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

TRS termination of:
[1] app(app(map,f),nil) -> nil
[2] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))
[3] app(flatten,app(app(node,x),xs)) ->
 app(app(cons,x),app(concat,app(app(map,flatten),xs)))
[4] app(concat,nil) -> nil
[5] app(concat,app(app(cons,x),xs)) -> app(app(append,x),app(concat,xs))
[6] app(app(append,nil),xs) -> xs
[7] app(app(append,app(app(cons,x),xs)),ys) ->
 app(app(cons,x),app(app(append,xs),ys))


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(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                            app(concat,
                                             app(app(map,flatten),xs)))>
<Marked_app(flatten,app(app(node,x),xs)) , Marked_app(cons,x)>
<Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                            app(app(map,flatten),xs))>
<Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)>
<Marked_app(flatten,app(app(node,x),xs)) , Marked_app(map,flatten)>
<Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                           app(concat,xs))>
<Marked_app(concat,app(app(cons,x),xs)) , Marked_app(append,x)>
<Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
<Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                   app(app(append,xs),ys))>
<Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),ys)>
<Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(append,xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                      ys)> 
      --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                             app(append,
                                                              xs),ys)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),xs)))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <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(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),xs)))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),xs)))>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                             app(concat,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(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),xs)))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),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(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                              app(app(map,flatten),xs))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                              app(app(map,flatten),xs))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),xs)))>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <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(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(cons,
                                                             x),
                                                            app(app(append,xs),
                                                             ys))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(concat,app(app(cons,x),xs)) , Marked_app(concat,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(concat,app(app(cons,x),xs)) , Marked_app(app(append,x),
                                                    app(concat,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(flatten,app(app(node,x),xs)) , Marked_app(app(map,flatten),
                                                     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(flatten,app(app(node,x),xs)) , Marked_app(concat,
                                                     app(app(map,flatten),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(flatten,app(app(node,x),xs)) , Marked_app(app(cons,x),
                                                     app(concat,
                                                      app(app(map,flatten),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(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(append,nil),xs) >= xs ;
  app(app(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(concat,nil) >= nil ;
  app(concat,app(app(cons,x),xs)) >= app(app(append,x),app(concat,xs)) ;
  app(flatten,app(app(node,x),xs)) >= app(app(cons,x),
                                       app(concat,app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) >= Marked_app(app(cons,x),
                                                     app(app(append,xs),ys)) ;
  Marked_app(app(append,app(app(cons,x),xs)),ys) >= Marked_app(app(append,xs),
                                                     ys) ;
  Marked_app(concat,app(app(cons,x),xs)) >= Marked_app(app(append,x),
                                             app(concat,xs)) ;
  Marked_app(concat,app(app(cons,x),xs)) >= Marked_app(concat,xs) ;
  Marked_app(flatten,app(app(node,x),xs)) >= Marked_app(app(map,flatten),xs) ;
  Marked_app(flatten,app(app(node,x),xs)) >= Marked_app(app(cons,x),
                                              app(concat,
                                               app(app(map,flatten),xs))) ;
  Marked_app(flatten,app(app(node,x),xs)) >= Marked_app(concat,
                                              app(app(map,flatten),xs)) ;
 }
 + Disjunctions:{ 
{
  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(append,app(app(cons,x),xs)),ys) > Marked_app(app(cons,x),
                                                    app(app(append,xs),ys)) ;
 }
{
  Marked_app(app(append,app(app(cons,x),xs)),ys) > Marked_app(app(append,xs),
                                                    ys) ;
 }
{
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(app(append,x),
                                            app(concat,xs)) ;
 }
{
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(concat,xs) ;
 }
{
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(map,flatten),xs) ;
 }
{
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(cons,x),
                                             app(concat,
                                              app(app(map,flatten),xs))) ;
 }
{
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(concat,
                                             app(app(map,flatten),xs)) ;
 }
 } 
=== 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(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(append,nil),xs) >= xs ;
  app(app(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(concat,nil) >= nil ;
  app(concat,app(app(cons,x),xs)) >= app(app(append,x),app(concat,xs)) ;
  app(flatten,app(app(node,x),xs)) >= app(app(cons,x),
                                       app(concat,app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) > Marked_app(app(cons,x),
                                                    app(app(append,xs),ys)) ;
  Marked_app(app(append,app(app(cons,x),xs)),ys) > Marked_app(app(append,xs),
                                                    ys) ;
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(app(append,x),
                                            app(concat,xs)) ;
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(concat,xs) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(map,flatten),xs) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(cons,x),
                                             app(concat,
                                              app(app(map,flatten),xs))) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(concat,
                                             app(app(map,flatten),xs)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(append,nil),xs) >= xs ;
  app(app(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(concat,nil) >= nil ;
  app(concat,app(app(cons,x),xs)) >= app(app(append,x),app(concat,xs)) ;
  app(flatten,app(app(node,x),xs)) >= app(app(cons,x),
                                       app(concat,app(app(map,flatten),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(append,app(app(cons,x),xs)),ys) > Marked_app(app(cons,x),
                                                    app(app(append,xs),ys)) ;
  Marked_app(app(append,app(app(cons,x),xs)),ys) > Marked_app(app(append,xs),
                                                    ys) ;
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(app(append,x),
                                            app(concat,xs)) ;
  Marked_app(concat,app(app(cons,x),xs)) > Marked_app(concat,xs) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(map,flatten),xs) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(app(cons,x),
                                             app(concat,
                                              app(app(map,flatten),xs))) ;
  Marked_app(flatten,app(app(node,x),xs)) > Marked_app(concat,
                                             app(app(map,flatten),xs)) ;
 }
 + 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.(4 bt (0) [6])
=== 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 33.258252 seconds (real time)
Cime Exit Status: 0