diff --git a/source/vir/src/func_to_air.rs b/source/vir/src/func_to_air.rs
index 35e09f9d79..300134b744 100644
--- a/source/vir/src/func_to_air.rs
+++ b/source/vir/src/func_to_air.rs
@@ -375,7 +375,7 @@ pub fn req_ens_to_air(
 /// if the function is a spec function.
 pub fn func_name_to_air(
     ctx: &Ctx,
-    diagnostics: &impl Diagnostics,
+    _diagnostics: &impl Diagnostics,
     function: &Function,
 ) -> Result<Commands, VirErr> {
     let mut commands: Vec<Command> = Vec::new();
@@ -400,15 +400,8 @@ pub fn func_name_to_air(
         commands.push(Arc::new(CommandX::Global(decl)));
 
         // Check whether we need to declare the recursive version too
-        if let Some(body) = &function.x.body {
-            let body_exp = crate::ast_to_sst::expr_to_exp_as_spec(
-                &ctx,
-                diagnostics,
-                &UpdateCell::new(HashMap::new()),
-                &params_to_pars(&function.x.params, false),
-                &body,
-            )?;
-            if crate::recursion::is_recursive_exp(ctx, &function.x.name, &body_exp) {
+        if function.x.body.is_some() {
+            if crate::recursion::fun_is_recursive(ctx, &function.x.name) {
                 let rec_f =
                     suffix_global_id(&fun_to_air_ident(&prefix_recursive_fun(&function.x.name)));
                 let mut rec_typs =
diff --git a/source/vir/src/recursion.rs b/source/vir/src/recursion.rs
index 32f8f5a0b8..a680192299 100644
--- a/source/vir/src/recursion.rs
+++ b/source/vir/src/recursion.rs
@@ -16,10 +16,7 @@ use crate::sst::{
     UniqueIdent,
 };
 use crate::sst_to_air::PostConditionKind;
-use crate::sst_visitor::{
-    exp_rename_vars, exp_visitor_check, exp_visitor_dfs, map_exp_visitor, map_stm_visitor,
-    stm_visitor_dfs, VisitorControlFlow,
-};
+use crate::sst_visitor::{exp_rename_vars, exp_visitor_check, map_exp_visitor, map_stm_visitor};
 use crate::util::vec_map_result;
 use air::ast::{Binder, Commands, Span};
 use air::ast_util::{ident_binder, str_ident, str_typ};
@@ -53,15 +50,6 @@ fn get_callee(ctx: &Ctx, target: &Fun, resolved_method: &Option<(Fun, Typs)>) ->
     }
 }
 
-fn is_self_call(
-    ctx: &Ctx,
-    target: &Fun,
-    resolved_method: &Option<(Fun, Typs)>,
-    name: &Fun,
-) -> bool {
-    get_callee(ctx, target, resolved_method) == Some(name.clone())
-}
-
 fn is_recursive_call(ctxt: &Ctxt, target: &Fun, resolved_method: &Option<(Fun, Typs)>) -> bool {
     if let Some(callee) = get_callee(ctxt.ctx, target, resolved_method) {
         callee == ctxt.recursive_function_name
@@ -315,45 +303,8 @@ fn terminates(
     }
 }
 
-pub(crate) fn is_recursive_exp(ctx: &Ctx, name: &Fun, body: &Exp) -> bool {
-    if ctx.global.func_call_graph.get_scc_size(&Node::Fun(name.clone())) > 1 {
-        // This function is part of a mutually recursive component
-        true
-    } else {
-        let mut scope_map = ScopeMap::new();
-        // Check for self-recursion, which SCC computation does not account for
-        match exp_visitor_dfs(body, &mut scope_map, &mut |exp, _scope_map| match &exp.x {
-            ExpX::Call(CallFun::Fun(x, resolved_method), _, _)
-                if is_self_call(ctx, x, resolved_method, name) =>
-            {
-                VisitorControlFlow::Stop(())
-            }
-            _ => VisitorControlFlow::Recurse,
-        }) {
-            VisitorControlFlow::Stop(()) => true,
-            _ => false,
-        }
-    }
-}
-
-pub(crate) fn is_recursive_stm(ctx: &Ctx, name: &Fun, body: &Stm) -> bool {
-    if ctx.global.func_call_graph.get_scc_size(&Node::Fun(name.clone())) > 1 {
-        // This function is part of a mutually recursive component
-        true
-    } else {
-        // Check for self-recursion, which SCC computation does not account for
-        match stm_visitor_dfs(body, &mut |stm| match &stm.x {
-            StmX::Call { fun, resolved_method, .. }
-                if is_self_call(ctx, fun, resolved_method, name) =>
-            {
-                VisitorControlFlow::Stop(())
-            }
-            _ => VisitorControlFlow::Recurse,
-        }) {
-            VisitorControlFlow::Stop(()) => true,
-            _ => false,
-        }
-    }
+pub(crate) fn fun_is_recursive(ctx: &Ctx, name: &Fun) -> bool {
+    ctx.global.func_call_graph.node_is_in_cycle(&Node::Fun(name.clone()))
 }
 
 fn mk_decreases_at_entry(ctxt: &Ctxt, span: &Span, exps: &Vec<Exp>) -> (Vec<LocalDecl>, Vec<Stm>) {
@@ -407,7 +358,7 @@ pub(crate) fn check_termination_exp(
     proof_body: Vec<Stm>,
     uses_decreases_by: bool,
 ) -> Result<(bool, Commands, Exp), VirErr> {
-    if !is_recursive_exp(ctx, &function.x.name, body) {
+    if !fun_is_recursive(ctx, &function.x.name) {
         return Ok((false, Arc::new(vec![]), body.clone()));
     }
     let num_decreases = function.x.decrease.len();
@@ -484,7 +435,7 @@ pub(crate) fn check_termination_stm(
     function: &Function,
     body: &Stm,
 ) -> Result<(Vec<LocalDecl>, Stm), VirErr> {
-    if !is_recursive_stm(ctx, &function.x.name, body) {
+    if !fun_is_recursive(ctx, &function.x.name) {
         return Ok((vec![], body.clone()));
     }
     let num_decreases = function.x.decrease.len();
diff --git a/source/vir/src/scc.rs b/source/vir/src/scc.rs
index 838f4161c0..5b2dadf959 100644
--- a/source/vir/src/scc.rs
+++ b/source/vir/src/scc.rs
@@ -180,6 +180,18 @@ impl<T: std::cmp::Eq + std::hash::Hash + Clone> Graph<T> {
         sorted
     }
 
+    pub fn node_has_direct_edge_to_itself(&self, t: &T) -> bool {
+        assert!(self.has_run);
+        assert!(self.h.contains_key(&t));
+        let v: NodeIndex = self.h[t];
+        for edge in self.nodes[v].edges.iter() {
+            if *edge == v {
+                return true;
+            }
+        }
+        false
+    }
+
     pub fn get_scc_size(&self, t: &T) -> usize {
         assert!(self.has_run);
         match self.mapping.get(&t) {
@@ -188,6 +200,10 @@ impl<T: std::cmp::Eq + std::hash::Hash + Clone> Graph<T> {
         }
     }
 
+    pub fn node_is_in_cycle(&self, t: &T) -> bool {
+        self.node_has_direct_edge_to_itself(t) || self.get_scc_size(t) > 1
+    }
+
     pub fn get_scc_rep(&self, t: &T) -> T {
         assert!(self.has_run);
         assert!(self.mapping.contains_key(&t));