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

TRS termination of:
[1] double(x) -> permute(x,x,a)
[2] permute(x,y,a) -> permute(isZero(x),x,b)
[3] permute(false,x,b) -> permute(ack(x,x),p(x),c)
[4] permute(true,x,b) -> 0
[5] permute(y,x,c) -> s(s(permute(x,y,a)))
[6] p(0) -> 0
[7] p(s(x)) -> x
[8] ack(0,x) -> plus(x,s(0))
[9] ack(s(x),0) -> ack(x,s(0))
[10] ack(s(x),s(y)) -> ack(x,ack(s(x),y))
[11] plus(0,y) -> y
[12] plus(s(x),y) -> plus(x,s(y))
[13] plus(x,s(s(y))) -> s(plus(s(x),y))
[14] plus(x,s(0)) -> s(x)
[15] plus(x,0) -> x
[16] isZero(0) -> true
[17] isZero(s(x)) -> false


Sub problem: 
guided: 

DP termination of:
<Marked_double(x) , Marked_permute(x,x,a)>
<Marked_permute(x,y,a) , Marked_permute(isZero(x),x,b)>
<Marked_permute(x,y,a) , Marked_isZero(x)>
<Marked_permute(false,x,b) , Marked_permute(ack(x,x),p(x),c)>
<Marked_permute(false,x,b) , Marked_ack(x,x)>
<Marked_permute(false,x,b) , Marked_p(x)>
<Marked_permute(y,x,c) , Marked_permute(x,y,a)>
<Marked_ack(0,x) , Marked_plus(x,s(0))>
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
<Marked_plus(s(x),y) , Marked_plus(x,s(y))>
<Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_permute(y,x,c) , Marked_permute(x,y,a)> 
      --> <Marked_permute(x,y,a) , Marked_permute(isZero(x),x,b)>
  <Marked_permute(false,x,b) , Marked_permute(ack(x,x),p(x),c)> 
     --> <Marked_permute(y,x,c) , Marked_permute(x,y,a)>
  <Marked_permute(x,y,a) , Marked_permute(isZero(x),x,b)> 
     --> <Marked_permute(false,x,b) , Marked_permute(ack(x,x),p(x),c)>
}

{  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
      --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
}

{  <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)> 
      --> <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
  <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  permute(false,x,b) >= permute(ack(x,x),p(x),c) ;
  permute(true,x,b) >= 0 ;
  permute(x,y,a) >= permute(isZero(x),x,b) ;
  permute(y,x,c) >= s(s(permute(x,y,a))) ;
  double(x) >= permute(x,x,a) ;
  isZero(0) >= true ;
  isZero(s(x)) >= false ;
  ack(0,x) >= plus(x,s(0)) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  plus(0,y) >= y ;
  plus(s(x),y) >= plus(x,s(y)) ;
  plus(x,0) >= x ;
  plus(x,s(0)) >= s(x) ;
  plus(x,s(s(y))) >= s(plus(s(x),y)) ;
  Marked_permute(false,x,b) >= Marked_permute(ack(x,x),p(x),c) ;
  Marked_permute(x,y,a) >= Marked_permute(isZero(x),x,b) ;
  Marked_permute(y,x,c) >= Marked_permute(x,y,a) ;
 }
 + Disjunctions:{ 
{
  Marked_permute(false,x,b) > Marked_permute(ack(x,x),p(x),c) ;
 }
{
  Marked_permute(x,y,a) > Marked_permute(isZero(x),x,b) ;
 }
{
  Marked_permute(y,x,c) > Marked_permute(x,y,a) ;
 }
 } 
=== 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 : 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 1.576290 seconds (real time)
Cime Exit Status: 0