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

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


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(x),y) , Marked_plus(p(s(x)),y)>
<Marked_plus(s(x),y) , Marked_p(s(x))>
<Marked_times(s(x),y) , Marked_plus(y,times(p(s(x)),y))>
<Marked_times(s(x),y) , Marked_times(p(s(x)),y)>
<Marked_times(s(x),y) , Marked_p(s(x))>
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_fac(s(x),y) , Marked_fac(p(s(x)),times(s(x),y))>
<Marked_fac(s(x),y) , Marked_p(s(x))>
<Marked_fac(s(x),y) , Marked_times(s(x),y)>
<Marked_factorial(x) , Marked_fac(x,s(0))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

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

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

{  <Marked_plus(s(x),y) , Marked_plus(p(s(x)),y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(p(s(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(0,x) >= x ;
  plus(s(x),y) >= s(plus(p(s(x)),y)) ;
  p(s(0)) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= plus(y,times(p(s(x)),y)) ;
  fac(0,x) >= x ;
  fac(s(x),y) >= fac(p(s(x)),times(s(x),y)) ;
  factorial(x) >= fac(x,s(0)) ;
  Marked_fac(s(x),y) >= Marked_fac(p(s(x)),times(s(x),y)) ;
 }
 + Disjunctions:{ 
{
  Marked_fac(s(x),y) > Marked_fac(p(s(x)),times(s(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 : 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 2.043056 seconds (real time)
Cime Exit Status: 0