";
 						strategies.get(c).add(varIndex);
+						psupports.get(c).set(varIndex);
 				    	if (mmap != null) 
 				    		mmap.get(c).put(strategies.get(c).size() - 1, (BitSet) tmp.clone());
 						for (i = tmp.nextSetBit(0); i >= 0; i = tmp.nextSetBit(i + 1)) {
@@ -369,28 +637,55 @@ public void buildStepGame(CSG csg, List<CSGRewards> rewards, List<Map<Integer, B
 				}	
 			}
 			utilities.put(jidx, new ArrayList<Double>());
+			ceVarMap.put(jidx, utilities.keySet().size() - 1);
 			for (c = 0; c < numCoalitions; c++) {
 				v = 0.0;
-				for (Iterator<Map.Entry<Integer, Double>> iter = csg.getTransitionsIterator(s, t); iter.hasNext(); ) {
-					Map.Entry<Integer, Double> e = iter.next();
-					v += e.getValue() * val[c][e.getKey()];
-				}
+				for (int d : csg.getChoice(s, t).getSupport()) {
+					if (!Double.isNaN(val[c][d])) {
+						v += csg.getChoice(s, t).get(d) * val[c][d];
+					}
+					else {
+						mainLog.println("val[c][d]: " + val[c][d]);
+						mainLog.println("\n## state " + s);
+						mainLog.println("-- strategies " + strategies);
+						mainLog.println("-- actions " + actions);
+						mainLog.println("-- utilities " + utilities);
+						throw new PrismException("Error in building game for state " + s);
+					} 
+				} 
 				if (rewards != null) {
 					if (rewards.get(c) != null)
 						v += rewards.get(c).getTransitionReward(s, t);		
 				}
-				v = Precision.round(v, 12, BigDecimal.ROUND_FLOOR);
+				v = Precision.round(v, 12, BigDecimal.ROUND_HALF_EVEN);
 				utilities.get(jidx).add(c, (min)? -1.0 * v : v); // might have to add min (v, 1.0) due to assertions for probabilistic
 			}
 		}	
 		//System.out.println("-- imap " + imap);
-		//System.out.println("\n## state " + s);
-		//System.out.println("-- strategies " + strategies);
-		//System.out.println("-- actions " + actions);
-		//System.out.println("-- utilities " + utilities);
+		//if (s == csg.getFirstInitialState()) {
+			//System.out.println("\n## state " + s);
+			//System.out.println("-- strategies " + strategies);
+			//System.out.println("-- actions " + actions);
+			//System.out.println("-- utilities " + utilities);
+			//System.out.println("-- mmap " + mmap);
+		//}
 	}
 	
-	public ArrayList<ArrayList<ArrayList<Double>>> buildBiMatrixGame(CSG csg, CSGRewards r1, CSGRewards r2, List<Map<Integer, BitSet>> mmap,  List<ArrayList<Integer>> nmap, double[][] val, int s, boolean min) throws PrismException {
+	/**
+	 * Builds a bimatrix game (two-player case). 
+	 * 
+	 * @param csg The CSG
+	 * @param r1 Rewards for the first coalition
+	 * @param r2 Rewards for the second coalition
+	 * @param mmap Index map
+	 * @param nmap Reduced index map
+	 * @param val Current values for each state 
+	 * @param s State index
+	 * @param min Whether minimising/maximising
+	 * @return
+	 * @throws PrismException
+	 */
+	public ArrayList<ArrayList<ArrayList<Double>>> buildBimatrixGame(CSG csg, CSGRewards r1, CSGRewards r2, List<Map<Integer, BitSet>> mmap,  List<ArrayList<Integer>> nmap, double[][] val, int s, boolean min) throws PrismException {
 		ArrayList<ArrayList<ArrayList<Double>>> bmgame = new ArrayList<ArrayList<ArrayList<Double>>>();
 		ArrayList<CSGRewards> rewards = null;
 		BitSet action = new BitSet();
@@ -450,11 +745,17 @@ public ArrayList<ArrayList<ArrayList<Double>>> buildBiMatrixGame(CSG csg, CSGRew
 		return bmgame;
 	}
 	
+	/**
+	 * Clear various structures used in model checking.
+	 * 
+	 */
 	public void clear() {
+		// Would be better to clear the internal arrays/maps
 		supports.clear();
 		allSupports.clear();
 		products.clear();
 		assertions.clear();
+		ceConstraints.clear();
 		gradient.clear();
 		payoffs.clear();
 		mapActionIndex.clear();
@@ -462,6 +763,7 @@ public void clear() {
 			supports.add(c, new ArrayList<BitSet>());
 			products.add(c, new ArrayList<ArrayList<Pair<BitSet, Double>>>());
 			assertions.put(c, new HashMap<Integer, ArrayList<Pair<BitSet, Double>>>());
+			ceConstraints.add(c, new ArrayList<HashMap<BitSet, Double>>());
 			gradient.put(c, new HashMap<Integer, ArrayList<Pair<BitSet, Double>>>());
 			for(int a = 0; a < strategies.get(c).size(); a++) {
 				products.get(c).add(a, new ArrayList<Pair<BitSet, Double>>());
@@ -474,16 +776,19 @@ public void clear() {
 		}
 	}
 	
+	/**
+	 * Builds info used in multi-player equilibria (Nash and Correlated).
+	 * 
+	 * @throws PrismException
+	 */
 	public void computeAssertions() throws PrismException {
 		int c, q;
 		BitSet ps;
 		BitSet acts = new BitSet();
 		for (c = 0; c < numCoalitions; c++) {
-			//System.out.println("\n-- player " + c + " ");
         	ps = (BitSet) players.clone();
         	ps.clear(c);
         	for (q = 0; q < strategies.get(c).size(); q++) {
-            	//System.out.println("-- action " + q);
         		acts.clear();
         		acts.set(strategies.get(c).get(q));
         		assertions.get(c).put(q, prodAction(acts, ps, q, c));
@@ -495,7 +800,6 @@ public void computeAssertions() throws PrismException {
 		System.out.println("-- strategies ");
 		System.out.println(strategies);		
 		
-		
 		System.out.println("-- assertions ");
 		for (c = 0; c < numCoalitions; c++) {
 			System.out.println("--- player " + c);
@@ -503,9 +807,8 @@ public void computeAssertions() throws PrismException {
         		System.out.println("---- action " + q + " " + assertions.get(c).get(q));
 		}
 		
-		/*
-		//System.out.println("-- gradient ");
-		//System.out.println(gradient);
+		System.out.println("-- gradient ");
+		System.out.println(gradient);
 		System.out.println("-- map ");
 		for (int i : map.keySet()) {
 			System.out.println(i + "= " + Arrays.toString(map.get(i)));
@@ -513,6 +816,16 @@ public void computeAssertions() throws PrismException {
 		*/
 	}
 	
+	/**
+	 * 
+	 * 
+	 * @param prod
+	 * @param sp
+	 * @param act
+	 * @param p
+	 * @return
+	 * @throws PrismException
+	 */
 	public ArrayList<Pair<BitSet, Double>> prodAction(BitSet prod, BitSet sp, int act, int p) throws PrismException {
 		prodAction(new Pair<BitSet, Double>(new BitSet(), 0.0), prod, sp, act, p);
 		ArrayList<Pair<BitSet, Double>> sum = new ArrayList<Pair<BitSet, Double>>();		
@@ -523,6 +836,16 @@ public ArrayList<Pair<BitSet, Double>> prodAction(BitSet prod, BitSet sp, int ac
 		return sum;
 	}
 	
+	/**
+	 * 
+	 * 
+	 * @param expr
+	 * @param prod
+	 * @param sp
+	 * @param act
+	 * @param p
+	 * @throws PrismException
+	 */
 	public void prodAction(Pair<BitSet, Double> expr, BitSet prod, BitSet sp, int act, int p) throws PrismException {
 		BitSet set;
 		BitSet curr = (BitSet) sp.clone();
@@ -566,6 +889,14 @@ else if(products.get(p).get(act) == null)
 		}
 	}
 	
+	/**
+	 * 
+	 * 
+	 * @param csg
+	 * @param target
+	 * @param n
+	 * @return
+	 */
 	public double[][] computeBoundedReachProbs(CSG csg, BitSet target, int n) {
 		double[][] sol = new double[n][csg.getNumStates()];
 		double[] sol1 = new double[csg.getNumStates()];
@@ -595,7 +926,23 @@ public double[][] computeBoundedReachProbs(CSG csg, BitSet target, int n) {
 		return sol;
 	} 
 	
-	public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs, BitSet[] targets, BitSet[] remain, int[] bounds, boolean min) throws PrismException {
+	/**
+	 * Deal with two-player bounded equilibria.
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param exprs
+	 * @param targets
+	 * @param remain
+	 * @param bounds
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs, BitSet[] targets, BitSet[] remain, int[] bounds, int eqType, int crit, boolean min) throws PrismException {
 		if (genStrat || exportAdv) {
 			throw new PrismException("Strategy synthesis for bounded properties is not supported yet.");
 		}
@@ -607,8 +954,7 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
 		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
 		double[][] val = new double[coalitions.size()][csg.getNumStates()];
-		double[][] eq;
-		double[] sw;
+		double[] eq;
 		double[] r = new double[csg.getNumStates()];
 		int i, j, n1, n2, k, s;
 		boolean rew;
@@ -618,8 +964,7 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 		
 		buildCoalitions(csg, coalitions);
 		findMaxRowsCols(csg);
-		setSolver();
-		mainLog.println("Starting bounded equilibria computation (solver=" + eqslps.getSolverName() + ")...");
+		mainLog.println("Starting bounded equilibria computation (solver=" + setSolver(eqType) + ")...");
 		dominated = new BitSet[numCoalitions];
 		dominating = new BitSet[numCoalitions];
 		
@@ -636,11 +981,10 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 				}
 			}
 			for (s = 0; s < csg.getNumStates(); s++) {
-				eq = stepEquilibria(csg, null, null, null, eqslps, null, sol, s, min);
-				sw = swne(eq, null, min);
-				tmp[0][s] = sw[1];
-				tmp[1][s] = sw[2];
-				r[s] = sw[1] + sw[2];
+				eq = stepEquilibriaTwoPlayer(csg, null, null, null, sol, s, eqType, crit, rew, min);
+				tmp[0][s] = eq[1];
+				tmp[1][s] = eq[2];
+				r[s] = eq[1] + eq[2];
 			}
 			mainLog.println("\nCoalition results (initial state): (" + tmp[0][csg.getFirstInitialState()] + "," + tmp[1][csg.getFirstInitialState()] + ")");
 			res.soln = r;
@@ -740,10 +1084,9 @@ public ModelCheckerResult computeBoundedEquilibria(CSG csg, List<Coalition> coal
 							if (!(exprs.get(i).getOperator() == ExpressionTemporal.R_C))
 								newRewards.set(i, null);
 						}
-						eq = stepEquilibria(csg, newRewards.get(0), newRewards.get(1), null, eqslps, null, sol, s, min);	
-						sw = swne(eq, null, min);
-						tmp[0][s] = sw[1];
-						tmp[1][s] = sw[2];
+						eq = stepEquilibriaTwoPlayer(csg, newRewards, null, null, sol, s, eqType, crit, rew, min);	
+						tmp[0][s] = eq[1];
+						tmp[1][s] = eq[2];
 					} 
 					else {
 						if (targets[0].get(s) && targets[1].get(s)) {
@@ -771,10 +1114,9 @@ else if(!phi1[2].get(s)) {
 							tmp[1][s] = 0.0;
 						}
 						else {
-							eq = stepEquilibria(csg, null, null, null, eqslps, null, sol, s, min);
-							sw = swne(eq, null, min);
-							tmp[0][s] = sw[1];
-							tmp[1][s] = sw[2];
+							eq = stepEquilibriaTwoPlayer(csg, null, null, null, sol, s, eqType, crit, rew, min);
+							tmp[0][s] = eq[1];
+							tmp[1][s] = eq[2];
 						}
 					}
 				}
@@ -841,271 +1183,166 @@ else if (n1 == 0) {
 		return res;		
 	}
 
