diff --git a/NEWS b/NEWS
index 844734f21..ad4324de0 100644
--- a/NEWS
+++ b/NEWS
@@ -48,7 +48,10 @@ New in spot 1.99.4a (not yet released)
     "trust_hoa": when true (the default) supported properties declared
     in HOA files are trusted even if they cannot be easily be verified.
 
-  * ltl_simplifier renamed to tl_simplifier.
+  * renamings:
+    ltl_simplifier -> tl_simplifier
+    tgba_statistics::transitions -> twa_statistics::edges
+    tgba_sub_statistics::sub_transitions -> twa_sub_statistics::transitions
 
   Python:
 
diff --git a/src/bin/common_aoutput.hh b/src/bin/common_aoutput.hh
index ee11b71e7..8b68618bd 100644
--- a/src/bin/common_aoutput.hh
+++ b/src/bin/common_aoutput.hh
@@ -128,16 +128,16 @@ public:
 
 	if (has('T'))
 	  {
-	    spot::tgba_sub_statistics s = sub_stats_reachable(haut->aut);
+	    spot::twa_sub_statistics s = sub_stats_reachable(haut->aut);
 	    haut_states_ = s.states;
-	    haut_edges_ = s.transitions;
-	    haut_trans_ = s.sub_transitions;
+	    haut_edges_ = s.edges;
+	    haut_trans_ = s.transitions;
 	  }
 	else if (has('E'))
 	  {
-	    spot::tgba_sub_statistics s = sub_stats_reachable(haut->aut);
+	    spot::twa_sub_statistics s = sub_stats_reachable(haut->aut);
 	    haut_states_ = s.states;
-	    haut_edges_ = s.transitions;
+	    haut_edges_ = s.edges;
 	  }
 	if (has('M'))
 	  {
diff --git a/src/bin/ltlcross.cc b/src/bin/ltlcross.cc
index 71f80e4a1..db48a3f0b 100644
--- a/src/bin/ltlcross.cc
+++ b/src/bin/ltlcross.cc
@@ -601,10 +601,10 @@ namespace
 	      if (verbose)
 		std::cerr << "info: getting statistics\n";
 	      st->ok = true;
-	      spot::tgba_sub_statistics s = sub_stats_reachable(res);
+	      spot::twa_sub_statistics s = sub_stats_reachable(res);
 	      st->states = s.states;
-	      st->edges = s.transitions;
-	      st->transitions = s.sub_transitions;
+	      st->edges = s.edges;
+	      st->transitions = s.transitions;
 	      st->acc = res->acc().num_sets();
 	      spot::scc_info m(res);
 	      unsigned c = m.scc_count();
@@ -927,9 +927,9 @@ namespace
 	  if (sm)
 	    {
 	      (*stats)[i].product_scc.push_back(sm->scc_count());
-	      spot::tgba_statistics s = spot::stats_reachable(sm->get_aut());
+	      spot::twa_statistics s = spot::stats_reachable(sm->get_aut());
 	      (*stats)[i].product_states.push_back(s.states);
-	      (*stats)[i].product_transitions.push_back(s.transitions);
+	      (*stats)[i].product_transitions.push_back(s.edges);
 	    }
 	  else
 	    {
diff --git a/src/taalgos/stats.cc b/src/taalgos/stats.cc
index 7e963154d..9742cc190 100644
--- a/src/taalgos/stats.cc
+++ b/src/taalgos/stats.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2008, 2014 Laboratoire de Recherche et Développement
-// de l'Epita (LRDE).
+// Copyright (C) 2008, 2014, 2015 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
 // et Marie Curie.
@@ -49,7 +49,7 @@ namespace spot
       void
       process_link(int, int, const ta_succ_iterator*)
       {
-        ++s_.transitions;
+        ++s_.edges;
       }
 
