diff --git a/spot/tl/contain.cc b/spot/tl/contain.cc
index a977edb35..f787c9906 100644
--- a/spot/tl/contain.cc
+++ b/spot/tl/contain.cc
@@ -24,6 +24,7 @@
 #include <spot/tl/simplify.hh>
 #include <spot/tl/formula.hh>
 #include <spot/twaalgos/product.hh>
+#include <spot/twaalgos/are_isomorphic.hh>
 
 namespace spot
 {
@@ -104,6 +105,12 @@ namespace spot
   bool
   language_containment_checker::equal(formula l, formula g)
   {
+    if (l == g)
+      return true;
+    record_* rl = register_formula_(l);
+    record_* rg = register_formula_(g);
+    if (isomorphism_checker::are_isomorphic(rl->translation, rg->translation))
+      return true;
     return contained(l, g) && contained(g, l);
   }
 
diff --git a/spot/twaalgos/are_isomorphic.cc b/spot/twaalgos/are_isomorphic.cc
index a53106fa0..751f804a3 100644
--- a/spot/twaalgos/are_isomorphic.cc
+++ b/spot/twaalgos/are_isomorphic.cc
@@ -123,29 +123,40 @@ namespace spot
   }
 
   bool
-  isomorphism_checker::is_isomorphic(const const_twa_graph_ptr aut)
+  isomorphism_checker::is_isomorphic_(const const_twa_graph_ptr aut)
   {
-    if (trivially_different(ref_, aut))
-      return false;
-
+    bool autdet = aut->prop_deterministic();
     if (ref_deterministic_)
       {
-        if (aut->prop_deterministic() || spot::is_deterministic(aut))
-          {
-            return are_isomorphic_det(ref_, aut);
-          }
+        if (autdet || spot::is_deterministic(aut))
+	  return are_isomorphic_det(ref_, aut);
       }
     else
       {
-        if (aut->prop_deterministic() ||
-            nondet_states_ != spot::count_nondet_states(aut))
-          {
-            return false;
-          }
+        if (autdet || nondet_states_ != spot::count_nondet_states(aut))
+	  return false;
       }
 
     auto tmp = make_twa_graph(aut, twa::prop_set::all());
     spot::canonicalize(tmp);
     return *tmp == *ref_;
   }
+
+  bool
+  isomorphism_checker::is_isomorphic(const const_twa_graph_ptr aut)
+  {
+    if (trivially_different(ref_, aut))
+      return false;
+    return is_isomorphic_(aut);
+  }
+
+  bool
+  isomorphism_checker::are_isomorphic(const const_twa_graph_ptr ref,
+				      const const_twa_graph_ptr aut)
+  {
+    if (trivially_different(ref, aut))
+      return false;
+    isomorphism_checker c(ref);
+    return c.is_isomorphic_(aut);
+  }
 }
diff --git a/spot/twaalgos/are_isomorphic.hh b/spot/twaalgos/are_isomorphic.hh
index f9f25eb7a..cb48d03da 100644
--- a/spot/twaalgos/are_isomorphic.hh
+++ b/spot/twaalgos/are_isomorphic.hh
@@ -25,7 +25,7 @@
 namespace spot
 {
   /// Check if two automata are isomorphic.
-  class SPOT_API isomorphism_checker
+  class SPOT_API isomorphism_checker final
   {
   public:
     isomorphism_checker(const const_twa_graph_ptr ref);
@@ -45,7 +45,14 @@ namespace spot
     bool
     is_isomorphic(const const_twa_graph_ptr aut);
 
+
+    /// \ingroup twa_misc
+    /// \brief Check whether two automata are isomorphic.
+    static bool are_isomorphic(const const_twa_graph_ptr ref,
+			       const const_twa_graph_ptr aut);
+
   private:
+    bool is_isomorphic_(const const_twa_graph_ptr aut);
     twa_graph_ptr ref_;
     bool ref_deterministic_ = false;
     unsigned nondet_states_ = 0;