diff --git a/Combinatorial_map/include/CGAL/Combinatorial_map_functionalities.h b/Combinatorial_map/include/CGAL/Combinatorial_map_functionalities.h
index 381a8a29087..3503720430d 100644
--- a/Combinatorial_map/include/CGAL/Combinatorial_map_functionalities.h
+++ b/Combinatorial_map/include/CGAL/Combinatorial_map_functionalities.h
@@ -26,6 +26,7 @@
 #include <boost/unordered_map.hpp>
 #include <CGAL/Random.h>
 #include <CGAL/Path_on_surface.h>
+#include <CGAL/Combinatorial_map_basic_operations.h>
 
 namespace CGAL {
   
@@ -129,6 +130,27 @@ namespace CGAL {
 
       std::cout<<"Paths are all valid ? "<<(are_paths_valid()?"YES":"NO")
                <<std::endl;
+      auto marktemp=m_map.get_new_mark();
+      Dart_handle dh2=NULL;
+      for (auto it=m_map.darts().begin(); it!=m_map.darts().end(); ++it)
+      {
+        if (!m_map.is_marked(it, marktemp))
+        {
+          std::cout<<"Degree="<<CGAL::template degree<Map, 0>(m_map, it)<<std::endl;
+          std::cout<<"Co-degree="<<CGAL::template codegree<Map, 2>(m_map, it)<<std::endl;
+          dh2=it;
+          do
+          {
+            m_map.mark(dh2, marktemp);
+            std::cout<<m_map.darts().index(dh2)<<"   "
+                    <<m_map.darts().index(m_map.template beta<0>(dh2))<<std::endl;
+            dh2=m_map.template beta<0,2>(dh2);
+          }
+          while(dh2!=it);
+        }
+      }
+      m_map.free_mark(marktemp);
+      m_map.display_darts(std::cout);
 #endif
     }
     
diff --git a/Combinatorial_map/include/CGAL/Creation_of_test_cases_for_paths.h b/Combinatorial_map/include/CGAL/Creation_of_test_cases_for_paths.h
index 3dccd77f60b..647e70040f0 100644
--- a/Combinatorial_map/include/CGAL/Creation_of_test_cases_for_paths.h
+++ b/Combinatorial_map/include/CGAL/Creation_of_test_cases_for_paths.h
@@ -348,6 +348,53 @@ void generate_g2_torus(Path& p, std::size_t i)
   }
 }
 
+template<typename Path>
+void generate_g1_v0_double_torus(Path& p)
+{ // 1st generator
+  p.clear();
+  p.push_back(p.get_map().darts().iterator_to(p.get_map().darts()[16]));
+  extend_straight_negative(p, 2);
+}
+
+template<typename Path>
+void generate_g1_v1_double_torus(Path& p)
+{ // 1st generator
+  p.clear();
+  p.push_back(p.get_map().darts().iterator_to(p.get_map().darts()[4]));
+  extend_straight_negative(p, 2);
+}
+
+template<typename Path>
+void generate_g1_v2_double_torus(Path& p)
+{ // 1st generator
+  p.clear();
+  p.push_back(p.get_map().darts().iterator_to(p.get_map().darts()[2]));
+  extend_straight_negative(p, 2);
+  p.reverse();
+}
+
+template<typename Path>
+void generate_g2_v1_double_torus(Path& p)
+{ // 2nd generator
+  p.clear();
+  p.push_back(p.get_map().darts().iterator_to(p.get_map().darts()[10]));
+  extend_straight_negative(p, 2);
+  extend_uturn_negative(p, 1);
+}
+
+template<typename Path>
+void generate_g1_double_torus(Path& p, std::size_t i)
+{
+  assert(i<3);
+  switch(i)
+  {
+    case 0: generate_g1_v0_double_torus(p); break;
+    case 1: generate_g1_v1_double_torus(p); break;
+    case 2: generate_g1_v2_double_torus(p); break;
+    default: assert(false);
+  }
+}
+
 } // namespace CGAL
 
