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

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


Sub problem: 
guided: 

DP termination of:
<Marked_ge(s(x),0) , Marked_ge(x,0)>
<Marked_ge(0,s(s(x))) , Marked_ge(0,s(x))>
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
<Marked_minus(0,s(x)) , Marked_minus(0,x)>
<Marked_minus(s(x),0) , Marked_minus(x,0)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_plus(0,s(x)) , Marked_plus(0,x)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_div(x,y) , Marked_ify(ge(y,s(0)),x,y)>
<Marked_div(x,y) , Marked_ge(y,s(0))>
<Marked_ify(true,x,y) , Marked_if(ge(x,y),x,y)>
<Marked_ify(true,x,y) , Marked_ge(x,y)>
<Marked_if(true,x,y) , Marked_div(minus(x,y),y)>
<Marked_if(true,x,y) , Marked_minus(x,y)>
<Marked_div(plus(x,y),z) , Marked_plus(div(x,z),div(y,z))>
<Marked_div(plus(x,y),z) , Marked_div(x,z)>
<Marked_div(plus(x,y),z) , Marked_div(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 9 components:

{  <Marked_div(plus(x,y),z) , Marked_div(y,z)> 
      --> <Marked_div(plus(x,y),z) , Marked_div(y,z)>
  <Marked_div(plus(x,y),z) , Marked_div(y,z)> 
     --> <Marked_div(plus(x,y),z) , Marked_div(x,z)>
  <Marked_div(plus(x,y),z) , Marked_div(y,z)> 
     --> <Marked_div(x,y) , Marked_ify(ge(y,s(0)),x,y)>
  <Marked_div(plus(x,y),z) , Marked_div(x,z)> 
     --> <Marked_div(plus(x,y),z) , Marked_div(y,z)>
  <Marked_div(plus(x,y),z) , Marked_div(x,z)> 
     --> <Marked_div(plus(x,y),z) , Marked_div(x,z)>
  <Marked_div(plus(x,y),z) , Marked_div(x,z)> 
     --> <Marked_div(x,y) , Marked_ify(ge(y,s(0)),x,y)>
  <Marked_if(true,x,y) , Marked_div(minus(x,y),y)> 
     --> <Marked_div(plus(x,y),z) , Marked_div(y,z)>
  <Marked_if(true,x,y) , Marked_div(minus(x,y),y)> 
     --> <Marked_div(plus(x,y),z) , Marked_div(x,z)>
  <Marked_if(true,x,y) , Marked_div(minus(x,y),y)> 
     --> <Marked_div(x,y) , Marked_ify(ge(y,s(0)),x,y)>
  <Marked_ify(true,x,y) , Marked_if(ge(x,y),x,y)> 
     --> <Marked_if(true,x,y) , Marked_div(minus(x,y),y)>
  <Marked_div(x,y) , Marked_ify(ge(y,s(0)),x,y)> 
     --> <Marked_ify(true,x,y) , Marked_if(ge(x,y),x,y)>
}

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

{  <Marked_minus(0,s(x)) , Marked_minus(0,x)> 
      --> <Marked_minus(0,s(x)) , Marked_minus(0,x)>
}

{  <Marked_minus(s(x),0) , Marked_minus(x,0)> 
      --> <Marked_minus(s(x),0) , Marked_minus(x,0)>
}

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

{  <Marked_ge(s(x),0) , Marked_ge(x,0)> 
      --> <Marked_ge(s(x),0) , Marked_ge(x,0)>
}

{  <Marked_ge(0,s(s(x))) , Marked_ge(0,s(x))> 
      --> <Marked_ge(0,s(s(x))) , Marked_ge(0,s(x))>
}