     private:
@@ -61,7 +61,7 @@ namespace spot
   std::ostream&
   ta_statistics::dump(std::ostream& out) const
   {
-    out << "transitions: " << transitions << std::endl;
+    out << "edges: " << edges << std::endl;
     out << "states: " << states << std::endl;
     return out;
   }
diff --git a/src/taalgos/stats.hh b/src/taalgos/stats.hh
index a26d7469b..0853dae03 100644
--- a/src/taalgos/stats.hh
+++ b/src/taalgos/stats.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2013, 2014 Laboratoire de Recherche et Développement
-// de l'Epita (LRDE).
+// Copyright (C) 2011, 2013, 2014, 2015 Laboratoire de Recherche et
+// Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -30,7 +30,7 @@ namespace spot
 
   struct SPOT_API ta_statistics
   {
-    unsigned transitions;
+    unsigned edges;
     unsigned states;
     unsigned acceptance_states;
 
diff --git a/src/tests/checkta.cc b/src/tests/checkta.cc
index b973756e2..eec5d5062 100644
--- a/src/tests/checkta.cc
+++ b/src/tests/checkta.cc
@@ -47,7 +47,7 @@ stats(std::string title, const spot::ta_ptr& ta)
 
   std::cout << std::left << std::setw(20) << title << " | "
 	    << std::right << std::setw(6) << s.states << " | "
-	    << std::setw(6) << s.transitions << " | "
+	    << std::setw(6) << s.edges << " | "
 	    << std::setw(6) << s.acceptance_states << '\n';
 }
 
@@ -58,7 +58,7 @@ stats(std::string title, const spot::twa_ptr& tg)
 
   std::cout << std::left << std::setw(20) << title << " | "
 	    << std::right << std::setw(6) << s.states << " | "
-	    << std::setw(6) << s.transitions << " | "
+	    << std::setw(6) << s.edges << " | "
 	    << std::setw(6) << "XXX" << '\n';
 }
 
diff --git a/src/tests/complementation.cc b/src/tests/complementation.cc
index 09568f917..aba54c06c 100644
--- a/src/tests/complementation.cc
+++ b/src/tests/complementation.cc
@@ -186,10 +186,10 @@ int main(int argc, char* argv[])
 
     auto safra_complement = spot::make_safra_complement(a);
 
-    spot::tgba_statistics a_size =  spot::stats_reachable(a);
+    spot::twa_statistics a_size =  spot::stats_reachable(a);
     std::cout << "Original: "
               << a_size.states << ", "
-              << a_size.transitions << ", "
+              << a_size.edges << ", "
               << a->acc().num_sets()
               << std::endl;
 
@@ -200,20 +200,20 @@ int main(int argc, char* argv[])
               << buchi->acc().num_sets()
               << std::endl;
 
-    spot::tgba_statistics b_size =  spot::stats_reachable(safra_complement);
+    spot::twa_statistics b_size =  spot::stats_reachable(safra_complement);
     std::cout << "Safra Complement: "
               << b_size.states << ", "
-              << b_size.transitions << ", "
+              << b_size.edges << ", "
               << safra_complement->acc().num_sets()
               << std::endl;
 
