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

TRS termination of:
[1] app(app(map,f),nil) -> nil
[2] app(app(map,f),app(app(cons,x),xs)) ->
 app(app(cons,app(f,x)),app(app(map,f),xs))
[3] app(app(minus,x),0) -> x
[4] app(app(minus,app(s,x)),app(s,y)) ->
 app(app(minus,app(p,app(s,x))),app(p,app(s,y)))
[5] app(p,app(s,x)) -> x
[6] app(app(div,0),app(s,y)) -> 0
[7] app(app(div,app(s,x)),app(s,y)) ->
 app(s,app(app(div,app(app(minus,x),y)),app(s,y)))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                               app(app(map,f),xs))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(cons,app(f,x))>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
<Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)>
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                        app(p,app(s,x))),
                                             app(p,app(s,y)))>
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(minus,app(p,app(s,x)))>
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(p,app(s,x))>
<Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(p,app(s,y))>
<Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(s,
                                           app(app(div,app(app(minus,x),y)),
                                            app(s,y)))>
<Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                      app(app(minus,x),y)),
                                           app(s,y))>
<Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(div,app(app(minus,x),y))>
<Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
<Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(minus,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
      --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y)))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),xs)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(minus,x),y)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(div,app(s,x)),app(s,y)) , Marked_app(app(div,
                                                               app(app(minus,x),
                                                                y)),app(s,y))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(minus,app(s,x)),app(s,y)) , Marked_app(app(minus,
                                                                 app(
                                                                  p,app(s,x))),
                                                      app(p,app(s,y)))>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(map,f),
                                                        xs)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(f,x)>
  <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs))> 
     --> <Marked_app(app(map,f),app(app(cons,x),xs)) , Marked_app(app(
                                                                   cons,
                                                                   app(f,x)),
                                                        app(app(map,f),xs))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(minus,app(s,x)),app(s,y)) >= app(app(minus,app(p,app(s,x))),
                                        app(p,app(s,y))) ;
  app(app(minus,x),0) >= x ;
  app(app(div,app(s,x)),app(s,y)) >= app(s,
                                      app(app(div,app(app(minus,x),y)),
                                       app(s,y))) ;
  app(app(div,0),app(s,y)) >= 0 ;
  app(p,app(s,x)) >= x ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)),
                                                 app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x) ;
  Marked_app(app(minus,app(s,x)),app(s,y)) >= Marked_app(app(minus,
                                                          app(p,app(s,x))),
                                               app(p,app(s,y))) ;
  Marked_app(app(div,app(s,x)),app(s,y)) >= Marked_app(app(minus,x),y) ;
  Marked_app(app(div,app(s,x)),app(s,y)) >= Marked_app(app(div,
                                                        app(app(minus,x),y)),
                                             app(s,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
 }
{
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
 }
{
  Marked_app(app(minus,app(s,x)),app(s,y)) > Marked_app(app(minus,
                                                         app(p,app(s,x))),
                                              app(p,app(s,y))) ;
 }
{
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(minus,x),y) ;
 }
{
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(div,
                                                       app(app(minus,x),y)),
                                            app(s,y)) ;
 }
 } 
=== 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(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(minus,app(s,x)),app(s,y)) >= app(app(minus,app(p,app(s,x))),
                                        app(p,app(s,y))) ;
  app(app(minus,x),0) >= x ;
  app(app(div,app(s,x)),app(s,y)) >= app(s,
                                      app(app(div,app(app(minus,x),y)),
                                       app(s,y))) ;
  app(app(div,0),app(s,y)) >= 0 ;
  app(p,app(s,x)) >= x ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
  Marked_app(app(minus,app(s,x)),app(s,y)) > Marked_app(app(minus,
                                                         app(p,app(s,x))),
                                              app(p,app(s,y))) ;
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(minus,x),y) ;
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(div,
                                                       app(app(minus,x),y)),
                                            app(s,y)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  app(app(map,f),nil) >= nil ;
  app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)),
                                          app(app(map,f),xs)) ;
  app(app(minus,app(s,x)),app(s,y)) >= app(app(minus,app(p,app(s,x))),
                                        app(p,app(s,y))) ;
  app(app(minus,x),0) >= x ;
  app(app(div,app(s,x)),app(s,y)) >= app(s,
                                      app(app(div,app(app(minus,x),y)),
                                       app(s,y))) ;
  app(app(div,0),app(s,y)) >= 0 ;
  app(p,app(s,x)) >= x ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)),
                                                app(app(map,f),xs)) ;
  Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ;
  Marked_app(app(minus,app(s,x)),app(s,y)) > Marked_app(app(minus,
                                                         app(p,app(s,x))),
                                              app(p,app(s,y))) ;
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(minus,x),y) ;
  Marked_app(app(div,app(s,x)),app(s,y)) > Marked_app(app(div,
                                                       app(app(minus,x),y)),
                                            app(s,y)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
No solution found for these parameters.(4 bt (0) [6])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 49.677191 seconds (real time)
Cime Exit Status: 0