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

TRS termination of:
[1] minus(minus(x,y),z) -> minus(x,plus(y,z))
[2] minus(0,y) -> 0
[3] minus(x,0) -> x
[4] minus(s(x),s(y)) -> minus(x,y)
[5] plus(0,y) -> y
[6] plus(s(x),y) -> plus(x,s(y))
[7] plus(s(x),y) -> s(plus(y,x))
[8] zero(s(x)) -> false
[9] zero(0) -> true
[10] p(s(x)) -> x
[11] p(0) -> 0
[12] div(x,y) -> quot(x,y,0)
[13] quot(s(x),s(y),z) -> quot(minus(p(ack(0,x)),y),s(y),s(z))
[14] quot(0,s(y),z) -> z
[15] ack(0,x) -> s(x)
[16] ack(0,x) -> plus(x,s(0))
[17] ack(s(x),0) -> ack(x,s(0))
[18] ack(s(x),s(y)) -> ack(x,ack(s(x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_minus(minus(x,y),z) , Marked_minus(x,plus(y,z))>
<Marked_minus(minus(x,y),z) , Marked_plus(y,z)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_plus(s(x),y) , Marked_plus(x,s(y))>
<Marked_plus(s(x),y) , Marked_plus(y,x)>
<Marked_div(x,y) , Marked_quot(x,y,0)>
<Marked_quot(s(x),s(y),z) , Marked_quot(minus(p(ack(0,x)),y),s(y),s(z))>
<Marked_quot(s(x),s(y),z) , Marked_minus(p(ack(0,x)),y)>
<Marked_quot(s(x),s(y),z) , Marked_p(ack(0,x))>
<Marked_quot(s(x),s(y),z) , Marked_ack(0,x)>
<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)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_quot(s(x),s(y),z) , Marked_quot(minus(p(ack(0,x)),y),s(y),s(z))> 
      --> <Marked_quot(s(x),s(y),z) , Marked_quot(minus(p(ack(0,x)),y),
                                       s(y),s(z))>
}

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
     --> <Marked_minus(minus(x,y),z) , Marked_minus(x,plus(y,z))>
  <Marked_minus(minus(x,y),z) , Marked_minus(x,plus(y,z))> 
     --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
  <Marked_minus(minus(x,y),z) , Marked_minus(x,plus(y,z))> 
     --> <Marked_minus(minus(x,y),z) , Marked_minus(x,plus(y,z))>
}

{  <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(s(x),y) , Marked_plus(y,x)> 
      --> <Marked_plus(s(x),y) , Marked_plus(y,x)>
  <Marked_plus(s(x),y) , Marked_plus(y,x)> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(y,x)>
  <Marked_plus(s(x),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(x),y) , Marked_plus(x,s(y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(minus(x,y),z) >= minus(x,plus(y,z)) ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  plus(0,y) >= y ;
  plus(s(x),y) >= plus(x,s(y)) ;
  plus(s(x),y) >= s(plus(y,x)) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  quot(0,s(y),z) >= z ;
  quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
  div(x,y) >= quot(x,y,0) ;
  ack(0,x) >= plus(x,s(0)) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_quot(s(x),s(y),z) >= Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
 }
 + Disjunctions:{ 
{
  Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
 }
 } 
=== 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 (Simple graph)
Found the following constraints:
{
  minus(minus(x,y),z) >= minus(x,plus(y,z)) ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  plus(0,y) >= y ;
  plus(s(x),y) >= plus(x,s(y)) ;
  plus(s(x),y) >= s(plus(y,x)) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  quot(0,s(y),z) >= z ;
  quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
  div(x,y) >= quot(x,y,0) ;
  ack(0,x) >= plus(x,s(0)) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  minus(minus(x,y),z) >= minus(x,plus(y,z)) ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  plus(0,y) >= y ;
  plus(s(x),y) >= plus(x,s(y)) ;
  plus(s(x),y) >= s(plus(y,x)) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  quot(0,s(y),z) >= z ;
  quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
  div(x,y) >= quot(x,y,0) ;
  ack(0,x) >= plus(x,s(0)) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(1021 bt (1125) [234])
=== 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 7.510251 seconds (real time)
Cime Exit Status: 0