diff --git a/spot/twacube_algos/convert.cc b/spot/twacube_algos/convert.cc
index a6f654fc6..5f0d4ccc2 100644
--- a/spot/twacube_algos/convert.cc
+++ b/spot/twacube_algos/convert.cc
@@ -19,6 +19,7 @@
 
 #include "config.h"
 #include <spot/twacube_algos/convert.hh>
+#include <spot/twaalgos/contains.hh>
 #include <assert.h>
 
 namespace spot
@@ -187,4 +188,76 @@ namespace spot
 
     return res;
   }
+
+  // FIXME this code is very close to twacube_to_twa, can we merge both?
+  bool are_equivalent(const spot::twacube_ptr twacube,
+                      const spot::const_twa_graph_ptr twa)
+  {
+    // Compute the necessary binder and extract atomic propositions
+    std::unordered_map<int, int> ap_binder;
+    std::vector<std::string>* aps_twa = extract_aps(twa, ap_binder);
+    std::vector<std::string> aps_twacube = twacube->ap();
+
+    // Comparator to compare two strings in case insensitive manner
+    std::function< bool (const std::string&, const std::string&) >
+      comparator = [](const std::string& lhs, const std::string& rhs){
+                     return lhs.compare(rhs) == 0;
+                   };
+
+    // Error. Not working on the same set of aps.
+    if (aps_twa->size() != aps_twacube.size() ||
+        !std::equal(aps_twa->begin(), aps_twa->end(),
+                   aps_twacube.begin(), comparator))
+      throw std::runtime_error("are_equivalent: not working on the same "
+                               "atomic propositions");
+
+    // Grab necessary variables
+    auto& theg = twacube->get_graph();
+    spot::cubeset cs = twacube->get_cubeset();
+
+    auto d = twa->get_dict();
+    auto res = make_twa_graph(d);
+
+    // Fix the acceptance of the resulting automaton
+    res->acc() = twacube->acc();
+
+    // Grep bdd id for each atomic propositions
+    std::vector<int> bdds_ref;
+    for (unsigned i = 0; i < aps_twacube.size(); ++i)
+      {
+        bdds_ref.push_back(ap_binder[i]);
+      }
+
+    // Build all resulting states
+    for (unsigned int i = 0; i < theg.num_states(); ++i)
+      {
+        unsigned st = res->new_state();
+        (void) st;
+        assert(st == i);
+      }
+
+    // Build all resulting conditions.
+    for (unsigned int i = 1; i <= theg.num_edges(); ++i)
+      {
+        bdd cond = bddtrue;
+        for (unsigned j = 0; j < cs.size(); ++j)
+          {
+            if (cs.is_true_var(theg.edge_data(i).cube_, j))
+              cond &= bdd_ithvar(bdds_ref[j]);
+            else if (cs.is_false_var(theg.edge_data(i).cube_, j))
+              cond &= bdd_nithvar(bdds_ref[j]);
+            // otherwise it 's a free variable do nothing
+          }
+
+        res->new_edge(theg.edge_storage(i).src, theg.edge_storage(i).dst,
+                      cond, theg.edge_data(i).acc_);
+      }
+
+    // Fix the initial state
+    res->set_init_state(twacube->get_initial());
+
+    bool result =  are_equivalent(res, twa);
+    delete aps_twa;
+    return result;
+  }
 }
diff --git a/spot/twacube_algos/convert.hh b/spot/twacube_algos/convert.hh
index 6c0874225..bdcfc7155 100644
--- a/spot/twacube_algos/convert.hh
+++ b/spot/twacube_algos/convert.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2016 Laboratoire de Recherche et Developpement de
+// Copyright (C) 2015, 2016, 2020 Laboratoire de Recherche et Developpement de
 // l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -53,4 +53,8 @@ namespace spot
   /// \brief Convert a twacube into a twa
   SPOT_API spot::twa_graph_ptr
   twacube_to_twa(spot::twacube_ptr twacube);
+
+  /// \brief Check wether a twacube and a twa are equivalent
+  SPOT_API bool are_equivalent(const spot::twacube_ptr twacube,
+                               const spot::const_twa_graph_ptr twa);
 }
diff --git a/tests/core/twacube.cc b/tests/core/twacube.cc
index 9e9b50892..1e5089ca8 100644
--- a/tests/core/twacube.cc
+++ b/tests/core/twacube.cc
@@ -49,6 +49,8 @@ int main()
 
   // Test translation
   auto aut = twa_to_twacube(tg);
+  assert(spot::are_equivalent(aut, tg));
+
   spot::print_dot(std::cout, tg, "A");
   std::cout << "-----------\n" << *aut << "-----------\n";