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

TRS termination of:
[1] app(app(append,nil),l) -> l
[2] app(app(append,app(app(cons,h),t)),l) ->
 app(app(cons,h),app(app(append,t),l))
[3] app(app(map,f),nil) -> nil
[4] app(app(map,f),app(app(cons,h),t)) ->
 app(app(cons,app(f,h)),app(app(map,f),t))
[5] app(app(append,app(app(append,l1),l2)),l3) ->
 app(app(append,l1),app(app(append,l2),l3))
[6] app(app(map,f),app(app(append,l1),l2)) ->
 app(app(append,app(app(map,f),l1)),app(app(map,f),l2))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                 app(app(append,t),l))>
<Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)>
<Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(append,t)>
<Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                              app(app(map,f),t))>
<Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(cons,app(f,h))>
<Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
<Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
<Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(append,l1),
                                                      app(app(append,l2),l3))>
<Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(append,l2),
                                                      l3)>
<Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(append,l2)>
<Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                             app(app(map,f),l1)),
                                                  app(app(map,f),l2))>
<Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(append,
                                                  app(app(map,f),l1))>
<Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)>
<Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
      --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                            app(map,f),
                                                            l2)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l2)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(map,f),l1)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(append,t),l)> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l2)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(map,f),
                                                           l1)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(append,l1),l2)) , Marked_app(
                                                           app(append,
                                                            app(app(map,f),l1)),
                                                           app(app(map,f),l2))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l2),l3)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(append,app(app(append,l1),l2)),l3) , Marked_app(
                                                               app(append,
                                                                l1),
                                                               app(app(
                                                                    append,
                                                                    l2),
                                                                l3))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(
                                                                  cons,
                                                                  app(f,h)),
                                                       app(app(map,f),t))>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(
                                                                    append,
                                                                    t),
                                                          l)>
  <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                   app(app(append,t),l))> 
     --> <Marked_app(app(append,app(app(cons,h),t)),l) , Marked_app(app(cons,h),
                                                          app(app(append,t),l))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(append,app(app(append,l1),l2)),l3) >= app(app(append,l1),
                                                 app(app(append,l2),l3)) ;
  app(app(append,app(app(cons,h),t)),l) >= app(app(cons,h),
                                            app(app(append,t),l)) ;
  app(app(append,nil),l) >= l ;
  app(app(map,f),app(app(append,l1),l2)) >= app(app(append,app(app(map,f),l1)),
                                             app(app(map,f),l2)) ;
  app(app(map,f),app(app(cons,h),t)) >= app(app(cons,app(f,h)),
                                         app(app(map,f),t)) ;
  app(app(map,f),nil) >= nil ;
  Marked_app(app(append,app(app(append,l1),l2)),l3) >= Marked_app(app(
                                                                   append,
                                                                   l1),
                                                        app(app(append,l2),l3)) ;
  Marked_app(app(append,app(app(append,l1),l2)),l3) >= Marked_app(app(
                                                                   append,
                                                                   l2),
                                                        l3) ;
  Marked_app(app(append,app(app(cons,h),t)),l) >= Marked_app(app(append,t),l) ;
  Marked_app(app(append,app(app(cons,h),t)),l) >= Marked_app(app(cons,h),
                                                   app(app(append,t),l)) ;
  Marked_app(app(map,f),app(app(append,l1),l2)) >= Marked_app(app(append,
                                                               app(app(map,f),
                                                                l1)),
                                                    app(app(map,f),l2)) ;
  Marked_app(app(map,f),app(app(append,l1),l2)) >= Marked_app(app(map,f),l1) ;
  Marked_app(app(map,f),app(app(append,l1),l2)) >= Marked_app(app(map,f),l2) ;
  Marked_app(app(map,f),app(app(cons,h),t)) >= Marked_app(app(cons,app(f,h)),
                                                app(app(map,f),t)) ;
  Marked_app(app(map,f),app(app(cons,h),t)) >= Marked_app(app(map,f),t) ;
  Marked_app(app(map,f),app(app(cons,h),t)) >= Marked_app(f,h) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(append,app(app(append,l1),l2)),l3) > Marked_app(app(append,l1),
                                                       app(app(append,l2),l3)) ;
 }
{
  Marked_app(app(append,app(app(append,l1),l2)),l3) > Marked_app(app(append,l2),
                                                       l3) ;
 }
{
  Marked_app(app(append,app(app(cons,h),t)),l) > Marked_app(app(append,t),l) ;
 }
{
  Marked_app(app(append,app(app(cons,h),t)),l) > Marked_app(app(cons,h),
                                                  app(app(append,t),l)) ;
 }
{
  Marked_app(app(map,f),app(app(append,l1),l2)) > Marked_app(app(append,
                                                              app(app(map,f),
                                                               l1)),
                                                   app(app(map,f),l2)) ;
 }
{
  Marked_app(app(map,f),app(app(append,l1),l2)) > Marked_app(app(map,f),l1) ;
 }
{
  Marked_app(app(map,f),app(app(append,l1),l2)) > Marked_app(app(map,f),l2) ;
 }
{
  Marked_app(app(map,f),app(app(cons,h),t)) > Marked_app(app(cons,app(f,h)),
                                               app(app(map,f),t)) ;
 }
{
  Marked_app(app(map,f),app(app(cons,h),t)) > Marked_app(app(map,f),t) ;
 }
{
  Marked_app(app(map,f),app(app(cons,h),t)) > Marked_app(f,h) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 14.142825 seconds (real time)
Cime Exit Status: 0