     if (formula)
     {
       auto a2 = spot::ltl_to_tgba_fm(spot::formula::Not(f1), dict);
-      spot::tgba_statistics a_size = spot::stats_reachable(a2);
+      spot::twa_statistics a_size = spot::stats_reachable(a2);
       std::cout << "Not Formula: "
                 << a_size.states << ", "
-                << a_size.transitions << ", "
+                << a_size.edges << ", "
                 << a2->acc().num_sets()
                 << std::endl;
     }
@@ -233,11 +233,11 @@ int main(int argc, char* argv[])
     auto nAnf = spot::make_safra_complement(Anf);
     auto ec = spot::couvreur99(spot::otf_product(nAf, nAnf));
     auto res = ec->check();
-    spot::tgba_statistics a_size =  spot::stats_reachable(ec->automaton());
+    spot::twa_statistics a_size =  spot::stats_reachable(ec->automaton());
     std::cout << "States: "
               << a_size.states << std::endl
               << "Transitions: "
-              << a_size.transitions << std::endl
+              << a_size.edges << std::endl
               << "Acc Cond: "
               << ec->automaton()->acc().num_sets()
               << std::endl;
diff --git a/src/tests/ikwiad.cc b/src/tests/ikwiad.cc
index 4c5b8b6a5..a76861bd7 100644
--- a/src/tests/ikwiad.cc
+++ b/src/tests/ikwiad.cc
@@ -1516,12 +1516,12 @@ checked_main(int argc, char** argv)
                   std::ios::fmtflags old = std::cout.flags();
                   std::cout << std::left << std::setw(25)
                             << echeck_algo << ", ";
-                  spot::tgba_statistics a_size =
+                  spot::twa_statistics a_size =
                                         spot::stats_reachable(ec->automaton());
                   std::cout << std::right << std::setw(10)
                             << a_size.states << ", "
                             << std::right << std::setw(10)
-                            << a_size.transitions << ", ";
+                            << a_size.edges << ", ";
                   std::cout << ec->automaton()->acc().num_sets()
                             << ", ";
 		  auto ecs = ec->emptiness_check_statistics();
diff --git a/src/tests/ltl2tgba.test b/src/tests/ltl2tgba.test
index 08fe5caca..fa81056f2 100755
--- a/src/tests/ltl2tgba.test
+++ b/src/tests/ltl2tgba.test
@@ -109,7 +109,7 @@ run 0 ../ikwiad -e -R3 '(G!{(b;1)*;a} && ({1;1[*3]*}[]->{(b&!a)[*2];!b&!a}))'
 # before and after degeneralization.
 for opt in '' -DT -DS; do
   ../ikwiad -ks -f -R3 $opt 'a U (b U c)' > stdout
-  grep 'transitions: 6$' stdout
+  grep 'edges: 6$' stdout
   grep 'states: 3$' stdout
 done
 
@@ -117,8 +117,8 @@ done
 # before and after degeneralization.
 for opt in '' -DT -DS; do
   ../ikwiad -kt -f -R3 $opt '!(Ga U b)' > stdout
-  grep 'sub trans.: 11$' stdout
-  grep 'transitions: 6$' stdout
+  grep 'transitions: 11$' stdout
+  grep 'edges: 6$' stdout
   grep 'states: 3$' stdout
 done
 
@@ -126,8 +126,8 @@ done
 # before and after degeneralization.
 for opt in '' -DT -DS; do
   ../ikwiad -kt -f -R3 $opt 'Ga U b' > stdout
-  grep 'sub trans.: 12$' stdout
-  grep 'transitions: 6$' stdout
+  grep 'transitions: 12$' stdout
+  grep 'edges: 6$' stdout
   grep 'states: 4$' stdout
 done
 
@@ -136,10 +136,10 @@ done
 f='(G (p -> F q)) && ((X (p) U q) || ! X (p U (p && q)))'
 for opt in '' -DT -DS; do
   ../ikwiad -ks -f -R3 $opt "$f" > stdout
-  grep 'transitions: 15$' stdout
+  grep 'edges: 15$' stdout
   grep 'states: 6$' stdout
   ../ikwiad -ks -f -R3f $opt "$f" > stdout
-  grep 'transitions: 15$' stdout
+  grep 'edges: 15$' stdout
   grep 'states: 6$' stdout
 done
 
@@ -147,16 +147,16 @@ done
 # has 7 states and 34 transitions after degeneralization.
 f='GFa & GFb & GFc & GFd & GFe & GFg'
 ../ikwiad -ks -DS -x -f "$f" > stdout
-grep 'transitions: 34$' stdout
+grep 'edges: 34$' stdout
 grep 'states: 7$' stdout
 
 # Make sure 'Ga & XXXX!a' is minimized to one state.
 f='Ga & XXXX!a'
 ../ikwiad -ks -f "$f" > stdout
-grep 'transitions: 4$' stdout
+grep 'edges: 4$' stdout
 grep 'states: 5$' stdout
 ../ikwiad -ks -Rm -f "$f" > stdout
-grep 'transitions: 0$' stdout
+grep 'edges: 0$' stdout
 grep 'states: 1$' stdout
 
 # Make sure a monitor for F(a & F(b)) accepts everything.
@@ -169,12 +169,12 @@ cmp stdout expected
 
 # This formula caused a segfault with Spot 0.7.
 run 0 ../ikwiad -Rm -ks -f "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
-grep 'transitions: 5$' stdout
+grep 'edges: 5$' stdout
 grep 'states: 3$' stdout
 