-	public ModelCheckerResult computeMultiReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, BitSet[] remain, boolean min) throws PrismException {
+	/**
+	 * Deal with multi-player bounded equilibria (unfinished).
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param exprs
+	 * @param targets
+	 * @param remain
+	 * @param bounds
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeMultiBoundedEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, List<ExpressionTemporal> exprs, BitSet[] targets, BitSet[] remain, int[] bounds, int eqType, int crit, boolean min) throws PrismException {
+		mainLog.println("\n# Running bounded multi-player equilibria...\n");
+		if (genStrat || exportAdv) {
+			throw new PrismException("Strategy synthesis for bounded properties is not yet supported");
+		}
 		ModelCheckerResult res = new ModelCheckerResult();
-		Declaration[] goals = new Declaration[coalitions.size()];
-		//Map<BitSet, BitSet> common = new HashMap<BitSet, BitSet>();
-		List<List<List<Map<BitSet, Double>>>> lstrat = null;
-		List<List<Map<BitSet, Double>>> sstrat = null;
 		List<Map<Integer, BitSet>> mmap = null;
-		Set<BitSet> games = new HashSet<BitSet>();
-		BitSet unsat = new BitSet();
-		BitSet ps;
 		double[][] sol;
 		double[][] val;
 		double[][] tmp;
 		double[][] eq;
 		double[] r;
 		double[] sw;
-		int i, j, k, n, p, s, t, v;
+		long timeTaken;
 		boolean done, rew;
+		int c, k, s, t = -1;
 		
+		sol = new double[coalitions.size()][csg.getNumStates()];
+		val = new double[coalitions.size()][csg.getNumStates()];
+		tmp = new double[coalitions.size()][csg.getNumStates()];
+		r = new double[csg.getNumStates()];
+
 		rew = rewards != null;
 		
 		buildCoalitions(csg, coalitions);
 		dominated = new BitSet[numCoalitions];
 		dominating = new BitSet[numCoalitions];
-		
-		VarList newvarlist = (VarList) csg.getVarList().clone();
-		
-		for (p = 0; p < coalitions.size(); p++) {
-			ps = (BitSet) players.clone();
-			ps.clear(p);
-			goals[p] = new Declaration("_" + p, new DeclarationBool());
-			buildSubGames(games, ps, p);
-			newvarlist.addVar(goals[p].getName(), goals[p].getDeclType(), 0, csg.getConstantValues());
-		}
-		games.add((BitSet) players.clone());
-		unsat.set(0, csg.getNumStates());		
-		for (BitSet subgame : games) {
-			//BitSet intersec = new BitSet();
-			//intersec.set(0, csg.getNumStates()); // intersec only seems to be used to define common, which later does not seem to be used
-			for (p = 0; p < coalitions.size(); p++) {
-				unsat.andNot(targets[p]);
-			//	if (subgame.get(p))
-			//		intersec.and(targets[p]); 
-			//	else
-			//		intersec.andNot(targets[p]);
-			}
-			//common.put(subgame, intersec); // common does not seem to be used afterwards
-		} 
-		
-		//System.out.println("-- common " + common);
-		
-		CSGSimple newmodel = new CSGSimple();
-		newmodel.copyPlayerInfo(csg);
-		newmodel.setActions(csg.getActions());
-		newmodel.setIndexes(csg.getIndexes());
-		newmodel.setIdles(csg.getIdles());
-		
-		List<State> newstatelist = new ArrayList<State>();
-		BitSet explored = new BitSet();
-		BitSet isubgame = new BitSet();
-		
-		s = csg.getFirstInitialState();
-		
-		State initial = new State(csg.getVarList().getNumVars() + numCoalitions);
-		for (v = 0; v < csg.getVarList().getNumVars(); v++) {
-			initial.setValue(v, csg.getStatesList().get(s).varValues[v]);
-		}
-		
-		Map<Integer, Integer> extmap = new HashMap<Integer, Integer>();
-				
-		if (unsat.get(s)) {
-			for (p = 0; p < numCoalitions; p++) {
-				initial.setValue(newvarlist.getIndex(goals[p].getName()), false);
-			}	
-		}
-		else {	
-			for (p = 0; p < numCoalitions; p++) {
-				if (targets[p].get(s)) {
-					initial.setValue(newvarlist.getIndex(goals[p].getName()), true);
-					isubgame.set(p);
-				}
-				else {
-					initial.setValue(newvarlist.getIndex(goals[p].getName()), false);
-				}
-			}
-		}
-		
-		//System.out.println("-- isubgame " + isubgame);
-		
-		mainLog.println("\nBuilding extended model...");
-
-		Map<Integer, Integer> nomap = new HashMap<Integer, Integer>();	
-		Map<BitSet, BitSet> subgames = new HashMap<BitSet, BitSet>();
-		
-		n = newmodel.addState();
-		newstatelist.add(n , initial);
-		newmodel.addInitialState(n);
-		
-		newmodel.setVarList(newvarlist);
-		newmodel.setStatesList(newstatelist);
-
-		nomap.put(n, s);
-		extmap.put(initial.hashCode(), n);
-		explored.set(n);
-		exploreSat(csg, newmodel, nomap, extmap, subgames, newstatelist, newvarlist, goals, targets, explored, isubgame, n);
-		
-		//System.out.println("-- nomap " + nomap);
-		
-		/*
-		for (BitSet subset : common.keySet()) {
-			for (s = common.get(subset).nextSetBit(0); s >= 0; s = common.get(subset).nextSetBit(s + 1)) {
-				subgames.put(subset, new BitSet());
-				subgames.get(subset).set(onmap.get(s));
-				exploreSat(csg, newmodel, subgames, onmap, newstatelist, newvarlist, goals, targets, subset, explored, onmap.get(s));
-			}
-		}
-		*/
-		
-		System.out.println("-- subgames " + subgames);
-
-		Path currentRelativePath = Paths.get("");
-		String path = currentRelativePath.toAbsolutePath().toString();		
-		PrismFileLog pflog = new PrismFileLog(path + "/newmodel.dot");
-		newmodel.exportToDotFile(pflog, null, true);
-	
-		pflog = new PrismFileLog(path + "/model.dot");
-		csg.exportToDotFile(pflog, null, true);
-		
-		mainLog.print("\n" + newmodel.infoStringTable() + "\n");
+		findMaxAvgAct(csg);
 				
-		sol = new double[coalitions.size()][newmodel.getNumStates()];
-		val = new double[coalitions.size()][newmodel.getNumStates()];
-		tmp = new double[coalitions.size()][newmodel.getNumStates()];
-		r = new double[newmodel.getNumStates()];
-				
-		List<CSGRewards> newrewards = null;
 		if (rew) {
-			newrewards = new ArrayList<CSGRewards>();
-			for (p = 0; p < numCoalitions; p++) {
-				newrewards.add(p, new CSGRewardsSimple(newmodel.getNumStates()));
+			t = exprs.get(0).getOperator();
+			for (int i = 1; i < exprs.size(); i++) {
+				if (t != exprs.get(i).getOperator())
+					throw new PrismException("Properties with mixed operators are not yet supported");
 			}
-			for (s = 0;  s < newmodel.getNumStates(); s++) {
-				for (p = 0; p < numCoalitions; p++) {
-					((CSGRewardsSimple) newrewards.get(p)).setStateReward(s, rewards.get(p).getStateReward(nomap.get(s)));
-					for (t = 0; t < newmodel.getNumChoices(s); t++) {
-						((CSGRewardsSimple) newrewards.get(p)).setTransitionReward(s, t, rewards.get(p).getTransitionReward(nomap.get(s), t));
+			if (t == ExpressionTemporal.R_C) {
+				for (c = 0; c < numCoalitions; c++) { 
+					for (s = 0; s < csg.getNumStates(); s++) {
+						sol[c][s] = 0.0;
 					}
 				}
 			}
-			for (BitSet subgame : subgames.keySet()) {
-				for (p = 0; p < numCoalitions; p++) {
-					if (subgame.get(p)) {
-						for (s = subgames.get(subgame).nextSetBit(0); s >= 0; s = subgames.get(subgame).nextSetBit(s + 1)) {
-							((CSGRewardsSimple) newrewards.get(p)).setStateReward(s, 0.0);
-							for (t = 0; t < newmodel.getNumChoices(s); t++) {
-								((CSGRewardsSimple) newrewards.get(p)).setTransitionReward(s, t, 0.0);
-							}						
-						}
+			else {
+				for (c = 0; c < numCoalitions; c++) { 
+					for (s = 0; s < csg.getNumStates(); s++) {
+						sol[c][s] = ((min)? -1 * rewards.get(c).getStateReward(s) : rewards.get(c).getStateReward(s));
 					}
 				}
 			}
 		}
 		else {
-			for (BitSet subgame : subgames.keySet()) {
-				for (p = 0; p < numCoalitions; p++) {
-					if (subgame.get(p)) {
-						for (s = subgames.get(subgame).nextSetBit(0); s >= 0; s = subgames.get(subgame).nextSetBit(s + 1)) {
-							sol[p][s] = 1.0;
-						}
-					}
+			for (s = 0; s < csg.getNumStates(); s++) {
+				for (c = 0; c < numCoalitions; c++) {
+					if (targets[c].get(s))
+						sol[c][s] = 1.0;
 				}
 			}
+		} 
+		
+		for (c = 0; c < numCoalitions; c++) {
+			Arrays.fill(tmp[c], 0.0);
+			Arrays.fill(val[c], 0.0);
 		}
-		/*
-		for (s = 0; s < newmodel.getNumStates(); s++) {
-			System.out.println("## old " + nomap.get(s) + " " + csg.getStatesList().get(nomap.get(s)));
-			System.out.println("## new " + s + " " + newmodel.getStatesList().get(s));
-			for (p = 0; p < numCoalitions; p++) {
-				System.out.println("-- player " + p);
-				System.out.println("-- state rewards old " + rewards.get(p).getStateReward(nomap.get(s)));
-				System.out.println("-- state rewards new " + newrewards.get(p).getStateReward(s));
-				for (t = 0; t < newmodel.getNumChoices(s); t++) {
-					System.out.println("-- trans rewards old " + csg.getAction(nomap.get(s), t) + " " + rewards.get(p).getTransitionReward(nomap.get(s), t));
-					System.out.println("-- trans rewards new " + newmodel.getAction(s, t) + " " + newrewards.get(p).getTransitionReward(s, t));
+	
+		switch (eqType) {
+			case CORR : {
+				int maxSize = 1;
+				for (c = 0; c < numCoalitions; c++) {
+					maxSize = maxSize * maxNumActions[c];
+				}
+				switch (lpSolver) {
+					case "Z3" :
+						ceSolver = new CSGCorrelatedZ3(maxSize, numCoalitions);
+						break;
+					default :
+						throw new PrismException("Solver not yet supported");
 				}
 			}
+			default : {
+				smtSupportEnumeration = new CSGSupportEnumerationZ3(maxNumActions, numCoalitions);
+			}
 		}
 		
