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

TRS termination of:
[1] plus(x,0) -> x
[2] plus(x,s(y)) -> s(plus(x,y))
[3] times(0,y) -> 0
[4] times(x,0) -> 0
[5] times(s(x),y) -> plus(times(x,y),y)
[6] p(s(s(x))) -> s(p(s(x)))
[7] p(s(0)) -> 0
[8] fac(s(x)) -> times(fac(p(s(x))),s(x))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_times(s(x),y) , Marked_plus(times(x,y),y)>
<Marked_times(s(x),y) , Marked_times(x,y)>
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_fac(s(x)) , Marked_times(fac(p(s(x))),s(x))>
<Marked_fac(s(x)) , Marked_fac(p(s(x)))>
<Marked_fac(s(x)) , Marked_p(s(x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_fac(s(x)) , Marked_fac(p(s(x)))> 
      --> <Marked_fac(s(x)) , Marked_fac(p(s(x)))>
}

{  <Marked_times(s(x),y) , Marked_times(x,y)> 
      --> <Marked_times(s(x),y) , Marked_times(x,y)>
}

{  <Marked_plus(x,s(y)) , Marked_plus(x,y)> 
      --> <Marked_plus(x,s(y)) , Marked_plus(x,y)>
}

{  <Marked_p(s(s(x))) , Marked_p(s(x))> 
      --> <Marked_p(s(s(x))) , Marked_p(s(x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(times(x,y),y) ;
  times(x,0) >= 0 ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  fac(s(x)) >= times(fac(p(s(x))),s(x)) ;
  Marked_fac(s(x)) >= Marked_fac(p(s(x))) ;
 }
 + Disjunctions:{ 
{
  Marked_fac(s(x)) > Marked_fac(p(s(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 : 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 0.753061 seconds (real time)
Cime Exit Status: 0