 # Adding -R3 used to make it work...
 run 0 ../ikwiad -R3 -Rm -ks -f "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
-grep 'transitions: 5$' stdout
+grep 'edges: 5$' stdout
 grep 'states: 3$' stdout
 
 # Make sure FGa|GFb has the same number of states/transitions when
@@ -189,7 +189,7 @@ cmp count.never count.hoa
 
 # The following automaton should have only 4 states.
 run 0 ../ikwiad -R3 -ks -f '(p&XF!p)|(!p&XFp)|X(Fp&F!p)' >stdout
-grep 'transitions: 7$' stdout
+grep 'edges: 7$' stdout
 grep 'states: 4$' stdout
 
 # A bug in the translation of !{xxx} when xxx reduces to false caused
diff --git a/src/tests/neverclaimread.test b/src/tests/neverclaimread.test
index 87f607474..158c72597 100755
--- a/src/tests/neverclaimread.test
+++ b/src/tests/neverclaimread.test
@@ -205,7 +205,7 @@ accept_T3:
 }
 EOF
 cat >expected<<EOF
-transitions: 6
+edges: 6
 states: 4
 EOF
 
diff --git a/src/tests/randtgba.cc b/src/tests/randtgba.cc
index 85aee7ae0..be80aa490 100644
--- a/src/tests/randtgba.cc
+++ b/src/tests/randtgba.cc
@@ -248,14 +248,14 @@ id(const char*, unsigned x)
   return static_cast<T>(x);
 }
 
-spot::tgba_statistics prod_stats;
+spot::twa_statistics prod_stats;
 
 static float
 prod_conv(const char* name, unsigned x)
 {
   float y = static_cast<float>(x);
   if (!strcmp(name, "transitions"))
-    return y / prod_stats.transitions * 100.0;
+    return y / prod_stats.edges * 100.0;
   return y / prod_stats.states * 100.0;
 }
 
@@ -958,7 +958,7 @@ main(int argc, char** argv)
 			{
 			  // To trigger a division by 0 if used erroneously.
 			  prod_stats.states = 0;
-			  prod_stats.transitions = 0;
+			  prod_stats.edges = 0;
 			}
 
 		      if (opt_z && ecs)
diff --git a/src/tests/renault.test b/src/tests/renault.test
index 3fa907173..b43755290 100755
--- a/src/tests/renault.test
+++ b/src/tests/renault.test
@@ -65,7 +65,7 @@ State: 9
 EOF
 
 cat >outexp <<EOF
-transitions: 12
+edges: 12
 states: 6
 EOF
 
diff --git a/src/tests/wdba2.test b/src/tests/wdba2.test
index 04d99ce2c..526076767 100755
--- a/src/tests/wdba2.test
+++ b/src/tests/wdba2.test
@@ -23,8 +23,8 @@
 set -e
 
