diff --git a/wrap/python/ajax/spotcgi.in b/wrap/python/ajax/spotcgi.in
index f9212907c..54e4a0f07 100755
--- a/wrap/python/ajax/spotcgi.in
+++ b/wrap/python/ajax/spotcgi.in
@@ -310,6 +310,11 @@ def print_stats(automaton, detinfo = False, ta = False):
         stats = spot.stats_reachable(automaton)
         detinfo = False
     else:
+        if (buchi_type == 't' and automaton.is_inherently_weak() and
+            automaton.acc().is_buchi()):
+            unbufprint("Note: this is a weak automaton, using transition-based "
+                       "or generalized acceptance does not bring any benefit."
+                       "</br>")
         stats = spot.sub_stats_reachable(automaton)
     unbufprint("<p>%d state" % stats.states)
     if stats.states > 1: