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

TRS termination of:
[1] plus(x,0) -> x
[2] plus(0,y) -> y
[3] plus(s(x),y) -> s(plus(x,y))
[4] times(0,y) -> 0
[5] times(s(0),y) -> y
[6] times(s(x),y) -> plus(y,times(x,y))
[7] div(0,y) -> 0
[8] div(x,y) -> quot(x,y,y)
[9] quot(0,s(y),z) -> 0
[10] quot(s(x),s(y),z) -> quot(x,y,z)
[11] quot(x,0,s(z)) -> s(div(x,s(z)))
[12] div(div(x,y),z) -> div(x,times(y,z))
[13] eq(0,0) -> true
[14] eq(s(x),0) -> false
[15] eq(0,s(y)) -> false
[16] eq(s(x),s(y)) -> eq(x,y)
[17] divides(y,x) -> eq(x,times(div(x,y),y))
[18] prime(s(s(x))) -> pr(s(s(x)),s(x))
[19] pr(x,s(0)) -> true
[20] pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
[21] if(true,x,y) -> false
[22] if(false,x,y) -> pr(x,y)


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_times(s(x),y) , Marked_plus(y,times(x,y))>
<Marked_times(s(x),y) , Marked_times(x,y)>
<Marked_div(x,y) , Marked_quot(x,y,y)>
<Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
<Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
<Marked_div(div(x,y),z) , Marked_div(x,times(y,z))>
<Marked_div(div(x,y),z) , Marked_times(y,z)>
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_divides(y,x) , Marked_eq(x,times(div(x,y),y))>
<Marked_divides(y,x) , Marked_times(div(x,y),y)>
<Marked_divides(y,x) , Marked_div(x,y)>
<Marked_prime(s(s(x))) , Marked_pr(s(s(x)),s(x))>
<Marked_pr(x,s(s(y))) , Marked_if(divides(s(s(y)),x),x,s(y))>
<Marked_pr(x,s(s(y))) , Marked_divides(s(s(y)),x)>
<Marked_if(false,x,y) , Marked_pr(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_if(false,x,y) , Marked_pr(x,y)> 
      --> <Marked_pr(x,s(s(y))) , Marked_if(divides(s(s(y)),x),x,s(y))>
  <Marked_pr(x,s(s(y))) , Marked_if(divides(s(s(y)),x),x,s(y))> 
     --> <Marked_if(false,x,y) , Marked_pr(x,y)>
}

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

{  <Marked_div(div(x,y),z) , Marked_div(x,times(y,z))> 
      --> <Marked_div(div(x,y),z) , Marked_div(x,times(y,z))>
  <Marked_div(div(x,y),z) , Marked_div(x,times(y,z))> 
     --> <Marked_div(x,y) , Marked_quot(x,y,y)>
  <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))> 
     --> <Marked_div(div(x,y),z) , Marked_div(x,times(y,z))>
  <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))> 
     --> <Marked_div(x,y) , Marked_quot(x,y,y)>
  <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)> 
     --> <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
  <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)> 
     --> <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
  <Marked_div(x,y) , Marked_quot(x,y,y)> 
     --> <Marked_quot(x,0,s(z)) , Marked_div(x,s(z))>
  <Marked_div(x,y) , Marked_quot(x,y,y)> 
     --> <Marked_quot(s(x),s(y),z) , Marked_quot(x,y,z)>
}

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

{  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(x,0) >= x ;
  times(0,y) >= 0 ;
  times(s(0),y) >= y ;
  times(s(x),y) >= plus(y,times(x,y)) ;
  div(0,y) >= 0 ;
  div(div(x,y),z) >= div(x,times(y,z)) ;
  div(x,y) >= quot(x,y,y) ;
  quot(0,s(y),z) >= 0 ;
  quot(s(x),s(y),z) >= quot(x,y,z) ;
  quot(x,0,s(z)) >= s(div(x,s(z))) ;
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  divides(y,x) >= eq(x,times(div(x,y),y)) ;
  pr(x,s(0)) >= true ;
  pr(x,s(s(y))) >= if(divides(s(s(y)),x),x,s(y)) ;
  prime(s(s(x))) >= pr(s(s(x)),s(x)) ;
  if(true,x,y) >= false ;
  if(false,x,y) >= pr(x,y) ;
  Marked_if(false,x,y) >= Marked_pr(x,y) ;
  Marked_pr(x,s(s(y))) >= Marked_if(divides(s(s(y)),x),x,s(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,x,y) > Marked_pr(x,y) ;
 }
{
  Marked_pr(x,s(s(y))) > Marked_if(divides(s(s(y)),x),x,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 : 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 17.834419 seconds (real time)
Cime Exit Status: 0