 #endif // CGAL_CREATION_OF_TEST_CASES_FOR_PATHS_H //
diff --git a/Combinatorial_map/include/CGAL/Path_on_surface.h b/Combinatorial_map/include/CGAL/Path_on_surface.h
index 45b5e74cd73..6b6a54b3dce 100644
--- a/Combinatorial_map/include/CGAL/Path_on_surface.h
+++ b/Combinatorial_map/include/CGAL/Path_on_surface.h
@@ -571,6 +571,14 @@ public:
       else
       { CGAL::extend_straight_positive(new_path, 1); }
     }
+
+    if (begin==middle && next_index(middle)==end)
+    { // TODO: check if we need to do also something for !case_seven ?
+      // if (case_seven)
+      { CGAL::extend_uturn_positive(new_path, 1); }
+      /* else
+      { assert(false); } // We think (?) that this case is not possible */
+    }
   }
 
   void push_l_shape_cycle_2()
@@ -583,10 +591,30 @@ public:
     CGAL::extend_straight_positive_until(*this, d1);
   }
 
+  bool push_l_shape_2darts()
+  {
+    Dart_const_handle d1=NULL;
+
+    if (next_negative_turn(0)==1)
+      d1=m_map.template beta<2,1>(get_ith_dart(0));
+    else if (next_negative_turn(1)==1)
+      d1=m_map.template beta<2,1>(get_ith_dart(1));
+    else return false;
+
+    clear();
+    push_back(d1);
+    CGAL::extend_uturn_positive(*this, 1);
+    //push_back(m_map.template beta<1>(d1));
+    return true;
+  }
+
   bool right_push_one_step()
   {
     if (is_empty()) { return false; }
 
+    if (length()==2)
+    { return push_l_shape_2darts(); }
+
     std::size_t begin, middle, end;
     std::size_t lastturn=m_path.size()-(is_closed()?0:1);
     std::size_t next_turn;
@@ -626,7 +654,8 @@ public:
       else
       {
         if (next_turn==1)
-        { // Here middle is a real middle; we already know begin (or we know
+        {
+          // Here middle is a real middle; we already know begin (or we know
           // that there is no -2 before if !prev2), we only need to compute
           // end.
           if (!prev2) { begin=middle; } // There is no -2 before this -1
@@ -676,7 +705,11 @@ public:
   {
     bool res=false;
     while(right_push_one_step())
-    { res=true; }
+    { res=true;
+      
+      std::cout<<"RP "; display();  display_pos_and_neg_turns();
+      std::cout<<std::endl;
+    }
     return res;
   }
 
@@ -686,18 +719,32 @@ public:
     if (!is_closed())
     { return; }
 
+    std::cout<<"##########################################"<<std::endl;
+    std::cout<<"Init "; display();
+    std::cout<<std::endl;
+    display_pos_and_neg_turns();
+    
     bool modified=false;
+    std::cout<<"RS "; remove_spurs_one_step();
+
+    display();
+    std::cout<<std::endl;
+
     do
     {
       modified=bracket_flattening_one_step();
-      if (!modified)
-      {
-        modified=remove_spurs_one_step();
-        if (!modified)
-        { modified=right_push_one_step(); }
-      }
+
+      std::cout<<"BF "; display();
+      std::cout<<std::endl;
+
+      modified=modified || remove_spurs_one_step();
+
+      std::cout<<"RS "; display();
+      std::cout<<std::endl;
     }
     while(modified);
+
+    right_push();
   }
 
   std::vector<std::size_t> compute_positive_turns() const
@@ -824,8 +871,8 @@ public:
       std::cout<<m_map.darts().index(get_ith_dart(i));
       if (i<length()-1) { std::cout<<" "; }
     }
-    if (is_closed())
-    { std::cout<<" "<<m_map.darts().index(get_ith_dart(0)); }
+     if (is_closed())
+     { std::cout<<" c "; } //<<m_map.darts().index(get_ith_dart(0)); }
   }
 
 protected:
diff --git a/Linear_cell_complex/examples/Linear_cell_complex/compute_example.cpp b/Linear_cell_complex/examples/Linear_cell_complex/compute_example.cpp
index 979182adb0c..94fac46be28 100644
--- a/Linear_cell_complex/examples/Linear_cell_complex/compute_example.cpp
+++ b/Linear_cell_complex/examples/Linear_cell_complex/compute_example.cpp
@@ -17,7 +17,7 @@
 typedef CGAL::Linear_cell_complex_for_combinatorial_map<2,3> LCC_3_cmap;
 typedef CGAL::Linear_cell_complex_for_generalized_map<2,3> LCC_3_gmap;
 
