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

TRS termination of:
[1] app(app(add,0),y) -> y
[2] app(app(add,app(s,x)),y) -> app(s,app(app(add,x),y))
[3] app(app(mult,0),y) -> 0
[4] app(app(mult,app(s,x)),y) -> app(app(add,app(app(mult,x),y)),y)
[5] app(app(app(rec,f),x),0) -> x
[6] app(app(app(rec,f),x),app(s,y)) ->
 app(app(f,app(s,y)),app(app(app(rec,f),x),y))
[7] fact -> app(app(rec,mult),app(s,0))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(add,app(s,x)),y) , Marked_app(s,app(app(add,x),y))>
<Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
<Marked_app(app(add,app(s,x)),y) , Marked_app(add,x)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(add,app(app(mult,x),y))>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
<Marked_app(app(mult,app(s,x)),y) , Marked_app(mult,x)>
<Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                           app(app(app(rec,f),x),y))>
<Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
<Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)>
<Marked_fact , Marked_app(app(rec,mult),app(s,0))>
<Marked_fact , Marked_app(rec,mult)>
<Marked_fact , Marked_app(s,0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
      --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),
                                                                x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),
                                                    y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),
                                                    y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y))> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),
                                                    y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),
                                                    y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,app(app(mult,x),y)),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(app(rec,f),x),
                                                    y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(f,app(s,y))>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(app(rec,f),x),app(s,y)) , Marked_app(app(f,app(s,y)),
                                                    app(app(app(rec,f),x),y))>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(mult,x),y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(mult,app(s,x)),y) , Marked_app(app(add,
                                                         app(app(mult,x),y)),
                                              y)>
  <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)> 
     --> <Marked_app(app(add,app(s,x)),y) , Marked_app(app(add,x),y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(app(rec,f),x),app(s,y)) >= app(app(f,app(s,y)),
                                      app(app(app(rec,f),x),y)) ;
  app(app(app(rec,f),x),0) >= x ;
  app(app(add,app(s,x)),y) >= app(s,app(app(add,x),y)) ;
  app(app(add,0),y) >= y ;
  app(app(mult,app(s,x)),y) >= app(app(add,app(app(mult,x),y)),y) ;
  app(app(mult,0),y) >= 0 ;
  fact >= app(app(rec,mult),app(s,0)) ;
  Marked_app(app(app(rec,f),x),app(s,y)) >= Marked_app(app(app(rec,f),x),y) ;
  Marked_app(app(app(rec,f),x),app(s,y)) >= Marked_app(app(f,app(s,y)),
                                             app(app(app(rec,f),x),y)) ;
  Marked_app(app(app(rec,f),x),app(s,y)) >= Marked_app(f,app(s,y)) ;
  Marked_app(app(add,app(s,x)),y) >= Marked_app(app(add,x),y) ;
  Marked_app(app(mult,app(s,x)),y) >= Marked_app(app(add,app(app(mult,x),y)),y) ;
  Marked_app(app(mult,app(s,x)),y) >= Marked_app(app(mult,x),y) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(app(rec,f),x),app(s,y)) > Marked_app(app(app(rec,f),x),y) ;
 }
{
  Marked_app(app(app(rec,f),x),app(s,y)) > Marked_app(app(f,app(s,y)),
                                            app(app(app(rec,f),x),y)) ;
 }
{
  Marked_app(app(app(rec,f),x),app(s,y)) > Marked_app(f,app(s,y)) ;
 }
{
  Marked_app(app(add,app(s,x)),y) > Marked_app(app(add,x),y) ;
 }
{
  Marked_app(app(mult,app(s,x)),y) > Marked_app(app(add,app(app(mult,x),y)),y) ;
 }
{
  Marked_app(app(mult,app(s,x)),y) > Marked_app(app(mult,x),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 (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 9.045635 seconds (real time)
Cime Exit Status: 0