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

TRS termination of:
[1] app(app(app(fold,f),nil),x) -> x
[2] app(app(app(fold,f),app(app(cons,h),t)),x) ->
 app(app(app(fold,f),t),app(app(f,x),h))
[3] app(sum,l) -> app(app(app(fold,add),l),0)
[4] app(app(app(fold,mul),l),1) -> app(prod,l)


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(app(fold,f),
                                                                 t),
                                                      app(app(f,x),h))>
<Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),t)>
<Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)>
<Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
<Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
<Marked_app(sum,l) , Marked_app(app(fold,add),l)>
<Marked_app(sum,l) , Marked_app(fold,add)>
<Marked_app(app(app(fold,mul),l),1) , Marked_app(prod,l)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
      --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(sum,l) , Marked_app(app(fold,add),l)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(f,x),h)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(fold,f),
                                                        t)> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(sum,l) , Marked_app(app(fold,add),l)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(sum,l) , Marked_app(app(app(fold,add),l),0)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(f,x)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(f,
                                                                x),h)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(fold,
                                                                f),t)>
  <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h))> 
     --> <Marked_app(app(app(fold,f),app(app(cons,h),t)),x) , Marked_app(
                                                               app(app(fold,f),
                                                                t),
                                                               app(app(f,x),h))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(fold,mul),l),1) >= app(prod,l) ;
  app(app(app(fold,f),app(app(cons,h),t)),x) >= app(app(app(fold,f),t),
                                                 app(app(f,x),h)) ;
  app(app(app(fold,f),nil),x) >= x ;
  app(sum,l) >= app(app(app(fold,add),l),0) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) >= Marked_app(app(
                                                                   app(
                                                                    fold,
                                                                    f),
                                                                   t),
                                                        app(app(f,x),h)) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) >= Marked_app(app(fold,f),
                                                        t) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) >= Marked_app(app(f,x),h) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) >= Marked_app(f,x) ;
  Marked_app(sum,l) >= Marked_app(app(app(fold,add),l),0) ;
  Marked_app(sum,l) >= Marked_app(app(fold,add),l) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(
                                                                  app(
                                                                   fold,
                                                                   f),
                                                                  t),
                                                       app(app(f,x),h)) ;
 }
{
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(fold,f),t) ;
 }
{
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(f,x),h) ;
 }
{
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(f,x) ;
 }
{
  Marked_app(sum,l) > Marked_app(app(app(fold,add),l),0) ;
 }
{
  Marked_app(sum,l) > Marked_app(app(fold,add),l) ;
 }
 } 
=== 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 (Simple graph)
Found the following constraints:
{
  app(app(app(fold,mul),l),1) >= app(prod,l) ;
  app(app(app(fold,f),app(app(cons,h),t)),x) >= app(app(app(fold,f),t),
                                                 app(app(f,x),h)) ;
  app(app(app(fold,f),nil),x) >= x ;
  app(sum,l) >= app(app(app(fold,add),l),0) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(
                                                                  app(
                                                                   fold,
                                                                   f),
                                                                  t),
                                                       app(app(f,x),h)) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(fold,f),t) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(f,x),h) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(f,x) ;
  Marked_app(sum,l) > Marked_app(app(app(fold,add),l),0) ;
  Marked_app(sum,l) > Marked_app(app(fold,add),l) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(app(fold,mul),l),1) >= app(prod,l) ;
  app(app(app(fold,f),app(app(cons,h),t)),x) >= app(app(app(fold,f),t),
                                                 app(app(f,x),h)) ;
  app(app(app(fold,f),nil),x) >= x ;
  app(sum,l) >= app(app(app(fold,add),l),0) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(
                                                                  app(
                                                                   fold,
                                                                   f),
                                                                  t),
                                                       app(app(f,x),h)) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(fold,f),t) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(app(f,x),h) ;
  Marked_app(app(app(fold,f),app(app(cons,h),t)),x) > Marked_app(f,x) ;
  Marked_app(sum,l) > Marked_app(app(app(fold,add),l),0) ;
  Marked_app(sum,l) > Marked_app(app(fold,add),l) ;
 }
 + 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.(6 bt (2) [5])
=== 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 12.192891 seconds (real time)
Cime Exit Status: 0