-		System.exit(1);
-		*/
-		if (genStrat || exportAdv) {
-			mmap = new ArrayList<Map<Integer, BitSet>>();
-			sstrat = new ArrayList<List<Map<BitSet, Double>>>();
-			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>();
-			for (i = 0; i < coalitions.size(); i++) {
-        		mmap.add(i, new HashMap<Integer, BitSet>());
-				lstrat.add(i, new ArrayList<List<Map<BitSet, Double>>>());
-				lstrat.get(i).add(0, new ArrayList<Map<BitSet, Double>>());
-				for (j = 0; j < newmodel.getNumStates(); j++) {	
-					lstrat.get(i).get(0).add(j, null);
-				}
-			} 
-		}
-				
-		for (p = 0; p < numCoalitions; p++) {
-			Arrays.fill(tmp[p], 0.0);
-			Arrays.fill(val[p], 0.0);
-		}
-		String sols;
+		smtSupportEnumeration.setIndexes(strategies);
+		smtSupportEnumeration.setNumPlayers(numCoalitions);
+		smtSupportEnumeration.init();
+		
+		nlpSupportEnumeration = new CSGSupportEnumerationGurobi(maxNumActions, numCoalitions);
+		nlpSupportEnumeration.setIndexes(strategies);
+		nlpSupportEnumeration.setNumPlayers(numCoalitions);
+		
 		done = true;
 		k = 0;
+		timeTaken = System.currentTimeMillis();
 		while (true) {
-			//System.out.print(k + ": ");
-			for (s = 0; s < newmodel.getNumStates(); s++) {
-				//System.out.println("\n## s " + s + " " + newmodel.getStatesList().get(s));		
-				if (genStrat || exportAdv) {
-					sstrat = new ArrayList<List<Map<BitSet, Double>>>();
-					for (i = 0; i < coalitions.size(); i++) {
-		        		mmap.get(i).clear();
-		        	}
-				}
-				if (rew) {
-					eq = stepEquilibria(newmodel, newrewards, mmap, sstrat, sol, s, min);
-					addStateRewards(eq, newrewards, s, min);
-				}
-				else {
-					eq = stepEquilibria(newmodel, null, mmap, sstrat, sol, s, min);
-				}
-				sw = swne(eq, sstrat, min);
-				for (p = 0; p < numCoalitions; p++) {
-					val[p][s] = sw[p + 1];
-				}
-				if (genStrat || exportAdv) {			
-					for (p = 0; p < coalitions.size(); p++) {
-						if (lstrat.get(p).get(0).get(s) == null) {
-							lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+			for (s = 0; s < csg.getNumStates(); s++) {
+				//System.out.println("\ns " + s);
+				sw = null;
+				switch (eqType) {
+					case CORR : {
+						if (rew) {
+							if (t == ExpressionTemporal.R_C) {
+								sw = stepCorrelatedEquilibria(csg, rewards, mmap, null, sol, s, min, crit);
+							}
+							else {
+								sw = stepCorrelatedEquilibria(csg, null, mmap, null, sol, s, min, crit);
+							}
+						}
+						break;
+					}
+					default : {
+						if (rew) {
+							if (t == ExpressionTemporal.R_C) {
+								eq = stepEquilibria(csg, rewards, mmap, null, sol, s, min);
+								addStateRewards(eq, rewards, s, min);
+							}
+							else {
+								eq = stepEquilibria(csg, null, mmap, null, sol, s, min);
+							}
 						}
-						else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(p)) && checkEquilibriumChange(sol, sw, s)) { // will have to change for min
-							lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+						else {
+							eq = stepEquilibria(csg, null, mmap, null, sol, s, min);
 						}
-					}		
+						sw = swne(eq, null, min);
+					}
+				}
+				for (c = 0; c < numCoalitions; c++) {
+					val[c][s] = sw[c + 1];
 				}
 			}
-			for (s = 0; s < newmodel.getNumStates(); s++) {
-				for (p = 0; p < numCoalitions; p++) {
-					sol[p][s] = val[p][s];
+			for (s = 0; s < csg.getNumStates(); s++) {
+				for (c = 0; c < numCoalitions; c++) {
+					sol[c][s] = val[c][s];
 				}
 				r[s] = 0.0;
-				for (p = 0; p < numCoalitions; p++) {
-					r[s] += sol[p][s];
+				for (c = 0; c < numCoalitions; c++) {
+					r[s] += sol[c][s];
 				}
 			}
-			//System.out.println();
-			sols = "(";
-			for (p = 0; p < numCoalitions; p++) {
-				if (p < numCoalitions - 1)
-					sols += sol[p][newmodel.getFirstInitialState()] + ",";
-				else
-					sols += sol[p][newmodel.getFirstInitialState()] + ")";
-				//System.out.println(p + " " + sol[p][newmodel.getFirstInitialState()]);
-				done = done & PrismUtils.doublesAreClose(sol[p], tmp[p], 1e-6, true);
+			for (c = 0; c < numCoalitions; c++) {
+				done = done & PrismUtils.doublesAreClose(sol[c], tmp[c], termCritParam, termCrit == TermCrit.ABSOLUTE);
 			}
-			System.out.println(k + ": " + sols);
 			k++;
-			if (done) {
+			if (done || k == bounds[0]) {
 				break;
 			}
 			else if (!done && k == maxIters) {
@@ -1113,115 +1350,577 @@ else if (!done && k == maxIters) {
 			}
 			else {
 				done = true;
-				for (p = 0; p < numCoalitions; p++) {
-					//System.out.println(Arrays.toString(sol[p]));
-					tmp[p] = Arrays.copyOf(sol[p], sol[p].length);
+				for (c = 0; c < numCoalitions; c++) {
+					tmp[c] = Arrays.copyOf(sol[c], sol[c].length);
 				}
 			}
 		}
+		timeTaken = System.currentTimeMillis() - timeTaken;
 		mainLog.println();
-		for (p = 0; p < numCoalitions; p++) {
-			mainLog.println("Result for coalition " + coalitions.get(p) + ": " + sol[p][newmodel.getFirstInitialState()] + " (value in the intial state).");
+		for (c = 0; c < numCoalitions; c++) {
+			mainLog.println("Result for coalition " + coalitions.get(c) + ": " + sol[c][csg.getFirstInitialState()] + " (value in the intial state).");
 		}
 		r = new double[csg.getNumStates()];
-		for (s = 0; s < newmodel.getNumStates(); s++) {
-			r[nomap.get(s)] = 0.0;
-			for (p = 0; p < numCoalitions; p++) {
-				r[nomap.get(s)] += sol[p][s];
+		for (s = 0; s < csg.getNumStates(); s++) {
+			r[s] = 0.0;
+			for (c = 0; c < numCoalitions; c++) {
+				r[s] += sol[c][s];
 			}
 		}
-		if (genStrat || exportAdv)
-			res.strat = new CSGStrategy(newmodel, lstrat, subgames, numCoalitions, CSGStrategyType.EQUILIBRIA_M);
 		res.soln = r;
 		res.numIters = k;
+		res.timeTaken = timeTaken /  1000.0;
 		return res;
 	}
 	
-	public boolean checkEquilibriumChange(double[][] sol, double[] eq, int s) {
-		int p;
-		boolean result = true;
-		for (p = 0; p < numCoalitions; p++) {
-			result = result && Double.compare(sol[p][s], eq[p + 1]) == 0;
-			if (!result)
-				return true;
-		}
-		return false;
-	}
-	
-	public void exploreSat(CSG csg, CSGSimple newmodel, Map<Integer, Integer> nomap, Map<Integer, Integer> extmap, Map<BitSet, BitSet> subgames, List<State> newstatelist, 
-									VarList newvarlist, Declaration[] goals, BitSet[] targets, BitSet explored, BitSet subgame, int s) {
-		int l;
-		explored.set(s);
-		if (!subgame.isEmpty()) { 
-			if (!subgames.containsKey(subgame))
-				subgames.put(subgame, new BitSet());
-			subgames.get(subgame).set(s);
-		}
-		for (int t = 0; t < csg.getNumChoices(nomap.get(s)); t++) {
-			Distribution d = new Distribution();
-			
-			for (Iterator<Map.Entry<Integer, Double>> iter = csg.getTransitionsIterator(nomap.get(s), t); iter.hasNext(); ) {
-				Map.Entry<Integer, Double> e = iter.next();
-				int u = e.getKey();
-				State ustate = new State(newstatelist.get(s));
-				BitSet usubgame = new BitSet();
-				usubgame.or(subgame);
-				for (int v = 0; v < csg.getVarList().getNumVars(); v++) {
-					ustate.setValue(v, csg.getStatesList().get(u).varValues[v]);
-				}
-				for (int p = 0; p < numCoalitions; p++) {
-					if (targets[p].get(u)) {
-						ustate.setValue(newvarlist.getIndex(goals[p].getName()), true);
-						usubgame.set(p);
-					}
-				}
-				int m;
-				if (!extmap.containsKey(ustate.hashCode())) {
-					m = newmodel.addState();
-					nomap.put(m, u);
-					extmap.put(ustate.hashCode(), m);
-					newstatelist.add(m, ustate);
-				}
-				else {
-					m = extmap.get(ustate.hashCode());
-				}
-				if (!explored.get(m)) 
-					exploreSat(csg, newmodel, nomap, extmap, subgames, newstatelist, newvarlist, goals, targets, explored, usubgame, m);
-				d.add(m, e.getValue());
-			}
-			l = newmodel.addActionLabelledChoice(s, d, csg.getAction(nomap.get(s), t));
-			newmodel.setIndexes(s, l, csg.getIndexes(nomap.get(s), t));
-		}
+	/**
+	 * 
+	 * 
+	 * @param n
+	 * @param s
+	 * @return
+	 */
+	public ModelCheckerResultMulti zeroModelCheckerResultMulti(int n, int s) {
+		ModelCheckerResultMulti res = new ModelCheckerResultMulti();
+		double[][] soln = new double[n][s];
+		for (int i = 0; i < n; i++) {
+			Arrays.fill(soln[i], 0.0);
+		}
+		res.solnMulti = soln;
+		return res;
 	}
 	
-	public void buildSubGames(Set<BitSet> games, BitSet sp, int p) {
-		BitSet prod = new BitSet();
-		prod.set(p);
-		games.add((BitSet) prod.clone());
-		for(int cp = sp.nextSetBit(0); cp >= 0; cp = sp.nextSetBit(cp + 1)) {
-			BitSet newprod = new BitSet();
-			newprod.or(prod);
-			newprod.set(cp);
-			games.add(newprod);
-		}
+	/**
+	 * 
+	 * 
+	 * @param csg
+	 * @param targets
+	 * @param remain
+	 * @return
+	 */
+	public ModelCheckerResultMulti initialiseModelCheckerResultMulti(CSG csg, BitSet[] targets, BitSet[] remain) {
+		ModelCheckerResultMulti res = new ModelCheckerResultMulti();
+		double[][] soln = new double[numCoalitions][csg.getNumStates()];
+		for (int i = 0; i < numCoalitions; i++) {
+			Arrays.fill(soln[i], 0.0);
+		}
+		res.solnMulti = soln;
+		return res;
 	}
 	
