diff --git a/doc/tl/tl.tex b/doc/tl/tl.tex
index 44be3006b..eb759ea44 100644
--- a/doc/tl/tl.tex
+++ b/doc/tl/tl.tex
@@ -1735,9 +1735,9 @@ $f_U$         &                       &              & $f_U\simp g$ &
 \hline
 $\X f$        &                       & $f\simp g_E$ & $f\simp g$   &                           &                           &                                     &                                     &                       &               &                      &                       \\
 \hline
-$f_1\U f_2$   & \band{f_1}{g}{f_2}{g} &              &              & \band{f_1}{g_1}{f_2}{g_2} & \band{f_1}{g_1}{f_2}{g_2} & \banD{f_1}{g_1}{f_2}{g_1}{f_2}{g_2} & \banD{f_1}{g_1}{f_2}{g_1}{f_2}{g_2} & \bone{f_2}{g}         &               &                      &                       \\
+$f_1\U f_2$   & \band{f_1}{g}{f_2}{g} &              &              & \band{f_1}{g_1}{f_2}{g_2} & \band{f_1}{g_1}{f_2}{g_2} & \banD{f_1}{g_2}{f_2}{g_1}{f_2}{g_2} & \banD{f_1}{g_2}{f_2}{g_1}{f_2}{g_2} & \bone{f_2}{g}         &               &                      &                       \\
 \hline
-$f_1\W f_2$   & \band{f_1}{g}{f_2}{g} &              &              & \band{f_1}{g_2}{f_2}{g_2} & \band{f_1}{g_1}{f_2}{g_2} & \banD{f_1}{g_1}{f_2}{g_1}{f_2}{g_2} &                                     & \band{f_1}{g}{f_2}{g} &               &                      &                       \\
+$f_1\W f_2$   & \band{f_1}{g}{f_2}{g} &              &              & \band{f_1}{g_2}{f_2}{g_2} & \band{f_1}{g_1}{f_2}{g_2} & \banD{f_1}{g_2}{f_2}{g_1}{f_2}{g_2} &                                     & \band{f_1}{g}{f_2}{g} &               &                      &                       \\
 \hline
 $f_1\R f_2$   & \bone{f_2}{g}         &              &              &                           & \band{f_1}{g_2}{f_2}{g_1} & \band{f_1}{g_1}{f_2}{g_2}           & \band{f_2}{g_1}{f_2}{g_2}           & \bone{f_2}{g}         &               &                      &                       \\
 \hline
diff --git a/src/ltltest/reduccmp.test b/src/ltltest/reduccmp.test
index 853aa450b..af361d6ed 100755
--- a/src/ltltest/reduccmp.test
+++ b/src/ltltest/reduccmp.test
@@ -324,6 +324,7 @@ for x in ../reduccmp ../reductaustr; do
      run 0 $x '!{a;b*;(a* && (b;c));c*}' '!a | X(!b M !{a[*] && {b;c}})'
      run 0 $x '{(a;c*;d)|(b;c)}' '(a & X(c W d)) | (b & Xc)'
      run 0 $x '!{(a;c*;d)|(b;c)}' '(X(!c M !d) | !a) & (X!c | !b)'
+     run 0 $x '(Xc R b) & (Xc W 0)' 'b & XGc'
 
      # not reduced
      run 0 $x '{a;(b[*2..4];c*;([*0]+{d;e}))*}!' \
diff --git a/src/ltltest/syntimpl.test b/src/ltltest/syntimpl.test
index 921ce2652..9ca48eb27 100755
--- a/src/ltltest/syntimpl.test
+++ b/src/ltltest/syntimpl.test
@@ -1,8 +1,9 @@
 #! /bin/sh
-# Copyright (C) 2009, 2010 Laboratoire de Recherche et Développement
-# de l'Epita (LRDE).
+# -*- coding: utf-8 -*-
+# Copyright (C) 2009, 2010, 2012 Laboratoire de Recherche et
+# Développement de l'Epita (LRDE).
 # Copyright (C) 2004 Laboratoire d'Informatique de Paris 6 (LIP6),
-# département Systèmes Répartis Coopératifs (SRC), Université Pierre
+# département Systèmes Répartis Coopératifs (SRC), Université Pierre
 # et Marie Curie.
 #
 # This file is part of Spot, a model checking library.
@@ -93,3 +94,8 @@ run 0 ../syntimpl 0 'a R b' 'a'
 
 run 0 ../syntimpl 0 'p2' 'p3 || G(p2 && p5)'
 run 0 ../syntimpl 0 '!(p3 || G(p2 && p5))' '!p2'
+
+run 0 ../syntimpl 0 'Xc W 0' 'Xc R b'
+run 1 ../syntimpl 0 '(c&b) W (b&a)' 'a R b'
+
+exit 0
\ No newline at end of file
diff --git a/src/ltlvisit/simplify.cc b/src/ltlvisit/simplify.cc
index 098a0fd9f..69d30983a 100644
--- a/src/ltlvisit/simplify.cc
+++ b/src/ltlvisit/simplify.cc
@@ -235,8 +235,16 @@ namespace spot
       bool
       implication(const formula* f1, const formula* f2)
       {
-	return (options.synt_impl && syntactic_implication(f1, f2))
-	  || (options.containment_checks && contained(f1, f2));
+	trace << "[->] does " << to_string(f1) << " implies "
+	      << to_string(f2) << " ?" << std::endl;
+	if ((options.synt_impl && syntactic_implication(f1, f2))
+	    || (options.containment_checks && contained(f1, f2)))
+	  {
+	    trace << "[->] Yes" << std::endl;
+	    return true;
+	  }
+	trace << "[->] No" << std::endl;
+	return false;
       }
 
       // Return true if f1 => f2 syntactically
@@ -3910,7 +3918,7 @@ namespace spot
 		else if ((fo == binop::U && (go == binop::R || go == binop::M))
 			 || (fo == binop::W && go == binop::R))
 		  {
-		    if (syntactic_implication(f1, g1)
+		    if (syntactic_implication(f1, g2)
 			&& syntactic_implication(f2, g1)
 			&& syntactic_implication(f2, g2))
 		      return true;