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

TRS termination of:
[1] ap(ap(f,x),x) -> ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))
[2] ap(ap(ap(foldr,g),h),nil) -> h
[3] ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) ->
 ap(ap(g,x),ap(ap(ap(foldr,g),h),xs))


Sub problem: 
guided: 

DP termination of:
<Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
<Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
<Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
<Marked_ap(ap(f,x),x) , Marked_ap(cons,x)>
<Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                   ap(ap(ap(foldr,g),h),xs))>
<Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
<Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                   xs)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),
                                                                h),xs)> 
      --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                             ap(ap(foldr,g),
                                                              h),xs)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                     xs)> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                     xs)> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(g,x),
                                                            ap(ap(ap(foldr,g),
                                                                h),xs))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                     xs)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                     xs)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(ap(foldr,g),h),
                                                     xs)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(ap(foldr,g),
                                                             h),xs)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(g,x),
                                                            ap(ap(ap(foldr,g),
                                                                h),xs))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(ap(foldr,g),
                                                             h),xs)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(g,x),
                                                            ap(ap(ap(foldr,g),
                                                                h),xs))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(ap(foldr,g),
                                                             h),xs)>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(g,x),
                                                            ap(ap(ap(foldr,g),
                                                                h),xs))>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(ap(foldr,g),
                                                             h),xs)>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(g,x)>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) , Marked_ap(
                                                            ap(g,x),
                                                            ap(ap(ap(foldr,g),
                                                                h),xs))>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(cons,x),nil)>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(x,ap(f,x))>
  <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))> 
     --> <Marked_ap(ap(f,x),x) , Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) >= ap(ap(g,x),
                                              ap(ap(ap(foldr,g),h),xs)) ;
  ap(ap(ap(foldr,g),h),nil) >= h ;
  ap(ap(f,x),x) >= ap(ap(x,ap(f,x)),ap(ap(cons,x),nil)) ;
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) >= Marked_ap(ap(ap(foldr,g),h),
                                                     xs) ;
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) >= Marked_ap(ap(g,x),
                                                     ap(ap(ap(foldr,g),h),xs)) ;
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) >= Marked_ap(g,x) ;
  Marked_ap(ap(f,x),x) >= Marked_ap(ap(cons,x),nil) ;
  Marked_ap(ap(f,x),x) >= Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil)) ;
  Marked_ap(ap(f,x),x) >= Marked_ap(x,ap(f,x)) ;
 }
 + Disjunctions:{ 
{
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) > Marked_ap(ap(ap(foldr,g),h),
                                                    xs) ;
 }
{
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) > Marked_ap(ap(g,x),
                                                    ap(ap(ap(foldr,g),h),xs)) ;
 }
{
  Marked_ap(ap(ap(foldr,g),h),ap(ap(cons,x),xs)) > Marked_ap(g,x) ;
 }
{
  Marked_ap(ap(f,x),x) > Marked_ap(ap(cons,x),nil) ;
 }
{
  Marked_ap(ap(f,x),x) > Marked_ap(ap(x,ap(f,x)),ap(ap(cons,x),nil)) ;
 }
{
  Marked_ap(ap(f,x),x) > Marked_ap(x,ap(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 : 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 8.622396 seconds (real time)
Cime Exit Status: 0