-	public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, BitSet[] remain, boolean min) throws PrismException {
-		ModelCheckerResult[] obj = new ModelCheckerResult[coalitions.size()];
+	/**
+	 * Deal with multi-player infinite-horizon equilibria (unfinished).
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param targets
+	 * @param remain
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeMultiReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, BitSet[] remain, int eqType, int crit, boolean min) throws PrismException {
+		System.out.println("# Multi-player equilibria new...");
 		ModelCheckerResult res = new ModelCheckerResult();
-		List<List<List<Map<BitSet, Double>>>> lstrat = null;
-		List<List<Map<BitSet, Double>>> sstrat = null;
-		List<Map<Integer, BitSet>> mmap = null;
-		BitSet[] only = new BitSet[targets.length];
-		BitSet[] phi1 = new BitSet[3];
-		BitSet known = new BitSet();
-		BitSet temp =  new BitSet();
-		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
-		double[][] val = new double[coalitions.size()][csg.getNumStates()];
-		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
-		double[][] eq;
+		Map<BitSet, ModelCheckerResultMulti> precomp;
+		Map<Integer, Set<BitSet>> subgames = new HashMap<Integer, Set<BitSet>>();
+		BitSet tmp;
+		double[][] sol;
+		double[] r;
+		int c, s;
+		boolean rew;
+		
+		rew = rewards != null;
+		precomp = new HashMap<BitSet, ModelCheckerResultMulti>();
+		
+		buildCoalitions(csg, coalitions);
+		dominated = new BitSet[numCoalitions];
+		dominating = new BitSet[numCoalitions];
+		findMaxAvgAct(csg);
+		
+		for (c = 1; c < coalitions.size(); c++) {
+			subgames.put(c, new HashSet<BitSet>());
+		}
+		
+		for (c = 0; c < coalitions.size(); c++) {
+			tmp = (BitSet) players.clone();
+			tmp.clear(c);
+			buildSubGames(subgames, tmp, c);
+		}
+		
+		System.out.println("# Subgames");
+		System.out.println(subgames);
+				
+		smtSupportEnumeration = new CSGSupportEnumerationZ3(maxNumActions, numCoalitions);
+		smtSupportEnumeration.setIndexes(strategies);
+		smtSupportEnumeration.setNumPlayers(numCoalitions);
+		smtSupportEnumeration.init();
+		
+		nlpSupportEnumeration = new CSGSupportEnumerationGurobi(maxNumActions, numCoalitions);
+		nlpSupportEnumeration.setIndexes(strategies);
+		nlpSupportEnumeration.setNumPlayers(numCoalitions);
+		
+		for (c = numCoalitions; c > 0; c--) {
+			if (c == numCoalitions) {
+				tmp = new BitSet();
+				tmp.set(0, numCoalitions);
+				precomp.put(tmp, zeroModelCheckerResultMulti(numCoalitions, csg.getNumStates()));
+			}
+			else {
+				for (BitSet E : subgames.get(c)) {
+					System.out.println(E);
+					precomp.put(E, computeMultiReachEquilibriaRewRec(csg, coalitions, rewards, targets, precomp, E, min, true));
+					System.out.println(Arrays.toString(precomp.get(E).solnMulti));
+					System.out.println("/");
+				}
+			}
+		}
+		
+		if (rew)
+			sol = computeMultiReachEquilibriaRewRec(csg, coalitions, rewards, targets, precomp, new BitSet(), min, true).solnMulti;
+		else
+			sol = computeMultiReachEquilibriaProbRec(csg, coalitions, targets, remain, new BitSet(), new BitSet(), min, true).solnMulti;
+
+		r = new double[csg.getNumStates()];
+		for (s = 0; s < csg.getNumStates(); s++) {
+			r[s] = 0.0;
+			for (c = 0; c < numCoalitions; c++) {
+				r[s] += sol[c][s];
+			}
+		}
+		res.soln = r;
+		System.exit(1);
+		return res;
+	}
+	
+	/**
+	 * Deal with multi-player infinite-horizon (probabilistic) equilibria (unfinished).
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param targets
+	 * @param remain
+	 * @param D
+	 * @param E
+	 * @param min
+	 * @param main
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResultMulti computeMultiReachEquilibriaProbRec(CSG csg, List<Coalition> coalitions, BitSet[] targets, BitSet[] remain, BitSet D, BitSet E, boolean min, boolean main) throws PrismException {
+		//System.out.println("# Multi-player equilibria rec...");
+		ModelCheckerResultMulti res = new ModelCheckerResultMulti();
+		List<List<List<Map<BitSet, Double>>>> lstrat = null;
+		List<List<Map<BitSet, Double>>> sstrat = null;
+		List<Map<Integer, BitSet>> mmap = null;
+		BitSet newD, newE, uniD, uniE;
+		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
+		double[][] val = new double[coalitions.size()][csg.getNumStates()];
+		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
+		double[][] sub;
+		double[][] eqs;
+		double[] sel;
+		String sols;
+		int c, i, j, k, s;
+		boolean done;
+				
+		if (genStrat || exportAdv) {
+			mmap = new ArrayList<Map<Integer, BitSet>>();
+			sstrat = new ArrayList<List<Map<BitSet, Double>>>();
+			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>();
+			for (i = 0; i < coalitions.size(); i++) {
+        		mmap.add(i, new HashMap<Integer, BitSet>());
+				lstrat.add(i, new ArrayList<List<Map<BitSet, Double>>>());
+				lstrat.get(i).add(0, new ArrayList<Map<BitSet, Double>>());
+				for (j = 0; j < csg.getNumStates(); j++) {	
+					lstrat.get(i).get(0).add(j, null);
+				}
+			} 
+		}
+		for (c = 0; c < numCoalitions; c++) {
+			Arrays.fill(tmp[c], 0.0);
+			Arrays.fill(val[c], 0.0);
+		}
+		//System.out.println("-- D");
+		//System.out.println(Arrays.toString(D));
+		//System.out.println("-- E");
+		//System.out.println(Arrays.toString(E));
+		done = true;
+		k = 0;
+		while (true) {
+			for (s = 0; s < csg.getNumStates(); s++) {
+				newD = new BitSet();
+				newE = new BitSet();
+				for (c = 0; c < numCoalitions; c++) {
+					if (targets[c].get(s)) {
+						newD.set(c);
+					}
+					if (remain[c] != null && !remain[c].isEmpty()) {
+						if (!targets[c].get(s) && !remain[c].get(s)) {
+							newE.set(c);
+						}
+					}
+				}
+				newD.andNot(D);
+				newD.andNot(E);
+				newE.andNot(D);
+				newE.andNot(E);
+				if (genStrat || exportAdv) {
+					sstrat = new ArrayList<List<Map<BitSet, Double>>>();
+					for (i = 0; i < coalitions.size(); i++) {
+						mmap.get(i).clear();
+					}
+				}
+				if (D.cardinality() + E.cardinality() == numCoalitions) {
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = D.get(c)? 1.0 : 0.0;
+					}	
+				}
+				else if (k == 0) {
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = targets[c].get(s)? 1.0 : 0.0;
+					}	
+				}
+				else if (!newD.isEmpty()) {
+					//System.out.println("* Subgame of state " + s + ": " + csg.getStatesList().get(s));
+					uniD = new BitSet();
+					uniD.or(D);
+					uniD.or(newD);
+					sub = computeMultiReachEquilibriaProbRec(csg, coalitions, targets, remain, uniD, E, min, false).solnMulti;
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = sub[c][s];
+					}
+				}
+				else if (!newE.isEmpty()) {
+					//System.out.println("* Subgame of state " + s + ": " + csg.getStatesList().get(s));
+					uniE = new BitSet();
+					uniE.or(E);
+					uniE.or(newE);
+					sub = computeMultiReachEquilibriaProbRec(csg, coalitions, targets, remain, D, uniE, min, false).solnMulti;	
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = sub[c][s];
+					}
+				} 
+				else {
+					for (c = 0; c < numCoalitions; c++) {
+						if (D.get(c))
+							sol[c][s] = 1.0;
+						else if (E.get(c))
+							sol[c][s] = 0.0;							
+					}
+					eqs = stepEquilibria(csg, null, mmap, sstrat, sol, s, min);
+					sel = swne(eqs, sstrat, min);
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = sel[c + 1];
+					}
+				}
+			}
+			for (s = 0; s < csg.getNumStates(); s++) {
+				for (c = 0; c < numCoalitions; c++) {
+					sol[c][s] = E.get(c)? 0.0 : D.get(c)? 1.0 : val[c][s];
+				}
+			}
+			sols = "(";
+			for (c = 0; c < numCoalitions; c++) {
+				if (c < numCoalitions - 1)
+					sols += sol[c][csg.getFirstInitialState()] + ",";
+				else
+					sols += sol[c][csg.getFirstInitialState()] + ")";
+				done = done & PrismUtils.doublesAreClose(sol[c], tmp[c], termCritParam, termCrit == TermCrit.ABSOLUTE);
+			}
+			if (main)
+				mainLog.println(k + ": " + sols);		
+			k++;
+			if (done && k > 1) {
+				break;
+			}
+			else if (!done && k == maxIters) {
+				throw new PrismException("Could not converge after " + k + " iterations");
+			}
+			else {
+				done = true;
+				for (c = 0; c < numCoalitions; c++) {
+					tmp[c] = Arrays.copyOf(sol[c], sol[c].length);
+				}
+			}
+		}
+		res.solnMulti = sol;
+		res.numIters = k;
+		return res;
+	}
+	
+	/**
+	 * Deal with multi-player infinite-horizon (probabilistic) equilibria (unfinished).
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param targets
+	 * @param subgames
+	 * @param D
+	 * @param min
+	 * @param main
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResultMulti computeMultiReachEquilibriaRewRec(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, Map<BitSet, ModelCheckerResultMulti> subgames, BitSet D, boolean min, boolean main) throws PrismException {
+		//System.out.println("# Multi-player equilibria rec...");
+		ModelCheckerResultMulti res = new ModelCheckerResultMulti();
+		ModelCheckerResultMulti sub;
+		List<List<List<Map<BitSet, Double>>>> lstrat = null;
+		List<List<Map<BitSet, Double>>> sstrat = null;
+		List<Map<Integer, BitSet>> mmap = null;
+		BitSet newD, uniD;
+		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
+		double[][] val = new double[coalitions.size()][csg.getNumStates()];
+		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
+		double[][] eqs;
+		double[] sel;
+		String sols;
+		int c, i, j, k, s;
+		boolean done;
+				
+		if (genStrat || exportAdv) {
+			mmap = new ArrayList<Map<Integer, BitSet>>();
+			sstrat = new ArrayList<List<Map<BitSet, Double>>>();
+			lstrat = new ArrayList<List<List<Map<BitSet, Double>>>>();
+			for (i = 0; i < coalitions.size(); i++) {
+        		mmap.add(i, new HashMap<Integer, BitSet>());
+				lstrat.add(i, new ArrayList<List<Map<BitSet, Double>>>());
+				lstrat.get(i).add(0, new ArrayList<Map<BitSet, Double>>());
+				for (j = 0; j < csg.getNumStates(); j++) {	
+					lstrat.get(i).get(0).add(j, null);
+				}
+			} 
+		}
+		for (c = 0; c < numCoalitions; c++) {
+			Arrays.fill(tmp[c], 0.0);
+			Arrays.fill(val[c], 0.0);
+		}
+		//System.out.println("-- D");
+		//System.out.println(D);
+		done = true;
+		k = 0;
+		while (true) {
+			for (s = 0; s < csg.getNumStates(); s++) {
+				newD = new BitSet();
+				for (c = 0; c < numCoalitions; c++) {
+					if (targets[c].get(s)) {
+						newD.set(c);
+					}
+				}
+				newD.andNot(D);
+				if (D.cardinality() == numCoalitions) {
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = 0.0;
+					}	
+				}
+				else if (k == 0) {
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = 0.0;
+					}	
+				}
+				else if (!newD.isEmpty()) {
+					//System.out.println("* Subgame of state " + s + ": " + csg.getStatesList().get(s));
+					if (genStrat || exportAdv) {
+						if (res.subGames == null)
+							res.subGames = new HashMap<BitSet, ModelCheckerResultMulti>();
+					}
+					uniD = new BitSet();
+					uniD.or(D);
+					uniD.or(newD);
+					/*
+					if (!subgames.containsKey(uniD)) {
+						sub = computeMultiReachEquilibriaRewRec(csg, coalitions, rewards, targets, subgames, uniD, min, false);
+						if (genStrat || exportAdv) {
+							res.subGames.put(sub.D, sub);
+						}
+						subgames.put(uniD, sub);
+					}
+					else {
+						sub = subgames.get(uniD);
+					}
+					*/
+					sub = subgames.get(uniD);
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = sub.solnMulti[c][s];
+					}
+				}
+				else {
+					if (genStrat || exportAdv) {
+						sstrat = new ArrayList<List<Map<BitSet, Double>>>();
+						for (c = 0; c < coalitions.size(); c++) {
+							mmap.get(c).clear();
+						}
+					}
+					for (c = 0; c < numCoalitions; c++) {
+						if (D.get(c))
+							sol[c][s] = 0.0;
+					}
+					eqs = stepEquilibria(csg, rewards, mmap, sstrat, sol, s, min);	
+					sel = swne(eqs, sstrat, min);
+					for (c = 0; c < numCoalitions; c++) {
+						val[c][s] = sel[c + 1];
+					}
+					if (genStrat || exportAdv) {
+						if (main && s==0) {
+							System.out.println(sstrat);
+						}
+						// Doesn't work like this, needs to add memory
+						for (c = 0; c < coalitions.size(); c++) {
+							if (lstrat.get(c).get(0).get(s) == null) {
+								lstrat.get(c).get(0).set(s, sstrat.get(0).get(c));
+							}
+							else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(c)) && checkEquilibriumChange(sol, sel, s)) { // will have to change for min
+								lstrat.get(c).get(0).set(s, sstrat.get(0).get(c));
+							}
+						}
+					}
+				}
+			}
+			for (s = 0; s < csg.getNumStates(); s++) {
+				for (c = 0; c < numCoalitions; c++) {
+					sol[c][s] = val[c][s];
+					sol[c][s] += (D.get(c))? 0.0 : ((min)? -1.0 * rewards.get(c).getStateReward(s) : rewards.get(c).getStateReward(s));
+				}
+			}
+			sols = "(";
+			for (c = 0; c < numCoalitions; c++) {
+				if (c < numCoalitions - 1)
+					sols += sol[c][csg.getFirstInitialState()] + ",";
+				else
+					sols += sol[c][csg.getFirstInitialState()] + ")";
+				done = done & PrismUtils.doublesAreClose(sol[c], tmp[c], termCritParam, termCrit == TermCrit.ABSOLUTE);
+			}
+			if (main)
+				mainLog.println(k + ": " + sols);		
+			k++;
+			if (done && k > 1) {
+				break;
+			}
+			else if (!done && k == maxIters) {
+				throw new PrismException("Could not converge after " + k + " iterations");
+			}
+			else {
+				done = true;
+				for (c = 0; c < numCoalitions; c++) {
+					tmp[c] = Arrays.copyOf(sol[c], sol[c].length);
+				}
+			}
+		}
+		if (genStrat || exportAdv) {
+			res.D = D;
+			res.strat = new CSGStrategy(csg, lstrat, null, numCoalitions, CSGStrategyType.EQUILIBRIA_M);
+			if (main) {
+				System.out.println(D);
+				System.out.println(res.strat);
+				for (Entry<BitSet, ModelCheckerResultMulti> entry1 : res.subGames.entrySet()) {
+					System.out.println(entry1.getKey());
+					System.out.println(entry1.getValue().strat);		
+					if (entry1.getValue().subGames != null) {
+						for (Entry<BitSet, ModelCheckerResultMulti> entry2 : entry1.getValue().subGames.entrySet()) {
+							System.out.println(entry2.getKey());
+							System.out.println(entry2.getValue().strat);		
+						}
+					}
+				}
+			}
+		}
+		res.solnMulti = sol;
+		res.numIters = k;
+		return res;	
+	}
+	
+	/**
+	 * 
+	 * 
+	 * @param sol
+	 * @param eq
+	 * @param s
+	 * @return
+	 */
+	public boolean checkEquilibriumChange(double[][] sol, double[] eq, int s) {
+		int p;
+		boolean result = true;
+		for (p = 0; p < numCoalitions; p++) {
+			result = result && Double.compare(sol[p][s], eq[p + 1]) == 0;
+			if (!result)
+				return true;
+		}
+		return false;
+	}
+	
+	/**
+	 * 
+	 * 
+	 * @param games
+	 * @param sp
+	 * @param p
+	 */
+	public void buildSubGames(Set<BitSet> games, BitSet sp, int p) {
+		BitSet prod = new BitSet();
+		prod.set(p);
+		games.add((BitSet) prod.clone());
+		for(int cp = sp.nextSetBit(0); cp >= 0; cp = sp.nextSetBit(cp + 1)) {
+			BitSet newprod = new BitSet();
+			newprod.or(prod);
+			newprod.set(cp);
+			games.add(newprod);
+		}
+	}
+	
+	/**
+	 * 
+	 * 
+	 * @param games
+	 * @param sp
+	 * @param p
+	 */
+	public void buildSubGames(Map<Integer, Set<BitSet>> games, BitSet sp, int p) {
+		BitSet prod = new BitSet();
+		prod.set(p);			
+		games.get(prod.cardinality()).add((BitSet) prod.clone());
+		for(int cp = sp.nextSetBit(0); cp >= 0; cp = sp.nextSetBit(cp + 1)) {
+			BitSet newprod = new BitSet();
+			newprod.or(prod);
+			newprod.set(cp);
+			games.get(newprod.cardinality()).add(newprod);
+		}
+	}
+	
+	/**
+	 * 
+	 * 
+	 * @param csg
+	 * @param coalitions
+	 * @param rewards
+	 * @param targets
+	 * @param remain
+	 * @param eqType
+	 * @param crit
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalitions, List<CSGRewards> rewards, BitSet[] targets, BitSet[] remain, int eqType, int crit, boolean min) throws PrismException {
+		ModelCheckerResult[] obj = new ModelCheckerResult[coalitions.size()];
+		ModelCheckerResult res = new ModelCheckerResult();
+		List<List<List<Map<BitSet, Double>>>> lstrat = null;
+		List<List<Map<BitSet, Double>>> sstrat = null;
+		List<Map<Integer, BitSet>> mmap = null;
+		BitSet[] only = new BitSet[targets.length];
+		BitSet[] phi1 = new BitSet[3];
+		BitSet known = new BitSet();
+		BitSet temp =  new BitSet();
+		double[][] sol = new double[coalitions.size()][csg.getNumStates()];
+		double[][] val = new double[coalitions.size()][csg.getNumStates()];
+		double[][] tmp = new double[coalitions.size()][csg.getNumStates()];
+		double[] eq;
 		double[] r = new double[csg.getNumStates()];
-		double[] sw;
+		//double[] sw;
 		int i, j, k, p, s;
 		boolean done, rew;
 		long timePrecomp;
@@ -1278,9 +1977,8 @@ public ModelCheckerResult computeReachEquilibria(CSG csg, List<Coalition> coalit
 		dominating = new BitSet[numCoalitions];
 		mainLog.println();
 		findMaxRowsCols(csg);
-		setSolver();
 		
