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

TRS termination of:
[1] minus(x,0) -> x
[2] minus(0,y) -> 0
[3] minus(s(x),s(y)) -> minus(p(s(x)),p(s(y)))
[4] minus(x,plus(y,z)) -> minus(minus(x,y),z)
[5] p(s(s(x))) -> s(p(s(x)))
[6] p(0) -> s(s(0))
[7] div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
[8] div(plus(x,y),z) -> plus(div(x,z),div(y,z))
[9] plus(0,y) -> y
[10] plus(s(x),y) -> s(plus(y,minus(s(x),s(0))))


Sub problem: 
guided: 

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

{  <Marked_plus(s(x),y) , Marked_plus(y,minus(s(x),s(0)))> 
      --> <Marked_plus(s(x),y) , Marked_plus(y,minus(s(x),s(0)))>
}

{  <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)> 
      --> <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)>
  <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)> 
     --> <Marked_minus(x,plus(y,z)) , Marked_minus(minus(x,y),z)>
  <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)> 
     --> <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(y)))>
  <Marked_minus(x,plus(y,z)) , Marked_minus(minus(x,y),z)> 
     --> <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)>
  <Marked_minus(x,plus(y,z)) , 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(minus(x,y),z)> 
     --> <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(y)))>
  <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(y)))> 
     --> <Marked_minus(x,plus(y,z)) , Marked_minus(x,y)>
  <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(y)))> 
     --> <Marked_minus(x,plus(y,z)) , Marked_minus(minus(x,y),z)>
  <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(y)))> 
     --> <Marked_minus(s(x),s(y)) , Marked_minus(p(s(x)),p(s(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:
{
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ;
  minus(x,0) >= x ;
  minus(x,plus(y,z)) >= minus(minus(x,y),z) ;
  p(0) >= s(s(0)) ;
  p(s(s(x))) >= s(p(s(x))) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ;
  div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ;
  div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ;
  Marked_div(s(x),s(y)) >= Marked_div(minus(x,y),s(y)) ;
  Marked_div(plus(x,y),z) >= Marked_div(x,z) ;
  Marked_div(plus(x,y),z) >= Marked_div(y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_div(s(x),s(y)) > Marked_div(minus(x,y),s(y)) ;
 }
{
  Marked_div(plus(x,y),z) > Marked_div(x,z) ;
 }
{
  Marked_div(plus(x,y),z) > Marked_div(y,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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: minus(0,y) >= 0
constraint: minus(s(x),s(y)) >= minus(p(s(x)),p(s(y)))
constraint: minus(x,0) >= x
constraint: minus(x,plus(y,z)) >= minus(minus(x,y),z)
constraint: p(0) >= s(s(0))
constraint: p(s(s(x))) >= s(p(s(x)))
constraint: plus(0,y) >= y
constraint: plus(s(x),y) >= s(plus(y,minus(s(x),s(0))))
constraint: div(s(x),s(y)) >= s(div(minus(x,y),s(y)))
constraint: div(plus(x,y),z) >= plus(div(x,z),div(y,z))
constraint: Marked_div(s(x),s(y)) >= Marked_div(minus(x,y),s(y))
constraint: Marked_div(plus(x,y),z) >= Marked_div(x,z)
constraint: Marked_div(plus(x,y),z) >= Marked_div(y,z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(p(s(x)),p(s(y))) ;
  minus(x,0) >= x ;
  minus(x,plus(y,z)) >= minus(minus(x,y),z) ;
  p(0) >= s(s(0)) ;
  p(s(s(x))) >= s(p(s(x))) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(y,minus(s(x),s(0)))) ;
  div(s(x),s(y)) >= s(div(minus(x,y),s(y))) ;
  div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ;
  Marked_plus(s(x),y) >= Marked_plus(y,minus(s(x),s(0))) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(s(x),y) > Marked_plus(y,minus(s(x),s(0))) ;
 }
 } 
=== 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 2.687409 seconds (real time)
Cime Exit Status: 0