-#define NB_TESTS 23 // 0 ... 22
+#define NB_TESTS 24 // 0 ... 23
 int nbtests=0;
 
 enum Transformation // enum for the type of transformations
@@ -402,8 +402,8 @@ bool test_some_random_paths_on_cube(bool draw, int testtorun)
   { res=false; }
 
   generate_random_bracket(path, 5, 12, 8, random); // Test 20
-  if (!unit_test(path, FULL_SIMPLIFICATION, 0, "(2^4 1 2^12 1 2^8 ...)",
-                   "2", draw, testtorun))
+  if (!unit_test(path, PUSH, 0, "(2^4 1 2^12 1 2^8 ...)",
+                   "2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 0 2 2 2 2 0 2 2 2 2 1 2 1", draw, testtorun))
   { res=false; }
 
   return true;
@@ -455,7 +455,7 @@ bool test_torus_quad(bool draw, int testtorun)
   { res=false; }
 
   // Test 23 (3 g2 cycles) TODO BUG IN TEST 23 !!!
-  /* paths.clear(); transformed_paths.clear();
+  paths.clear(); transformed_paths.clear();
   for (int i=0; i<3; ++i)
   {
     paths.push_back(CGAL::Path_on_surface<LCC_3_cmap>(lcc));
@@ -468,11 +468,40 @@ bool test_torus_quad(bool draw, int testtorun)
                           "canonize paths on torus gen2",
                           draw, testtorun))
   { res=false; }
-  */
 
   return res;
 }
+///////////////////////////////////////////////////////////////////////////////
+bool test_double_torus_quad(bool draw, int testtorun)
+{
+  bool res=true;
 
+  LCC_3_cmap lcc;
+  if (!CGAL::load_off(lcc, "./data/double-torus.off"))
+  {
+    std::cout<<"PROBLEM reading file ./data/double-torus.off"<<std::endl;
+    exit(EXIT_FAILURE);
+  }
+
+  CGAL::Combinatorial_map_tools<LCC_3_cmap> cmt(lcc);
+
+  std::vector<CGAL::Path_on_surface<LCC_3_cmap> > paths;
+  std::vector<CGAL::Path_on_surface<LCC_3_cmap> > transformed_paths;
+
+  // Test 21 (3 g1 cycles)
+  for (int i=0; i<3; ++i)
+  {
+    paths.push_back(CGAL::Path_on_surface<LCC_3_cmap>(lcc));
+    CGAL::generate_g1_double_torus(paths[i], i);
+    transformed_paths.push_back
+        (cmt.transform_original_path_into_quad_surface(paths[i]));
+  }
+
+  if (!unit_test_canonize(paths, transformed_paths,
+                          "canonize paths on double torus gen1",
+                          draw, testtorun))
+  { res=false; }
+}
 ///////////////////////////////////////////////////////////////////////////////
 bool test_elephant(bool draw, int testtorun) // TODO LATER
 {
@@ -600,11 +629,17 @@ int main(int argc, char** argv)
     return EXIT_FAILURE;
   }
 
-  if (!test_torus_quad(draw, testN))
+  if (!test_double_torus_quad(draw, testN))
+  {
+    std::cout<<"TEST DOUBLE TORUS FAILED."<<std::endl;
+    return EXIT_FAILURE;
+  }
+
+  /* if (!test_torus_quad(draw, testN))
   {
     std::cout<<"TEST TORUS FAILED."<<std::endl;
     return EXIT_FAILURE;
-  }
+  } */
 
   /* TODO LATER if (!test_file(draw, testN))
   {