-		mainLog.println("Starting equilibria computation (solver=" + eqslps.getSolverName() + ")...");
+		mainLog.println("Starting equilibria computation (solver=" + setSolver(eqType) + ")...");
 		mainLog.println("Checking whether all objctives are reachable...");
 		
 		if (assumptionCheck) {
@@ -1376,25 +2074,32 @@ else if (!phi1[2].get(s)) {
 			        		mmap.add(p, new HashMap<Integer, BitSet>());
 			        	}
 					}
-					if (rew) {
-						eq = stepEquilibria(csg, rewards.get(0), rewards.get(1), mmap, eqslps, sstrat, sol, s, min);
-					}
-					else {
-						eq = stepEquilibria(csg, null, null, mmap, eqslps, sstrat, sol, s, min);
-					}
-					sw = swne(eq, sstrat, min);
-					val[0][s] = sw[1];
-					val[1][s] = sw[2];
+					eq = stepEquilibriaTwoPlayer(csg, rewards, mmap, sstrat, sol, s, eqType, crit, rew, min);
+					val[0][s] = eq[1];
+					val[1][s] = eq[2];
 					// player -> iteration -> state -> indexes -> value
-					if (genStrat || exportAdv) {			
-						for (p = 0; p < coalitions.size(); p++) {
-							if (lstrat.get(p).get(0).get(s) == null) {
-								lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+					if (genStrat || exportAdv) {	
+						switch (eqType) {
+							case CORR: {
+								if (lstrat.get(0).get(0).get(s) == null) {
+									lstrat.get(0).get(0).set(s, sstrat.get(0).get(0));
+								}
+								else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(0)) && checkEquilibriumChange(sol, eq, s)) {
+									lstrat.get(0).get(0).set(s, sstrat.get(0).get(0));
+								}
+								break;
 							}
-							else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(p)) && checkEquilibriumChange(sol, sw, s)) {
-								lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+							default: {
+								for (p = 0; p < coalitions.size(); p++) {
+									if (lstrat.get(p).get(0).get(s) == null) {
+										lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+									}
+									else if (!lstrat.get(0).get(0).get(s).equals(sstrat.get(0).get(p)) && checkEquilibriumChange(sol, eq, s)) {
+										lstrat.get(p).get(0).set(s, sstrat.get(0).get(p));
+									}
+								}
 							}
-						}		
+						}
 					}					
 				}
 				// loop over states
@@ -1437,15 +2142,104 @@ else if (!done && k == maxIters) {
 		mainLog.println("Coalition results (initial state): (" + sol[0][csg.getFirstInitialState()] + "," + sol[1][csg.getFirstInitialState()] + ")");
 		res.soln = r;
 		if (genStrat || exportAdv) 	{
-			if (rew)
-				res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_R);
-			else
-				res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_P);
+			switch (eqType) {
+				case CORR: {
+					if (rew)
+						res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_CE_R);
+					else
+						res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_CE_P);
+					break;
+				}
+				default: { 
+					if (rew)
+						res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_R);
+					else
+						res.strat = new CSGStrategy(csg, lstrat, obj, targets, CSGStrategyType.EQUILIBRIA_P);
+				}	
+			}
 		}
 		res.numIters = k;
 		return res;		
 	}
 	
+	/**
+	 * Selects the equilibrium that minimises the difference among the highest and lowest payoffs.
+	 * 
+	 * @param eqs The set of equilibria
+	 * @param strats Strategy to be updated
+	 * @param min If minimising
+	 * @return
+	 */
+	public double[] fair(double[][] eqs, List<List<Map<BitSet, Double>>> strats, boolean min) {
+		List<Map<BitSet, Double>> dist = null;
+		BitSet ifr = new BitSet();
+		double[] eq = new double[numCoalitions+1];
+		double[][] df = new double[eqs.length][2];
+		double diff;
+		int i, p;
+		for (p = 0; p < numCoalitions; p++) { // gets first equilibrium
+			eq[0] += eqs[0][p];
+			eq[p+1] = eqs[0][p];
+		}
+		df[0][0] = Arrays.stream(eqs[0]).max().getAsDouble();
+		df[0][1] = Arrays.stream(eqs[0]).min().getAsDouble();
+		diff = df[0][0] - df[0][1];
+		ifr.set(0);
+		if (strats != null)
+			dist = strats.get(0);
+		for (i = 1; i < eqs.length; i++) { 
+			df[i][0] = Arrays.stream(eqs[i]).max().getAsDouble();
+			df[i][1] = Arrays.stream(eqs[i]).min().getAsDouble();
+			if (Double.compare(df[i][0]-df[i][1], diff) < 0) {
+				diff = df[i][0]-df[i][1];
+				ifr.clear();
+				ifr.set(i);
+			}
+			else if (Double.compare(df[i][0]-df[i][1], diff) == 0) {
+				ifr.set(i);
+			}
+		}
+		if (ifr.cardinality() == 1) { //if there is one single equilibrium that minimises the difference, we're done
+			i = ifr.nextSetBit(0);
+			eq[0] = 0.0;
+			for (p = 0; p < numCoalitions; p++) {
+				eq[0] += eqs[i][p];
+				eq[p+1] = eqs[i][p];
+			}
+			if(strats != null)
+				dist = strats.get(i);
+			final List<Map<BitSet, Double>> strat = dist;
+			if (strats != null)
+				strats.removeIf((List<Map<BitSet, Double>> e) -> !e.equals(strat));
+			if (min) {
+				for (i = 0; i < eq.length; i++)
+					eq[i] = -1.0 * eq[i];
+			}
+			return eq;
+		}
+		else { // if not, we have to look at the sum
+			double[][] neweqs = new double[ifr.cardinality()][numCoalitions];
+			int j = 0;
+			for (i = ifr.nextSetBit(0); i >=0; i = ifr.nextSetBit(i+1)) {
+				for (p = 0; p < numCoalitions; p++) {
+					neweqs[j][p] = eqs[i][p];
+					if (strats != null)
+						Collections.swap(strats, i, j);
+				}
+				j++;
+			}
+			return swne(neweqs, strats, min);
+		}
+	}
+	
+	/**
+	 * Selects the equilibrium that maximises the sum of payoffs.
+	 * 
+	 * @param eqs The set of equilibria. 
+	 * @param strats The strategy to be updated.
+	 * @param min If minimising.
+	 * @return
+	 */
 	public double[] swne(double[][] eqs, List<List<Map<BitSet, Double>>> strats, boolean min) {
 		List<Map<BitSet, Double>> dist = null;
 		BitSet isw = new BitSet();
@@ -1502,6 +2296,14 @@ else if (Double.compare(sum, eq[0]) == 0) {
 		return eq;
 	}
 	