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

{  <Marked_plus(0,s(x)) , Marked_plus(0,x)> 
      --> <Marked_plus(0,s(x)) , Marked_plus(0,x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ge(0,0) >= true ;
  ge(0,s(0)) >= false ;
  ge(0,s(s(x))) >= ge(0,s(x)) ;
  ge(s(x),0) >= ge(x,0) ;
  ge(s(x),s(y)) >= ge(x,y) ;
  minus(0,0) >= 0 ;
  minus(0,s(x)) >= minus(0,x) ;
  minus(s(x),0) >= s(minus(x,0)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  plus(0,0) >= 0 ;
  plus(0,s(x)) >= s(plus(0,x)) ;
  plus(s(x),y) >= s(plus(x,y)) ;
  ify(true,x,y) >= if(ge(x,y),x,y) ;
  ify(false,x,y) >= divByZeroError ;
  div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ;
  div(x,y) >= ify(ge(y,s(0)),x,y) ;
  if(true,x,y) >= s(div(minus(x,y),y)) ;
  if(false,x,y) >= 0 ;
  Marked_div(plus(x,y),z) >= Marked_div(x,z) ;
  Marked_div(plus(x,y),z) >= Marked_div(y,z) ;
  Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) ;
  Marked_if(true,x,y) >= Marked_div(minus(x,y),y) ;
  Marked_ify(true,x,y) >= Marked_if(ge(x,y),x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_div(plus(x,y),z) > Marked_div(x,z) ;
 }
{
  Marked_div(plus(x,y),z) > Marked_div(y,z) ;
 }
{
  Marked_div(x,y) > Marked_ify(ge(y,s(0)),x,y) ;
 }
{
  Marked_if(true,x,y) > Marked_div(minus(x,y),y) ;
 }
{
  Marked_ify(true,x,y) > Marked_if(ge(x,y),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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: ge(0,0) >= true
constraint: ge(0,s(0)) >= false
constraint: ge(0,s(s(x))) >= ge(0,s(x))
constraint: ge(s(x),0) >= ge(x,0)
constraint: ge(s(x),s(y)) >= ge(x,y)
constraint: minus(0,0) >= 0
constraint: minus(0,s(x)) >= minus(0,x)
constraint: minus(s(x),0) >= s(minus(x,0))
constraint: minus(s(x),s(y)) >= minus(x,y)
constraint: plus(0,0) >= 0
constraint: plus(0,s(x)) >= s(plus(0,x))
constraint: plus(s(x),y) >= s(plus(x,y))
constraint: ify(true,x,y) >= if(ge(x,y),x,y)
constraint: ify(false,x,y) >= divByZeroError
constraint: div(plus(x,y),z) >= plus(div(x,z),div(y,z))
constraint: div(x,y) >= ify(ge(y,s(0)),x,y)
constraint: if(true,x,y) >= s(div(minus(x,y),y))
constraint: if(false,x,y) >= 0
constraint: Marked_div(plus(x,y),z) >= Marked_div(x,z)
constraint: Marked_div(plus(x,y),z) >= Marked_div(y,z)
constraint: Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y)
constraint: Marked_if(true,x,y) >= Marked_div(minus(x,y),y)
constraint: Marked_ify(true,x,y) >= Marked_if(ge(x,y),x,y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ge(0,0) >= true ;
  ge(0,s(0)) >= false ;
  ge(0,s(s(x))) >= ge(0,s(x)) ;
  ge(s(x),0) >= ge(x,0) ;
  ge(s(x),s(y)) >= ge(x,y) ;
  minus(0,0) >= 0 ;
  minus(0,s(x)) >= minus(0,x) ;
  minus(s(x),0) >= s(minus(x,0)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  plus(0,0) >= 0 ;
  plus(0,s(x)) >= s(plus(0,x)) ;
  plus(s(x),y) >= s(plus(x,y)) ;
  ify(true,x,y) >= if(ge(x,y),x,y) ;
  ify(false,x,y) >= divByZeroError ;
  div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ;
  div(x,y) >= ify(ge(y,s(0)),x,y) ;
  if(true,x,y) >= s(div(minus(x,y),y)) ;
  if(false,x,y) >= 0 ;
  Marked_minus(s(x),s(y)) >= Marked_minus(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_minus(s(x),s(y)) > Marked_minus(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 timeout reached
=== 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 51.313925 seconds (real time)
Cime Exit Status: 0