 cat >expected <<EOF
-sub trans.: 16
-transitions: 8
+transitions: 16
+edges: 8
 states: 4
 nondeterministic states: 0
 EOF
diff --git a/src/twaalgos/dtbasat.cc b/src/twaalgos/dtbasat.cc
index 861298a2f..ba41867ab 100644
--- a/src/twaalgos/dtbasat.cc
+++ b/src/twaalgos/dtbasat.cc
@@ -785,9 +785,8 @@ namespace spot
 	out << target_state_number << ',';
 	if (res)
 	  {
-	    tgba_sub_statistics st = sub_stats_reachable(res);
-	    out << st.states << ',' << st.transitions
-		<< ',' << st.sub_transitions;
+	    twa_sub_statistics st = sub_stats_reachable(res);
+	    out << st.states << ',' << st.edges << ',' << st.transitions;
 	  }
 	else
 	  {
diff --git a/src/twaalgos/dtgbasat.cc b/src/twaalgos/dtgbasat.cc
index 643cc5136..09ac57911 100644
--- a/src/twaalgos/dtgbasat.cc
+++ b/src/twaalgos/dtgbasat.cc
@@ -1170,9 +1170,8 @@ namespace spot
 	out << target_state_number << ',';
 	if (res)
 	  {
-	    tgba_sub_statistics st = sub_stats_reachable(res);
-	    out << st.states << ',' << st.transitions
-		<< ',' << st.sub_transitions;
+	    twa_sub_statistics st = sub_stats_reachable(res);
+	    out << st.states << ',' << st.edges << ',' << st.transitions;
 	  }
 	else
 	  {
diff --git a/src/twaalgos/stats.cc b/src/twaalgos/stats.cc
index 8201a01bc..de09ff0e0 100644
--- a/src/twaalgos/stats.cc
+++ b/src/twaalgos/stats.cc
@@ -36,7 +36,7 @@ namespace spot
     class stats_bfs: public tgba_reachable_iterator_breadth_first
     {
     public:
-      stats_bfs(const const_twa_ptr& a, tgba_statistics& s)
+      stats_bfs(const const_twa_ptr& a, twa_statistics& s)
 	: tgba_reachable_iterator_breadth_first(a), s_(s)
       {
       }
@@ -51,17 +51,17 @@ namespace spot
       process_link(const state*, int, const state*, int,
 		   const twa_succ_iterator*)
       {
-	++s_.transitions;
+	++s_.edges;
       }
 
     private:
-      tgba_statistics& s_;
+      twa_statistics& s_;
     };
 
     class sub_stats_bfs: public stats_bfs
     {
     public:
-      sub_stats_bfs(const const_twa_ptr& a, tgba_sub_statistics& s)
+      sub_stats_bfs(const const_twa_ptr& a, twa_sub_statistics& s)
 	: stats_bfs(a, s), s_(s), seen_(bddtrue)
       {
       }
@@ -70,7 +70,7 @@ namespace spot
       process_link(const state*, int, const state*, int,
 		   const twa_succ_iterator* it)
       {
-	++s_.transitions;
+	++s_.edges;
 
 	bdd cond = it->current_condition();
 	bdd newvars = bdd_exist(bdd_support(cond), seen_);
@@ -87,49 +87,49 @@ namespace spot
 	    // transitions we counted so far are actually double
 	    // subtransitions.  If we have two new variables, they where
 	    // quadruple transitions, etc.
-	    s_.sub_transitions <<= count;
+	    s_.transitions <<= count;
 	  }
 	while (cond != bddfalse)
 	  {
 	    cond -= bdd_satoneset(cond, seen_, bddtrue);
-	    ++s_.sub_transitions;
+	    ++s_.transitions;
 	  }
       }
 
     private:
-      tgba_sub_statistics& s_;
+      twa_sub_statistics& s_;
       bdd seen_;
     };
   } // anonymous
 
 
-  std::ostream& tgba_statistics::dump(std::ostream& out) const
+  std::ostream& twa_statistics::dump(std::ostream& out) const
   {
-    out << "transitions: " << transitions << std::endl;
-    out << "states: " << states << std::endl;
+    out << "edges: " << edges << '\n';
+    out << "states: " << states << '\n';
     return out;
   }
 
-  std::ostream& tgba_sub_statistics::dump(std::ostream& out) const
+  std::ostream& twa_sub_statistics::dump(std::ostream& out) const
   {
-    out << "sub trans.: " << sub_transitions << std::endl;
-    this->tgba_statistics::dump(out);
+    out << "transitions: " << transitions << '\n';
+    this->twa_statistics::dump(out);
     return out;
   }
 
-  tgba_statistics
+  twa_statistics
   stats_reachable(const const_twa_ptr& g)
   {
-    tgba_statistics s;
+    twa_statistics s;
     stats_bfs d(g, s);
     d.run();
     return s;
   }
 