+	/**
+	 * 
+	 * 
+	 * @param indexes
+	 * @param eqs
+	 * @param eq
+	 * @return
+	 */
 	public int findMaxEqIndexes(BitSet indexes, double[][] eqs, double eq[]) {
 		int idx;
 		BitSet tmp = new BitSet();
@@ -1540,21 +2342,15 @@ else if (Double.compare(eqs[i][p], max) == 0) {
 		}
 	}
 	
-	public void extractStrategyFromSupport(ArrayList<Map<BitSet, Double>> eqstrat, List<Map<Integer, BitSet>> mmap, BitSet support) {
-		BitSet indx;
-		int a, i, p;
-		for (p = 0; p < numCoalitions; p++) {
-			indx = new BitSet();
-			for (a = 0; a < strategies.get(p).size(); a++) {
-				indx.set(strategies.get(p).get(a));
-			}
-			indx.and(support);
-			i = indx.nextSetBit(0);
-			eqstrat.add(p, new HashMap<BitSet, Double>());
-			eqstrat.get(p).put(mmap.get(p).get(strategies.get(p).indexOf(i)), 1.0); // indexOf should be changed
-		}
-	}
-	
+	/**
+	 * 
+	 * 
+	 * @param eqs
+	 * @param csgRewards1
+	 * @param csgRewards2
+	 * @param s
+	 * @param min
+	 */
 	public void addStateRewards(double[][] eqs, CSGRewards csgRewards1, CSGRewards csgRewards2, int s, boolean min) {
 		for (int e = 0; e < eqs.length; e++) {
 			if (csgRewards1 != null)
@@ -1564,6 +2360,14 @@ public void addStateRewards(double[][] eqs, CSGRewards csgRewards1, CSGRewards c
 		}
 	}
 	
+	/**
+	 * 
+	 * 
+	 * @param eqs
+	 * @param rewards
+	 * @param s
+	 * @param min
+	 */
 	public void addStateRewards(double[][] eqs, List<CSGRewards> rewards, int s, boolean min) {
 		int e, p;
 		for (e = 0; e < eqs.length; e++) {
@@ -1574,254 +2378,414 @@ public void addStateRewards(double[][] eqs, List<CSGRewards> rewards, int s, boo
 		}
 	}
 	
