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

TRS termination of:
[1] app(app(append,nil),ys) -> ys
[2] app(app(append,app(app(cons,x),xs)),ys) ->
 app(app(cons,x),app(app(append,xs),ys))
[3] app(app(flatwith,f),app(leaf,x)) -> app(app(cons,app(f,x)),nil)
[4] app(app(flatwith,f),app(node,xs)) -> app(app(flatwithsub,f),xs)
[5] app(app(flatwithsub,f),nil) -> nil
[6] app(app(flatwithsub,f),app(app(cons,x),xs)) ->
 app(app(append,app(app(flatwith,f),x)),app(app(flatwithsub,f),xs))


Sub problem: 
guided: 

DP termination of:
<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)>
<Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,app(f,x)),nil)>
<Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(cons,app(f,x))>
<Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
<Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)>
<Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(flatwithsub,f)>
<Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                  append,
                                                                  app(
                                                                   app(
                                                                    flatwith,
                                                                    f),
                                                                   x)),
                                                       app(app(flatwithsub,f),
                                                        xs))>
<Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(append,
                                                       app(app(flatwith,f),x))>
<Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                  flatwith,
                                                                  f),
                                                       x)>
<Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(flatwith,f)>
<Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                  flatwithsub,
                                                                  f),
                                                       xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                          xs)> 
      --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                 app(
                                                                  flatwithsub,
                                                                  f),
                                                                 xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwithsub,
                                                                    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(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    flatwith,
                                                                    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(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs))> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,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(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,f),xs)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,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(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , 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(flatwith,f),app(leaf,x)) , Marked_app(app(cons,app(f,x)),nil)> 
     --> <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(
                                                            app(append,
                                                             xs),ys)>
  <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,app(f,x)),nil)> 
     --> <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(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 f),x)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    f),
                                                                 xs))>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 f),xs)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(f,x)>
  <Marked_app(app(append,app(app(cons,x),xs)),ys) , Marked_app(app(append,xs),
                                                     ys)> 
     --> <Marked_app(app(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <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(cons,x),
                                                     app(app(append,xs),ys))> 
     --> <Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwithsub,
                                                                 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(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(flatwith,
                                                                 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(flatwithsub,f),app(app(cons,x),xs)) , Marked_app(
                                                                app(append,
                                                                 app(
                                                                  app(
                                                                   flatwith,
                                                                   f),
                                                                  x)),
                                                                app(app(
                                                                    flatwithsub,
                                                                    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(flatwith,f),app(node,xs)) , Marked_app(app(flatwithsub,
                                                                 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(flatwith,f),app(leaf,x)) , 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(flatwith,f),app(leaf,x)) , Marked_app(app(cons,
                                                                app(f,x)),
                                                     nil)>
  <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))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(app(append,nil),ys) >= ys ;
  app(app(flatwith,f),app(leaf,x)) >= app(app(cons,app(f,x)),nil) ;
  app(app(flatwith,f),app(node,xs)) >= app(app(flatwithsub,f),xs) ;
  app(app(flatwithsub,f),app(app(cons,x),xs)) >= app(app(append,
                                                      app(app(flatwith,f),x)),
                                                  app(app(flatwithsub,f),xs)) ;
  app(app(flatwithsub,f),nil) >= nil ;
  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(flatwith,f),app(leaf,x)) >= Marked_app(app(cons,app(f,x)),nil) ;
  Marked_app(app(flatwith,f),app(leaf,x)) >= Marked_app(f,x) ;
  Marked_app(app(flatwith,f),app(node,xs)) >= Marked_app(app(flatwithsub,f),xs) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) >= Marked_app(app(
                                                                    append,
                                                                    app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                         app(app(flatwithsub,f),
                                                          xs)) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) >= Marked_app(app(
                                                                    flatwith,
                                                                    f),
                                                         x) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) >= Marked_app(app(
                                                                    flatwithsub,
                                                                    f),
                                                         xs) ;
 }
 + Disjunctions:{ 
{
  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(flatwith,f),app(leaf,x)) > Marked_app(app(cons,app(f,x)),nil) ;
 }
{
  Marked_app(app(flatwith,f),app(leaf,x)) > Marked_app(f,x) ;
 }
{
  Marked_app(app(flatwith,f),app(node,xs)) > Marked_app(app(flatwithsub,f),xs) ;
 }
{
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   append,
                                                                   app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                        app(app(flatwithsub,f),
                                                         xs)) ;
 }
{
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwith,
                                                                   f),
                                                        x) ;
 }
{
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwithsub,
                                                                   f),
                                                        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 : 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(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(app(append,nil),ys) >= ys ;
  app(app(flatwith,f),app(leaf,x)) >= app(app(cons,app(f,x)),nil) ;
  app(app(flatwith,f),app(node,xs)) >= app(app(flatwithsub,f),xs) ;
  app(app(flatwithsub,f),app(app(cons,x),xs)) >= app(app(append,
                                                      app(app(flatwith,f),x)),
                                                  app(app(flatwithsub,f),xs)) ;
  app(app(flatwithsub,f),nil) >= nil ;
  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(flatwith,f),app(leaf,x)) >= Marked_app(app(cons,app(f,x)),nil) ;
  Marked_app(app(flatwith,f),app(leaf,x)) > Marked_app(f,x) ;
  Marked_app(app(flatwith,f),app(node,xs)) > Marked_app(app(flatwithsub,f),xs) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   append,
                                                                   app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                        app(app(flatwithsub,f),
                                                         xs)) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwith,
                                                                   f),
                                                        x) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwithsub,
                                                                   f),
                                                        xs) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(append,app(app(cons,x),xs)),ys) >= app(app(cons,x),
                                              app(app(append,xs),ys)) ;
  app(app(append,nil),ys) >= ys ;
  app(app(flatwith,f),app(leaf,x)) >= app(app(cons,app(f,x)),nil) ;
  app(app(flatwith,f),app(node,xs)) >= app(app(flatwithsub,f),xs) ;
  app(app(flatwithsub,f),app(app(cons,x),xs)) >= app(app(append,
                                                      app(app(flatwith,f),x)),
                                                  app(app(flatwithsub,f),xs)) ;
  app(app(flatwithsub,f),nil) >= nil ;
  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(flatwith,f),app(leaf,x)) >= Marked_app(app(cons,app(f,x)),nil) ;
  Marked_app(app(flatwith,f),app(leaf,x)) > Marked_app(f,x) ;
  Marked_app(app(flatwith,f),app(node,xs)) > Marked_app(app(flatwithsub,f),xs) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   append,
                                                                   app(
                                                                    app(
                                                                    flatwith,
                                                                    f),
                                                                    x)),
                                                        app(app(flatwithsub,f),
                                                         xs)) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwith,
                                                                   f),
                                                        x) ;
  Marked_app(app(flatwithsub,f),app(app(cons,x),xs)) > Marked_app(app(
                                                                   flatwithsub,
                                                                   f),
                                                        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 24.974237 seconds (real time)
Cime Exit Status: 0