-  tgba_sub_statistics
+  twa_sub_statistics
   sub_stats_reachable(const const_twa_ptr& g)
   {
-    tgba_sub_statistics s;
+    twa_sub_statistics s;
     sub_stats_bfs d(g, s);
     d.run();
     return s;
@@ -169,16 +169,16 @@ namespace spot
 
     if (has('t'))
       {
-	tgba_sub_statistics s = sub_stats_reachable(aut);
+	twa_sub_statistics s = sub_stats_reachable(aut);
 	states_ = s.states;
-	edges_ = s.transitions;
-	trans_ = s.sub_transitions;
+	edges_ = s.edges;
+	trans_ = s.transitions;
       }
     else if (has('s') || has('e'))
       {
-	tgba_sub_statistics s = sub_stats_reachable(aut);
+	twa_sub_statistics s = sub_stats_reachable(aut);
 	states_ = s.states;
-	edges_ = s.transitions;
+	edges_ = s.edges;
       }
 
     if (has('a'))
diff --git a/src/twaalgos/stats.hh b/src/twaalgos/stats.hh
index b625454ff..5c75fff48 100644
--- a/src/twaalgos/stats.hh
+++ b/src/twaalgos/stats.hh
@@ -32,27 +32,27 @@ namespace spot
   /// \addtogroup twa_misc
   /// @{
 
-  struct SPOT_API tgba_statistics
+  struct SPOT_API twa_statistics
   {
-    unsigned transitions;
+    unsigned edges;
     unsigned states;
 
-    tgba_statistics() { transitions = 0; states = 0; }
+    twa_statistics() { edges = 0; states = 0; }
     std::ostream& dump(std::ostream& out) const;
   };
 
-  struct SPOT_API tgba_sub_statistics: public tgba_statistics
+  struct SPOT_API twa_sub_statistics: public twa_statistics
   {
-    unsigned sub_transitions;
+    unsigned transitions;
 
-    tgba_sub_statistics() { sub_transitions = 0; }
+    twa_sub_statistics() { transitions = 0; }
     std::ostream& dump(std::ostream& out) const;
   };
 
   /// \brief Compute statistics for an automaton.
-  SPOT_API tgba_statistics stats_reachable(const const_twa_ptr& g);
+  SPOT_API twa_statistics stats_reachable(const const_twa_ptr& g);
   /// \brief Compute sub statistics for an automaton.
-  SPOT_API tgba_sub_statistics sub_stats_reachable(const const_twa_ptr& g);
+  SPOT_API twa_sub_statistics sub_stats_reachable(const const_twa_ptr& g);
 
 
   class SPOT_API printable_formula: public printable_value<formula>
diff --git a/wrap/python/ajax/spotcgi.in b/wrap/python/ajax/spotcgi.in
index cc5560705..696c72176 100755
--- a/wrap/python/ajax/spotcgi.in
+++ b/wrap/python/ajax/spotcgi.in
@@ -349,16 +349,14 @@ def print_stats(automaton, detinfo = False, ta = False):
             unbufprint(" (deterministic)")
         else:
             unbufprint(" (%d nondeterministic)" % nondet)
-    if not hasattr(stats, 'sub_transitions'):
-        unbufprint(", %d transition" % stats.transitions)
-        if stats.transitions > 1:
+    if not hasattr(stats, 'transitions'):
+        unbufprint(", %d edge" % stats.edges)
+        if stats.edges > 1:
             unbufprint("s")
     else:
         unbufprint(", %d edge%s (%d transition%s)"
-                   % (stats.transitions,
-                      's' if stats.transitions > 1 else '',
-                      stats.sub_transitions,
-                      's' if stats.sub_transitions > 1 else ''))
+                   % (stats.edges, 's' if stats.edges > 1 else '',
+                      stats.transitions, 's' if stats.transitions > 1 else ''))
     if hasattr(automaton, 'get_acceptance'):
         acc = automaton.get_acceptance()
         if (automaton.is_sba() and automaton.acc().is_buchi() and
@@ -372,9 +370,9 @@ def print_stats(automaton, detinfo = False, ta = False):
     # Decide whether we will render the automaton or not.
     # (A webserver is not a computation center...)
     if stats.states > 64:
-        return "Automaton has too much states"
-    if float(stats.transitions)/stats.states > 10:
-        return "Automaton has too much transitions per state"
+        return "Automaton has too many states"
+    if float(stats.edges)/stats.states > 10:
+        return "Automaton has too many edges per state"
     return False
 
 def format_formula(f, kind='div'):