-	public double[][] stepEquilibria(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats, double[][] val, int s, boolean min) throws PrismException {
-		Pair<CSGResultStatus, ArrayList<Double>> eqsresult;
-		ArrayList<Double> eq;
-		ArrayList<ArrayList<Double>> eqs = new ArrayList<ArrayList<Double>>();
+	/**
+	 * 
+	 * 
+	 * @param eqs
+	 * @param rewards
+	 * @param s
+	 * @param min
+	 */
+	public void addStateRewards(double[] eqs, List<CSGRewards> rewards, int s, boolean min) {
+		for (int p = 0; p < numCoalitions; p++) {
+			if (rewards.get(p) != null)
+				eqs[p+1] +=  ((min)? -1.0 * rewards.get(p).getStateReward(s) : rewards.get(p).getStateReward(s));
+		}
+	}
+	
+	/**
+	 * 
+	 * 
+	 * @param csg
+	 * @param rewards
+	 * @param mmap
+	 * @param strats
+	 * @param val
+	 * @param s
+	 * @param min
+	 * @param crit
+	 * @return
+	 * @throws PrismException
+	 */
+	public double[] stepCorrelatedEquilibria(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats, 
+											 double[][] val, int s, boolean min, int crit) throws PrismException {
+		EquilibriumResult result;
 		ArrayList<Map<BitSet, Double>> eqstrat = null;
-		BitSet active;
-		BitSet support = null;
-		long time;
-		double[][] result;
-		double sumt, sumv, v;
-		int n, p, p1, p2;
-			
+		BitSet idx = null, ps, tmp = null;
+		double[] eqs = new double[numCoalitions+1];
+		int c, i, q; 
 		buildStepGame(csg, rewards, mmap, val, s, min);
-		active = csg.getConcurrentPlayers(s);
-
-		time = System.currentTimeMillis();
-		if (active.cardinality() == 1) { // in case just one player has a choice
-			result = new double[1][numCoalitions];
-			p1 = active.nextSetBit(0);
-			v = Double.NEGATIVE_INFINITY;
-			sumv = Double.NEGATIVE_INFINITY;
-			sumt = Double.NEGATIVE_INFINITY;
-			for (BitSet entry : utilities.keySet()) {
-				sumv = 0.0;
-				for (p2 = 0; p2 < numCoalitions; p2++) {
-					sumv += utilities.get(entry).get(p2); // computes sum of utilities
-				}
-				if (utilities.get(entry).get(p1) > v) { // maximises for player who has a choice
-					support = entry;
-					sumt = 0.0;
-					v = utilities.get(entry).get(p1);
-					for (p2 = 0; p2 < numCoalitions; p2++) {
-						result[0][p2] = utilities.get(entry).get(p2);
-						sumt += utilities.get(entry).get(p2); // sum of the utilities for the selected entry
-					}
+		clear();
+		computeAssertions();
+		for (c = 0; c < numCoalitions; c++) {
+			for (q = 0; q < strategies.get(c).size(); q++) {
+				ceConstraints.get(c).add(q, new HashMap<BitSet, Double>());
+				for (Pair<BitSet, Double> e : assertions.get(c).get(q)) {
+					ps = new BitSet();
+					ps.or(e.getKey());
+					ceConstraints.get(c).get(q).put(ps, e.second);
+				}
+			}
+		}
+		if (genStrat || exportAdv) {
+			eqstrat = new ArrayList<Map<BitSet, Double>>();
+			eqstrat.add(new HashMap<BitSet, Double>());
+			tmp = new BitSet();
+		}
+		if (utilities.size() == 1) {
+			for (BitSet e : utilities.keySet()) {
+				for (c = 0; c < numCoalitions; c++) {
+					eqs[0] += utilities.get(e).get(c);
+					eqs[c+1] = utilities.get(e).get(c);
 				}
-				else if (utilities.get(entry).get(p1) == v && sumv > sumt) { // case utility for player is the same but sum is higher
-					support = entry;
-					sumt = 0.0;
-					for (p2 = 0; p2 < numCoalitions; p2++) {
-						result[0][p2] = utilities.get(entry).get(p2);
-						sumt += utilities.get(entry).get(p2);
+				if (genStrat || exportAdv) {
+					idx = new BitSet();
+					for (c = 0; c < numCoalitions; c++) {
+						tmp.clear();
+						tmp.or(psupports.get(c));
+						tmp.and(e);
+						i = tmp.nextSetBit(0);
+						idx.or(mmap.get(c).get(strategies.get(c).indexOf(i)));
 					}
+					eqstrat.get(0).put(idx, 1.0);
 				}
 			}
 			if (genStrat || exportAdv) {
-				eqstrat = new ArrayList<Map<BitSet, Double>>();
-				extractStrategyFromSupport(eqstrat, mmap, support);
-				strats.add(eqstrat);
+				strats.add(0, eqstrat);
 			}
-			return result;
-		} 
-		else {	
-			boolean allzero = true;
-			for (BitSet entry : utilities.keySet()) {
-				for (p = 0; p < numCoalitions; p++) {
-					allzero = allzero && Double.compare(utilities.get(entry).get(p), 0.0) == 0;
-					if (!allzero)
-						break;
+		}
+		else {
+			result = ceSolver.computeEquilibrium(utilities, ceConstraints, strategies, ceVarMap, crit);
+			if (result.getStatus() == CSGResultStatus.SAT) {
+				eqs[0] = 0.0;
+				for (Double d : result.getPayoffVector()) {
+					eqs[0] += d;
 				}
-				if (!allzero)
-					break;
-			}
-			if (allzero) {
-				result = new double[1][numCoalitions];
-				Arrays.fill(result[0], 0.0);
-				if (genStrat || exportAdv) {
-					eqstrat = new ArrayList<Map<BitSet, Double>>();
-					extractStrategyFromSupport(eqstrat, mmap, (BitSet) utilities.keySet().toArray()[0]);
-					strats.add(eqstrat);
+				Arrays.fill(eqs, 0.0);
+				for (c = 0; c < numCoalitions; c++) {
+					eqs[c+1] = result.getPayoffVector().get(c);
 				}
-				return result;
-			}
-			if (utilities.keySet().size() == 1) {
-				result = new double[1][numCoalitions];
-				for (BitSet entry : utilities.keySet()) {
-					for (p = 0; p < numCoalitions; p++) {
-						result[0][p] = utilities.get(entry).get(p);
-					}
+				for (BitSet e : ceVarMap.keySet()) {
 					if (genStrat || exportAdv) {
-						eqstrat = new ArrayList<Map<BitSet, Double>>();
-						extractStrategyFromSupport(eqstrat, mmap, entry);
-						strats.add(eqstrat);
+						idx = new BitSet();
+						for (c = 0; c < numCoalitions; c++) {
+							tmp.clear();
+							tmp.or(psupports.get(c));
+							tmp.and(e);
+							i = tmp.nextSetBit(0);
+							idx.or(mmap.get(c).get(strategies.get(c).indexOf(i)));
+						}
+						if (Double.compare(result.getStrategy().get(0).get(ceVarMap.get(e)), 0.0) > 0)
+							eqstrat.get(0).put(idx, result.getStrategy().get(0).get(ceVarMap.get(e)));
 					}
 				}
-				//System.out.println("-- actions " + actions);
-				//System.out.println("-- strategies " + strategies);
-				//System.out.println(utilities);
-				return result;
+				if (genStrat || exportAdv) {
+					strats.add(0, eqstrat);
+				}
+			}
+			else {
+				throw new PrismException(ceSolver.getSolverName() + " could not find an optimal solution for state " + s);
 			}
+		}
+		if (rewards != null)
+			addStateRewards(eqs, rewards, s, min);
+		if (min) {
+			for (i = 0; i < eqs.length; i++)
+				eqs[i] = -1.0 * eqs[i];
+		}
+		return eqs;
+	}
+	
+	/*
+	public ArrayList<EquilibriumResult> stepParallelEquilibriaGurobi(HashSet<BitSet> supports) {
+		ArrayList<EquilibriumResult> eqs = new ArrayList<EquilibriumResult>();
+		List<Callable<EquilibriumResult>> tasks = new ArrayList<Callable<EquilibriumResult>>();
+		//supportCount = 0;
+		//System.out.println("Total supports: " + supports.size());
+		for (final BitSet supp : supports) {
+			Callable<EquilibriumResult> c = new Callable<EquilibriumResult>() {
+				@Override
+				public EquilibriumResult call() throws Exception {
+					return stepEquilibriaGurobi(supp);
+				}
+			};
+			tasks.add(c);
+		}
+		//ExecutorService exec = Executors.newCachedThreadPool();
+		//ExecutorService exec = Executors.newFixedThreadPool(allSupports.size());
+		ExecutorService exec = Executors.newFixedThreadPool(5);
+		//ExecutorService exec = Executors.newFixedThreadPool(Runtime.getRuntime().availableProcessors());
+		//ExecutorService exec = Executors.newSingleThreadExecutor();
+		try {
+			List<Future<EquilibriumResult>> results = exec.invokeAll(tasks);
+			for (Future<EquilibriumResult> result : results) {	
+				if (result.get().getStatus() == CSGResultStatus.SAT) {
+					eqs.add(result.get());
+				}
+			}
+		} 
+		catch (Exception e) {
+			e.printStackTrace();
+		}
+		finally {
+			exec.shutdown();
+		}
+		return eqs;
+	}
+	
+	public EquilibriumResult stepEquilibriaGurobi(BitSet supp) {
+		CSGSupportEnumerationGurobi nlpSupportEnumeration;
+		EquilibriumResult result = null;
+		nlpSupportEnumeration = new CSGSupportEnumerationGurobi(maxNumActions, numCoalitions);
+		nlpSupportEnumeration.setIndexes(strategies);
+		nlpSupportEnumeration.setNumPlayers(numCoalitions);
+		nlpSupportEnumeration.translateAssertions(assertions, mapActionIndex);
+		result = nlpSupportEnumeration.computeEquilibria(supp, mapActionIndex);
+		return result;	
+	}
+	*/
+	
+	/**
+	 * 
+	 * 
+	 * @param csg
+	 * @param rewards
+	 * @param mmap
+	 * @param strats
+	 * @param val
+	 * @param s
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public double[][] stepEquilibria(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats, 
+									 double[][] val, int s, boolean min) throws PrismException {
+		EquilibriumResult eqsresult;
+		EquilibriumResult eqsresultnlp;
+		ArrayList<ArrayList<Double>> equilibria = new ArrayList<ArrayList<Double>>();
+		ArrayList<Map<BitSet, Double>> eqstrat = null;
+		BitSet active;
+		long time;
+		double[][] result;
+		int n, p;
+
+		buildStepGame(csg, rewards, mmap, val, s, min);
+		active = csg.getConcurrentPlayers(s);
+
+		time = System.currentTimeMillis();
+
+		// Case when just one player has a choice
+		if (active.cardinality() == 1) { 
+			return findSWNEOnePlayer(mmap, strats, eqstrat, active);
+		} 
+		else {	
 			clear();
 			computeAssertions();
 			for (p = 0; p < numCoalitions; p++) {
 				dominated[p] = findDominated(p);
 				dominating[p] = findDominating(p);
-				//dominated[p] = new BitSet();
-				//dominating[p] = new BitSet();
-				//if (!dominated[p].isEmpty()) 
-					//System.out.println("dominated " + p + " " + dominated[p]);
-				//if (!dominating[p].isEmpty()) 
-					//System.out.println("dominating " + p + " " + dominating[p]);
-			}
-			//System.out.println("## " + s);
-			buildAllSupports();
-			
-			eqssmt.setIndexes(strategies);
-			eqssmt.setNumPlayers(numCoalitions);
-			eqssmt.init();
-			eqssmt.translateAssertions(assertions, mapActionIndex);
-			
-			/*
-			eqss.setNumPlayers(numCoalitions);
-			eqss.setIndexes(strategies);
-			eqss.setAssertions(assertions);
-			eqss.setGradient(gradient);
-			eqss.init();
-			*/
-			
-			/*
-			//if (s == ?) {
-				System.out.println("\n-- assertions ");
-				for (int c = 0; c < numCoalitions; c++) {
-					System.out.println("--- player " + c);
-		        	for (int q = 0; q < strategies.get(c).size(); q++)
-		        		System.out.println("---- action " + actions.get(c).get(q) + " is " + strategies.get(c).get(q)  + " " + assertions.get(c).get(q));
-				}
-			//}
-			*/
-			
-			/*
-			if (genStrat || exportAdv) {
-				eqstrat = new ArrayList<Map<BitSet, Double>>();
-				for (int p = 0; p < 2; p++) {
-					eqstrat.add(p, new HashMap<BitSet, Double>());
-					for (int t : nash.getStrat().get(e).get(p).getSupport()) {
-						eqstrat.get(p).put(mmap.get(p).get(t), nash.getStrat().get(e).get(p).get(t));
-					}								
-				} 
-				strats.add(e, eqstrat);
 			}
-			*/
-			
-			if (allSupports.size() == 1) {
+			buildAllSupports();
+			if (checkAllZeroEntries()) {
 				result = new double[1][numCoalitions];
-				for (BitSet entry : allSupports) {
-					for (p = 0; p < numCoalitions; p++) {
-						result[0][p] = utilities.get(entry).get(p);
-					}
-					/*
-					String act = "";
-					if (s == ?) {
-						//for (int i = entry.nextSetBit(0); i >= 0; i = entry.nextSetBit(i + 1)) {	
-						//	act += "[" +  csg.getActions().get(i) + "]";
-						//}
-						System.out.println("## Equilibrium (unique entry or dominating) " + entry + " " + act);
-					}
-					*/
-					if (genStrat || exportAdv) {
-						eqstrat = new ArrayList<Map<BitSet, Double>>();
-						extractStrategyFromSupport(eqstrat, mmap, entry);
-						strats.add(eqstrat);
-					}
+				Arrays.fill(result[0], 0.0);
+				if (genStrat || exportAdv) {
+					eqstrat = new ArrayList<Map<BitSet, Double>>();
+					extractStrategyFromSupport(mmap, eqstrat, (BitSet) utilities.keySet().toArray()[0]);
+					strats.add(eqstrat);
 				}
 				return result;
 			}
+			if (utilities.size() == 1) {
+				return findSWNEUniqueSupport(mmap, strats, eqstrat);
+			}
+
+			smtSupportEnumeration.translateAssertions(assertions, mapActionIndex);
+			//nlpSupportEnumeration.translateAssertions(assertions, mapActionIndex);
+			
+			if (allSupports.size()== 1) {
+				return findSWNEUniqueSupport(mmap, strats, eqstrat);
+			}
 			else {
-				//System.out.println("Solver call");
-				//System.out.println(utilities);
-				for (int supp = 0; supp < allSupports.size(); supp++) {
-					//if (allSupports.get(supp).cardinality() == 25)
-					//System.out.println("\n ## Support " + allSupports.get(supp));
-					//System.out.println("## Support " + allSupports.get(supp));
-					eqsresult = eqssmt.computeEquilibria(allSupports.get(supp), mapActionIndex, s);
-					//eqsresult = new Pair<CSGResultStatus, ArrayList<Double>>(CSGResultStatus.UNKNOWN, new ArrayList<Double>());
-					if (eqsresult.first == CSGResultStatus.SAT) {
-						/*
-						String act = "";
-						if (s == 0) {
-							//System.out.println(csg.getActions());
-							//for (int i = allSupports.get(supp).nextSetBit(0); i >= 0; i = allSupports.get(supp).nextSetBit(i + 1)) {	
-							//	act += "[" +  csg.getActions().get(i) + "]";
-							//}
-							System.out.println("## Equilibrium " + allSupports.get(supp) + " " + act);
+				HashSet<BitSet> unknown = new HashSet<BitSet>();
+				HashSet<BitSet> unsat = new HashSet<BitSet>();
+				HashSet<BitSet> sat = new HashSet<BitSet>();
+
+				//System.out.println(allSupports.size());
+				for (BitSet supp : allSupports) {
+					
+					//System.out.println("\n" + supp);
+					if (supp.cardinality() < numCoalitions) {
+						mainLog.println("Support: " + supp);
+						for (int k = 0; k < numCoalitions; k++) {
+							mainLog.println("Player " + k);
+							mainLog.println("Dominating: " + dominating[k]);
+							mainLog.println("Dominated: " + dominated[k]);	
+							mainLog.println("Action indexes: " + actionIndexes[k]);
+							mainLog.println("Strategies:" + strategies.get(k));
+							mainLog.println("Supports:" + supports.get(k));
 						}
-						*/
-						eq = eqsresult.second;
-						eqs.add(eq);
-						//System.out.println("-- mmap " + mmap);
-						//System.out.println("-- strat " + eqssmt.getStrat());
+						throw new PrismException("Problem with support");
+					}
+					
+					eqsresult = smtSupportEnumeration.computeEquilibria(supp, mapActionIndex);				
+					//eqsresult = nlpSupportEnumeration.computeEquilibria(supp, mapActionIndex);		
+
+					
+					if (eqsresult.getStatus() == CSGResultStatus.SAT) {
+						sat.add(supp);
+						
+						//eqsresult = nlpSupportEnumeration.computeEquilibria(supp, mapActionIndex);		
+						
+						equilibria.add(eqsresult.getPayoffVector());
 						if (genStrat || exportAdv) {
-							eqstrat = new ArrayList<Map<BitSet, Double>>();
-							for (p = 0; p < numCoalitions; p++) {
-								eqstrat.add(p, new HashMap<BitSet, Double>());
-								for (int t : eqssmt.getStrat().get(p).getSupport()) {
-									eqstrat.get(p).put(mmap.get(p).get(t), eqssmt.getStrat().get(p).get(t));
-								}
-								//System.out.println("-- strat " + p + " " + eqstrat.get(p));
-							}
-							strats.add(eqstrat);
-							//System.out.println("-- strats " + strats);
+							strats.add(extractStrategyFromEquilibrium(eqsresult, mmap));
 						}
+						//System.out.println(equilibria);
+						
+						/*
+						if (eqsresult.getStatus() != eqsresultnlp.getStatus()) {
+							System.out.println("SMT: " + eqsresult.getStatus());
+							System.out.println("NLP: " + eqsresultnlp.getStatus());
+							throw new PrismException("Solvers differ.");
+						}
+						*/
+						//System.out.println("sat");
+					}
+					else if (eqsresult.getStatus() == CSGResultStatus.UNKNOWN) {	
+						unknown.add(supp);
 						
