diff --git a/theano/gof/destroyhandler.py b/theano/gof/destroyhandler.py
index f32cb48a5ad..278aff8d156 100644
--- a/theano/gof/destroyhandler.py
+++ b/theano/gof/destroyhandler.py
@@ -394,19 +394,25 @@ def get_destroyers_of(r):
                 return []
         fgraph.destroyers = get_destroyers_of
 
-        def recursive_destroys_finder(clients_list):
-            for (app, idx) in clients_list:
-                if app == 'output':
-                    continue
-                destroy_maps = getattr(app.op, 'destroy_map', {}).values()
-                if idx in [dmap for sublist in destroy_maps for dmap in sublist]:
-                    return True
-                for var in getattr(app.op, 'view_map', {}).keys():
-                    if recursive_destroys_finder(app.outputs[var].clients):
+        def has_destroyers(protected_list):
+            visited_app_set = set()
+
+            def recursive_destroys_finder(clients_list):
+                for (app, idx) in clients_list:
+                    if app in visited_app_set:
+                        continue
+                    else:
+                        visited_app_set.add(app)
+                    if app == 'output':
+                        continue
+                    destroy_maps = getattr(app.op, 'destroy_map', {}).values()
+                    if idx in [dmap for sublist in destroy_maps for dmap in sublist]:
                         return True
-            return False
+                    for var in getattr(app.op, 'view_map', {}).keys():
+                        if recursive_destroys_finder(app.outputs[var].clients):
+                            return True
+                return False
 
-        def has_destroyers(protected_list):
             for protected_var in protected_list:
                 if recursive_destroys_finder(protected_var.clients):
                     return True