- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] app(f,app(s,x)) -> app(f,x)
[2] app(g,app(app(cons,0),y)) -> app(g,y)
[3] app(g,app(app(cons,app(s,x)),y)) -> app(s,x)
[4] app(h,app(app(cons,x),y)) -> app(h,app(g,app(app(cons,x),y)))
[5] app(app(map,fun),nil) -> nil
[6] app(app(map,fun),app(app(cons,x),xs)) ->
 app(app(cons,app(fun,x)),app(app(map,fun),xs))
[7] app(app(filter,fun),nil) -> nil
[8] app(app(filter,fun),app(app(cons,x),xs)) ->
 app(app(app(app(filter2,app(fun,x)),fun),x),xs)
[9] app(app(app(app(filter2,true),fun),x),xs) ->
 app(app(cons,x),app(app(filter,fun),xs))
[10] app(app(app(app(filter2,false),fun),x),xs) -> app(app(filter,fun),xs)


Sub problem: 
guided: 

DP termination of:
<Marked_app(f,app(s,x)) , Marked_app(f,x)>
<Marked_app(g,app(app(cons,0),y)) , Marked_app(g,y)>
<Marked_app(h,app(app(cons,x),y)) , Marked_app(h,app(g,app(app(cons,x),y)))>
<Marked_app(h,app(app(cons,x),y)) , Marked_app(g,app(app(cons,x),y))>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,app(fun,x)),
                                                 app(app(map,fun),xs))>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(cons,app(fun,x))>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
<Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                   fun),
                                                               x),xs)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                               fun),x)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(fun,x)),
                                                    fun)>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(filter2,
                                                    app(fun,x))>
<Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,fun),xs))>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(cons,x)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(filter,fun),
                                                     xs)>
<Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(filter,fun)>
<Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(filter,fun),
                                                      xs)>
<Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(filter,fun)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                    filter,
                                                                    fun),
                                                         xs)> 
      --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                                app(filter,
                                                                 fun),
                                                                xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(map,fun),xs)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,false),fun),x),xs) , Marked_app(
                                                               app(filter,
                                                                fun),
                                                               xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(filter,
                                                               fun),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(app(app(filter2,true),fun),x),xs) , Marked_app(
                                                              app(cons,
                                                               x),
                                                              app(app(
                                                                   filter,
                                                                   fun),
                                                               xs))>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(filter2,
                                                              app(fun,x)),
                                                             fun)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  filter2,
                                                                  app(fun,x)),
                                                              fun),x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(filter,fun),app(app(cons,x),xs)) , Marked_app(
                                                             app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(fun,x)),
                                                                  fun),
                                                              x),xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    map,
                                                                    fun),
                                                          xs)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(fun,x)>
  <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs))> 
     --> <Marked_app(app(map,fun),app(app(cons,x),xs)) , Marked_app(app(
                                                                    cons,
                                                                    app(fun,x)),
                                                          app(app(map,fun),xs))>
}

{  <Marked_app(f,app(s,x)) , Marked_app(f,x)> 
      --> <Marked_app(f,app(s,x)) , Marked_app(f,x)>
}

{  <Marked_app(h,app(app(cons,x),y)) , Marked_app(h,app(g,app(app(cons,x),y)))> 
      --> <Marked_app(h,app(app(cons,x),y)) , Marked_app(h,
                                               app(g,app(app(cons,x),y)))>
}

{  <Marked_app(g,app(app(cons,0),y)) , Marked_app(g,y)> 
      --> <Marked_app(g,app(app(cons,0),y)) , Marked_app(g,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(app(filter2,true),fun),x),xs) >= app(app(cons,x),
                                                app(app(filter,fun),xs)) ;
  app(app(app(app(filter2,false),fun),x),xs) >= app(app(filter,fun),xs) ;
  app(app(map,fun),app(app(cons,x),xs)) >= app(app(cons,app(fun,x)),
                                            app(app(map,fun),xs)) ;
  app(app(map,fun),nil) >= nil ;
  app(app(filter,fun),app(app(cons,x),xs)) >= app(app(app(app(filter2,
                                                           app(fun,x)),
                                                       fun),x),xs) ;
  app(app(filter,fun),nil) >= nil ;
  app(f,app(s,x)) >= app(f,x) ;
  app(g,app(app(cons,app(s,x)),y)) >= app(s,x) ;
  app(g,app(app(cons,0),y)) >= app(g,y) ;
  app(h,app(app(cons,x),y)) >= app(h,app(g,app(app(cons,x),y))) ;
  Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app(cons,x),
                                                       app(app(filter,fun),xs)) ;
  Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs) ;
  Marked_app(app(app(app(filter2,false),fun),x),xs) >= Marked_app(app(
                                                                   filter,
                                                                   fun),
                                                        xs) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(cons,
                                                              app(fun,x)),
                                                   app(app(map,fun),xs)) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(map,fun),xs) ;
  Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                 x),xs) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                 fun),
                                                      x) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(filter2,
                                                                 app(fun,x)),
                                                      fun) ;
  Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(cons,x),
                                                      app(app(filter,fun),xs)) ;
 }
{
  Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(filter,fun),
                                                      xs) ;
 }
{
  Marked_app(app(app(app(filter2,false),fun),x),xs) > Marked_app(app(
                                                                  filter,
                                                                  fun),
                                                       xs) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(cons,
                                                             app(fun,x)),
                                                  app(app(map,fun),xs)) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(map,fun),xs) ;
 }
{
  Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                    fun),
                                                                x),xs) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                    filter2,
                                                                    app(fun,x)),
                                                                fun),
                                                     x) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(filter2,
                                                                app(fun,x)),
                                                     fun) ;
 }
{
  Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 27.312202 seconds (real time)
Cime Exit Status: 0