-						time = System.currentTimeMillis() - time;
-						//mainLog.println("\nFound an equilibirum in  " + time / 1000.0 + " seconds.");
-						//System.out.println(eq);
-						//System.exit(1);
+						//eqsresult = nlpSupportEnumeration.computeEquilibria(supp, mapActionIndex);	
+						/*
+						if (eqsresult.getStatus() == CSGResultStatus.SAT) {
+							equilibria.add(eqsresult.getPayoffVector());
+						}
+						*/
+						//System.out.println("unknown");
+					}
+					else if (eqsresult.getStatus() == CSGResultStatus.UNSAT) {
+						unsat.add(supp);
+						//System.out.println("unsat");
+						/*
+						if (eqsresult.getStatus() != eqsresultnlp.getStatus()) {
+							System.out.println("SMT: " + eqsresult.getStatus());
+							System.out.println("NLP: " + eqsresultnlp.getStatus());
+							throw new PrismException("Solvers differ.");
+						}
+						*/
 					}
+				}
+
+				if (sat.size() != 0) {
 					/*
-					else if (eqsresult.first == CSGResultStatus.UNKNOWN) {// && allSupports.get(supp).cardinality() == 18) {
-						//System.out.println("UNKNOWN " + allSupports.get(supp));
-						eqss.setNumPlayers(numCoalitions);
-						eqss.setMap(map);
-						eqss.setIndexes(strategies);
-						eqss.setAssertions(assertions);
-						eqss.setGradient(gradient);
-						eqss.init();
-						//System.out.println("## Support " + allSupports.get(supp));
-						eqsresult = eqss.computeEquilibria(allSupports.get(supp), map, s);
-						if (eqsresult.first == CSGResultStatus.SAT) {
-							//System.out.println("## Equilibrium found " + allSupports.get(supp));
-							eq = eqsresult.second;
-							eqs.add(eq);
-							
-							time = System.currentTimeMillis() - time;
-							mainLog.println("\nFound an equilibirum in  " + time / 1000.0 + " seconds.");
-							System.out.println(eq);
-							System.exit(1);	
+					for (EquilibriumResult eq : stepParallelEquilibriaGurobi(sat)) {
+						equilibria.add(eq.getPayoffVector());
+						if (genStrat || exportAdv) {
+							strats.add(extractStrategyFromEquilibrium(eq, mmap));
 						}
+						//if (s == csg.getFirstInitialState()) {
+						//	System.out.println("-- strat " + eq.getStrategy());
+						//} 
 					}
 					*/
 				}
-			}
-		
-			//System.out.println(eqs);
-						
-			result = new double[eqs.size()][numCoalitions];
-		
-			for (n = 0; n < eqs.size(); n++) {
+				//System.out.println("Sat supports: " + sat.size() + " " + (System.currentTimeMillis() - par)/1000.00 + " s");
+
+				//par = System.currentTimeMillis();
+				//System.out.println("Unknown supports: " + unknown.size());
+				if (unknown.size() != 0) {
+					/*
+					for (EquilibriumResult eq : stepParallelEquilibriaGurobi(unknown)) {
+						equilibria.add(eq.getPayoffVector());		
+						if (genStrat || exportAdv) {
+							strats.add(extractStrategyFromEquilibrium(eq, mmap));
+						}
+						//if (s == csg.getFirstInitialState()) {
+						//	System.out.println("-- strat " + eq.getStrategy());
+						//}
+					}			
+					*/
+				}
+
+				//System.out.println("Unknown supports: " + unknown.size() + " " + (System.currentTimeMillis() - par)/1000.00 + " s");
+			}		
+			result = new double[equilibria.size()][numCoalitions];
+			for (n = 0; n < equilibria.size(); n++) {
 				for (p = 0; p < numCoalitions; p++) {
-					result[n][p] = eqs.get(n).get(p);
+					result[n][p] = equilibria.get(n).get(p);
 				}
 			}
 		}
 		return result;
 	}
 	
-	public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csgRewards2, List<Map<Integer, BitSet>> mmap, CSGLabeledPolytopes nash,
-			List<List<Map<BitSet, Double>>> strats, double[][] val, int s, boolean min) throws PrismException {
+	/**
+	 * Returns the equilibrium (array of values) and updates strategies for the two-player case.
+	 * 
+	 * @param csg
+	 * @param rewards
+	 * @param mmap
+	 * @param strats
+	 * @param val
+	 * @param s
+	 * @param eqType
+	 * @param crit
+	 * @param rew
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public double[] stepEquilibriaTwoPlayer(CSG csg, List<CSGRewards> rewards, List<Map<Integer, BitSet>> mmap, List<List<Map<BitSet, Double>>> strats,
+			 								double[][] val, int s, int eqType, int crit, boolean rew, boolean min) throws PrismException {
+		double[][] equilibria;
+		double[] equilibrium;
+		
+		switch (eqType) {
+			case CORR : {
+				if (rew) {
+					equilibrium = stepCorrelatedEquilibria(csg, rewards, mmap, strats, val, s, min, crit);
+				}
+				else 
+					equilibrium = stepCorrelatedEquilibria(csg, null, mmap, strats, val, s, min, crit);
+				break;
+			}
+			default : {
+				if (rew) {
+					equilibria = stepNashEquilibria(csg, rewards.get(0), rewards.get(1), mmap, strats, val, s, min);	
+				}
+				else {
+					equilibria = stepNashEquilibria(csg, null, null, mmap, strats, val, s, min);	
+				}
+				switch (crit) {
+					case FAIR : {
+						equilibrium = fair(equilibria, strats, min);
+						break;
+					} 
+					default : {
+						equilibrium = swne(equilibria, strats, min);
+					}
+				}
+			}
+		}
+		return equilibrium;
+	}
+	
+	/**
+	 * Computes Nash equilibria for a bimatrix game.
+	 * 
+	 * @param csg
+	 * @param csgRewards1
+	 * @param csgRewards2
+	 * @param mmap
+	 * @param strats
+	 * @param val
+	 * @param s
+	 * @param min
+	 * @return
+	 * @throws PrismException
+	 */
+	public double[][] stepNashEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csgRewards2, List<Map<Integer, BitSet>> mmap,
+									 List<List<Map<BitSet, Double>>> strats, double[][] val, int s, boolean min) throws PrismException {
 		Map<BitSet, Double> d1 = null;
 		Map<BitSet, Double> d2 = null;
 		ArrayList<Map<BitSet, Double>> eqstrat;
@@ -1839,7 +2803,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 			mmap.add(p, new HashMap<Integer, BitSet>());
 			nmap.add(p, new ArrayList<Integer>());
 		}
-		bmgame = buildBiMatrixGame(csg, csgRewards1, csgRewards2, mmap, nmap, val, s, min);	
+		bmgame = buildBimatrixGame(csg, csgRewards1, csgRewards2, mmap, nmap, val, s, min);	
 		nrows = bmgame.get(0).size();
 		ncols = bmgame.get(0).get(0).size();
 		val1s = new double[nrows][ncols];
@@ -1913,20 +2877,20 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 					addStateRewards(result, csgRewards1, csgRewards2, s, min);
 				}
 				else { // both players have choices and matrices are not trivial, call solver
-					nash.update(nrows, ncols, val1s, val2s);
-					nash.compEq();
-					nash.compPayoffs();
-					result = new double[nash.getNeq()][2];
-					for (int e = 0; e < nash.getNeq(); e++) {
-						result[e][0] = nash.getP1p()[e];
-						result[e][1] = nash.getP2p()[e];
+					smtLabeleldPolytopes.update(nrows, ncols, val1s, val2s);
+					smtLabeleldPolytopes.computeEquilibria();
+					smtLabeleldPolytopes.compPayoffs();
+					result = new double[smtLabeleldPolytopes.getNeq()][2];
+					for (int e = 0; e < smtLabeleldPolytopes.getNeq(); e++) {
+						result[e][0] = smtLabeleldPolytopes.getP1p()[e];
+						result[e][1] = smtLabeleldPolytopes.getP2p()[e];
 						if (genStrat || exportAdv) {
 							eqstrat = new ArrayList<Map<BitSet, Double>>();
 							for (int p = 0; p < 2; p++) {
 								eqstrat.add(p, new HashMap<BitSet, Double>());
 								//System.out.println("-- strat from solver " + nash.getStrat().get(e).get(p).getSupport());
-								for (int t : nash.getStrat().get(e).get(p).getSupport()) {
-									eqstrat.get(p).put(mmap.get(p).get(nmap.get(p).get(t)), nash.getStrat().get(e).get(p).get(t));
+								for (int t : smtLabeleldPolytopes.getStrat().get(e).get(p).getSupport()) {
+									eqstrat.get(p).put(mmap.get(p).get(nmap.get(p).get(t)), smtLabeleldPolytopes.getStrat().get(e).get(p).get(t));
 								}
 							} 
 							strats.add(e, eqstrat);
@@ -1950,7 +2914,7 @@ public double[][] stepEquilibria(CSG csg, CSGRewards csgRewards1, CSGRewards csg
 				addStateRewards(result, csgRewards1, csgRewards2, s, min);
 			}
 		} 
-		else { // just one of the players have choices
+		else { // just one of the players has choices
 			result = new double[1][2];
 			double vt1, vt2, sumv, sumt;
 			if(genStrat || exportAdv) {

From 7c568445274fa937c9b7b38c5d425eb7f2a253e0 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:32:53 +0100
Subject: [PATCH 29/30] Disables Gurobi

---
 prism/src/explicit/CSGModelCheckerEquilibria.java | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/prism/src/explicit/CSGModelCheckerEquilibria.java b/prism/src/explicit/CSGModelCheckerEquilibria.java
index 12c6c7e85..eb9b3a9e7 100644
--- a/prism/src/explicit/CSGModelCheckerEquilibria.java
+++ b/prism/src/explicit/CSGModelCheckerEquilibria.java
@@ -1286,9 +1286,11 @@ public ModelCheckerResult computeMultiBoundedEquilibria(CSG csg, List<Coalition>
 		smtSupportEnumeration.setNumPlayers(numCoalitions);
 		smtSupportEnumeration.init();
 		
+		/*
 		nlpSupportEnumeration = new CSGSupportEnumerationGurobi(maxNumActions, numCoalitions);
 		nlpSupportEnumeration.setIndexes(strategies);
 		nlpSupportEnumeration.setNumPlayers(numCoalitions);
+		*/
 		
 		done = true;
 		k = 0;
@@ -1459,9 +1461,11 @@ public ModelCheckerResult computeMultiReachEquilibria(CSG csg, List<Coalition> c
 		smtSupportEnumeration.setNumPlayers(numCoalitions);
 		smtSupportEnumeration.init();
 		
+		/*
 		nlpSupportEnumeration = new CSGSupportEnumerationGurobi(maxNumActions, numCoalitions);
 		nlpSupportEnumeration.setIndexes(strategies);
 		nlpSupportEnumeration.setNumPlayers(numCoalitions);
+		*/
 		
 		for (c = numCoalitions; c > 0; c--) {
 			if (c == numCoalitions) {

From 3ddf50aa93091c7bb15e9786488ee9aec1cc2f76 Mon Sep 17 00:00:00 2001
From: gabrielhrs <gabriel.santos@cs.ox.ac.uk>
Date: Tue, 11 Apr 2023 14:40:04 +0100
Subject: [PATCH 30/30] Test SWNE/SWCE/SFNE/SFCE two-player

---
 .../verify/csgs/nash/test_diff_sw_fr.prism    | 30 +++++++++++++++++++
 .../csgs/nash/test_diff_sw_fr.prism.props     |  8 +++++
 2 files changed, 38 insertions(+)
 create mode 100644 prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism
 create mode 100644 prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism.props

diff --git a/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism b/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism
new file mode 100644
index 000000000..518ad992f
--- /dev/null
+++ b/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism
@@ -0,0 +1,30 @@
+csg
+
+player p1 m1 endplayer
+player p2 m2 endplayer
+
+module m1
+	s : bool init false;
+	[a1] !s -> (s'=!s);
+	[b1] !s -> (s'=!s);
+endmodule
+
+module m2
+	[a2] !s -> true;
+	[b2] !s -> true;
+endmodule
+
+rewards "r1"
+	[a1,a2] !s : 5.0;
+	[a1,b2] !s : 2.0;
+	[b1,a2] !s : 6.0;
+	[b1,b2] !s : 0.0;
+endrewards
+
+rewards "r2"
+	[a1,a2] !s : 5.0;
+	[a1,b2] !s : 6.0;
+	[b1,a2] !s : 2.0;
+	[b1,b2] !s : 1.0;
+endrewards
+
diff --git a/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism.props b/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism.props
new file mode 100644
index 000000000..1eb2cef01
--- /dev/null
+++ b/prism-tests/functionality/verify/csgs/nash/test_diff_sw_fr.prism.props
@@ -0,0 +1,8 @@
+// RESULT: 16/2
+<<p1:p2>>{NE,SW}max=?(R{"r1"}[C<=1] + R{"r2"}[C<=1]) 
+// RESULT: 15/2
+<<p1:p2>>{NE,FR}max=?(R{"r1"}[C<=1] + R{"r2"}[C<=1])
+// RESULT: 44/5
+<<p1:p2>>{CE,SW}max=?(R{"r1"}[C<=1] + R{"r2"}[C<=1]) 
+// RESULT: 26/3
+<<p1:p2>>{CE,FR}max=?(R{"r1"}[C<=1] + R{"r2"}[C<=1])