diff --git a/lucene/core/src/java/org/apache/lucene/util/graph/GraphTokenStreamFiniteStrings.java b/lucene/core/src/java/org/apache/lucene/util/graph/GraphTokenStreamFiniteStrings.java
index 3ea862c53013..048cf0ab00c9 100644
--- a/lucene/core/src/java/org/apache/lucene/util/graph/GraphTokenStreamFiniteStrings.java
+++ b/lucene/core/src/java/org/apache/lucene/util/graph/GraphTokenStreamFiniteStrings.java
@@ -18,6 +18,7 @@
 package org.apache.lucene.util.graph;
 
 import static org.apache.lucene.util.automaton.Operations.DEFAULT_DETERMINIZE_WORK_LIMIT;
+import static org.apache.lucene.util.automaton.Operations.MAX_RECURSION_LEVEL;
 
 import java.io.IOException;
 import java.util.ArrayList;
@@ -46,7 +47,6 @@
  */
 public final class GraphTokenStreamFiniteStrings {
 
-  private static final int MAX_RECURSION_DEPTH = 1024;
   private AttributeSource[] tokens = new AttributeSource[4];
   private final Automaton det;
   private final Transition transition = new Transition();
@@ -270,9 +270,13 @@ private static void articulationPointsRecurse(
     int numT = a.initTransition(state, t);
     for (int i = 0; i < numT; i++) {
       a.getNextTransition(t);
-      if (visited.get(t.dest) == false && d < MAX_RECURSION_DEPTH) {
+      if (visited.get(t.dest) == false) {
         parent[t.dest] = state;
-        articulationPointsRecurse(a, t.dest, d + 1, depth, low, parent, visited, points);
+        if (d < MAX_RECURSION_LEVEL) {
+          articulationPointsRecurse(a, t.dest, d + 1, depth, low, parent, visited, points);
+        } else {
+          continue;
+        }
         childCount++;
         if (low[t.dest] >= depth[state]) {
           isArticulation = true;
diff --git a/lucene/core/src/test/org/apache/lucene/util/graph/TestGraphTokenStreamFiniteStrings.java b/lucene/core/src/test/org/apache/lucene/util/graph/TestGraphTokenStreamFiniteStrings.java
index 88a14696cac8..56fadc901445 100644
--- a/lucene/core/src/test/org/apache/lucene/util/graph/TestGraphTokenStreamFiniteStrings.java
+++ b/lucene/core/src/test/org/apache/lucene/util/graph/TestGraphTokenStreamFiniteStrings.java
@@ -16,6 +16,8 @@
  */
 package org.apache.lucene.util.graph;
 
+import static org.apache.lucene.util.automaton.Operations.MAX_RECURSION_LEVEL;
+
 import java.util.ArrayList;
 import java.util.Iterator;
 import org.apache.lucene.analysis.TokenStream;
@@ -663,12 +665,11 @@ public void testMultipleSidePathsWithGaps() throws Exception {
   }
 
   public void testLongTokenStreamStackOverflowError() throws Exception {
+
     ArrayList<Token> tokens =
         new ArrayList<Token>() {
           {
-            add(token("turbo", 1, 1));
-            add(token("fast", 0, 2));
-            add(token("charged", 1, 1));
+            add(token("fast", 1, 1));
             add(token("wi", 1, 1));
             add(token("wifi", 0, 2));
             add(token("fi", 1, 1));
@@ -682,6 +683,33 @@ public void testLongTokenStreamStackOverflowError() throws Exception {
 
     TokenStream ts = new CannedTokenStream(tokens.toArray(new Token[0]));
     GraphTokenStreamFiniteStrings graph = new GraphTokenStreamFiniteStrings(ts);
-    graph.articulationPoints(); // This will cause a java.lang.StackOverflowError
+
+    Iterator<TokenStream> it = graph.getFiniteStrings();
+    assertTrue(it.hasNext());
+    it.next();
+    assertTrue(it.hasNext());
+    it.next();
+    assertFalse(it.hasNext());
+
+    int[] points = graph.articulationPoints(); // This will cause a java.lang.StackOverflowError
+    assertEquals(points[0], 1);
+    assertEquals(points[1], 3);
+    assertEquals(points.length, MAX_RECURSION_LEVEL - 2);
+
+    assertFalse(graph.hasSidePath(0));
+    it = graph.getFiniteStrings(0, 1);
+    assertTrue(it.hasNext());
+    assertTokenStream(it.next(), new String[] {"fast"}, new int[] {1});
+    assertFalse(it.hasNext());
+    Term[] terms = graph.getTerms("field", 0);
+    assertArrayEquals(terms, new Term[] {new Term("field", "fast")});
+
+    assertTrue(graph.hasSidePath(1));
+    it = graph.getFiniteStrings(1, 3);
+    assertTrue(it.hasNext());
+    assertTokenStream(it.next(), new String[] {"wi", "fi"}, new int[] {1, 1});
+    assertTrue(it.hasNext());
+    assertTokenStream(it.next(), new String[] {"wifi"}, new int[] {1});
+    assertFalse(it.hasNext());
   }
 }