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

TRS termination of:
[1] app(app(twice,f),x) -> app(f,app(f,x))
[2] app(app(map,f),nil) -> nil
[3] app(app(map,f),app(app(cons,h),t)) ->
 app(app(cons,app(f,h)),app(app(map,f),t))
[4] app(app(fmap,nil),x) -> nil
[5] app(app(fmap,app(app(cons,f),t_f)),x) ->
 app(app(cons,app(f,x)),app(app(fmap,t_f),x))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
<Marked_app(app(twice,f),x) , Marked_app(f,x)>
<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(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                 app(app(fmap,t_f),x))>
<Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(cons,app(f,x))>
<Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
<Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)>
<Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(fmap,t_f)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
      --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(
                                                           app(fmap,t_f),
                                                           x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(fmap,t_f),x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x))> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <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(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <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(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <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(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <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(twice,f),x) , Marked_app(f,x)>
  <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(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <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(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,x)> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    fmap,
                                                                    t_f),
                                                          x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(f,x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(fmap,app(app(cons,f),t_f)),x) , Marked_app(app(
                                                                    cons,
                                                                    app(f,x)),
                                                          app(app(fmap,t_f),x))>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(app(map,f),t)>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(map,f),app(app(cons,h),t)) , Marked_app(f,h)>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <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(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,x)>
  <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))> 
     --> <Marked_app(app(twice,f),x) , Marked_app(f,app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(twice,f),x) >= app(f,app(f,x)) ;
  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 ;
  app(app(fmap,app(app(cons,f),t_f)),x) >= app(app(cons,app(f,x)),
                                            app(app(fmap,t_f),x)) ;
  app(app(fmap,nil),x) >= nil ;
  Marked_app(app(twice,f),x) >= Marked_app(f,app(f,x)) ;
  Marked_app(app(twice,f),x) >= Marked_app(f,x) ;
  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(fmap,app(app(cons,f),t_f)),x) >= Marked_app(app(cons,app(f,x)),
                                                   app(app(fmap,t_f),x)) ;
  Marked_app(app(fmap,app(app(cons,f),t_f)),x) >= Marked_app(app(fmap,t_f),x) ;
  Marked_app(app(fmap,app(app(cons,f),t_f)),x) >= Marked_app(f,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(twice,f),x) > Marked_app(f,app(f,x)) ;
 }
{
  Marked_app(app(twice,f),x) > Marked_app(f,x) ;
 }
{
  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(fmap,app(app(cons,f),t_f)),x) > Marked_app(app(cons,app(f,x)),
                                                  app(app(fmap,t_f),x)) ;
 }
{
  Marked_app(app(fmap,app(app(cons,f),t_f)),x) > Marked_app(app(fmap,t_f),x) ;
 }
{
  Marked_app(app(fmap,app(app(cons,f),t_f)),x) > Marked_app(f,x) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 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 9.357260 seconds (real time)
Cime Exit Status: 0