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

TRS termination of:
[1] app(app(.,1),x) -> x
[2] app(app(.,x),1) -> x
[3] app(app(.,app(i,x)),x) -> 1
[4] app(app(.,x),app(i,x)) -> 1
[5] app(app(.,app(i,y)),app(app(.,y),z)) -> z
[6] app(app(.,y),app(app(.,app(i,y)),z)) -> z
[7] app(i,1) -> 1
[8] app(i,app(i,x)) -> x
[9] app(app(map,f),nil) -> nil
[10] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))
[11] app(app(filter,f),nil) -> nil
[12] app(app(filter,f),app(app(cons,x),xs)) ->
 app(app(app(app(filter2,app(f,x)),f),x),xs)
[13] app(app(app(app(filter2,true),f),x),xs) ->
 app(app(cons,x),app(app(filter,f),xs))
[14] app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,f),xs)


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(cons,app(f,x))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
<Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                 f),x),
                                                  xs)>
<Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(filter2,
                                                                 app(f,x)),
                                                             f),x)>
<Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                             app(f,x)),
                                                  f)>
<Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(filter2,app(f,x))>
<Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                   app(app(filter,f),xs))>
<Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(cons,x)>
<Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),xs)>
<Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(filter,f)>
<Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),xs)>
<Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(filter,f)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                       xs)> 
      --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                              app(filter,
                                                               f),xs)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(app(filter,f),
                                                      xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(filter,f),
                                                     xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(app(cons,x),
                                                     app(app(filter,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(app(app(filter2,false),f),x),xs) , Marked_app(
                                                             app(filter,
                                                              f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(filter,
                                                             f),xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(app(app(filter2,true),f),x),xs) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(filter,f),
                                                             xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(filter2,
                                                            app(f,x)),
                                                           f)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(filter2,
                                                                app(f,x)),
                                                            f),x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(filter,f),app(app(cons,x),xs)) , Marked_app(
                                                           app(app(app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                f),x),
                                                           xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(app(filter2,true),f),x),xs) >= app(app(cons,x),
                                              app(app(filter,f),xs)) ;
  app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ;
  app(app(.,app(i,x)),x) >= 1 ;
  app(app(.,app(i,y)),app(app(.,y),z)) >= z ;
  app(app(.,1),x) >= x ;
  app(app(.,x),app(i,x)) >= 1 ;
  app(app(.,x),1) >= x ;
  app(app(.,y),app(app(.,app(i,y)),z)) >= z ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(app(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)),
                                                     f),x),xs) ;
  app(app(filter,f),nil) >= nil ;
  app(i,app(i,x)) >= x ;
  app(i,1) >= 1 ;
  Marked_app(app(app(app(filter2,true),f),x),xs) >= Marked_app(app(cons,x),
                                                     app(app(filter,f),xs)) ;
  Marked_app(app(app(app(filter2,true),f),x),xs) >= Marked_app(app(filter,f),
                                                     xs) ;
  Marked_app(app(app(app(filter2,false),f),x),xs) >= Marked_app(app(filter,f),
                                                      xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                   app(
                                                                    filter2,
                                                                    app(f,x)),
                                                                   f),
                                                               x),xs) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(app(app(
                                                                   filter2,
                                                                   app(f,x)),
                                                               f),x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(app(filter2,
                                                               app(f,x)),
                                                    f) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(f,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x),
                                                    app(app(filter,f),xs)) ;
 }
{
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ;
 }
{
  Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f),
                                                     xs) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
 }
{
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(f,x)),
                                                                  f),
                                                              x),xs) ;
 }
{
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  filter2,
                                                                  app(f,x)),
                                                              f),x) ;
 }
{
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2,
                                                              app(f,x)),
                                                   f) ;
 }
{
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(f,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 (Simple graph)
Found the following constraints:
{
  app(app(app(app(filter2,true),f),x),xs) >= app(app(cons,x),
                                              app(app(filter,f),xs)) ;
  app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ;
  app(app(.,app(i,x)),x) >= 1 ;
  app(app(.,app(i,y)),app(app(.,y),z)) >= z ;
  app(app(.,1),x) >= x ;
  app(app(.,x),app(i,x)) >= 1 ;
  app(app(.,x),1) >= x ;
  app(app(.,y),app(app(.,app(i,y)),z)) >= z ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(app(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)),
                                                     f),x),xs) ;
  app(app(filter,f),nil) >= nil ;
  app(i,app(i,x)) >= x ;
  app(i,1) >= 1 ;
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x),
                                                    app(app(filter,f),xs)) ;
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ;
  Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f),
                                                     xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(f,x)),
                                                                  f),
                                                              x),xs) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  filter2,
                                                                  app(f,x)),
                                                              f),x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2,
                                                              app(f,x)),
                                                   f) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(app(app(filter2,true),f),x),xs) >= app(app(cons,x),
                                              app(app(filter,f),xs)) ;
  app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ;
  app(app(.,app(i,x)),x) >= 1 ;
  app(app(.,app(i,y)),app(app(.,y),z)) >= z ;
  app(app(.,1),x) >= x ;
  app(app(.,x),app(i,x)) >= 1 ;
  app(app(.,x),1) >= x ;
  app(app(.,y),app(app(.,app(i,y)),z)) >= z ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(map,f),nil) >= nil ;
  app(app(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)),
                                                     f),x),xs) ;
  app(app(filter,f),nil) >= nil ;
  app(i,app(i,x)) >= x ;
  app(i,1) >= 1 ;
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x),
                                                    app(app(filter,f),xs)) ;
  Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ;
  Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f),
                                                     xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  app(
                                                                   filter2,
                                                                   app(f,x)),
                                                                  f),
                                                              x),xs) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app(
                                                                  filter2,
                                                                  app(f,x)),
                                                              f),x) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2,
                                                              app(f,x)),
                                                   f) ;
  Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(6 bt (0) [8])
=== 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 43.088106 seconds (real time)
Cime Exit Status: 0