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

TRS termination of:
[1] plus(x,y) -> ifPlus(isZero(x),x,inc(y))
[2] ifPlus(true,x,y) -> p(y)
[3] ifPlus(false,x,y) -> plus(p(x),y)
[4] times(x,y) -> timesIter(0,x,y,0)
[5] timesIter(i,x,y,z) -> ifTimes(ge(i,x),i,x,y,z)
[6] ifTimes(true,i,x,y,z) -> z
[7] ifTimes(false,i,x,y,z) -> timesIter(inc(i),x,y,plus(z,y))
[8] isZero(0) -> true
[9] isZero(s(0)) -> false
[10] isZero(s(s(x))) -> isZero(s(x))
[11] inc(0) -> s(0)
[12] inc(s(x)) -> s(inc(x))
[13] inc(x) -> s(x)
[14] p(0) -> 0
[15] p(s(x)) -> x
[16] p(s(s(x))) -> s(p(s(x)))
[17] ge(x,0) -> true
[18] ge(0,s(y)) -> false
[19] ge(s(x),s(y)) -> ge(x,y)
[20] f0(0,y,x) -> f1(x,y,x)
[21] f1(x,y,z) -> f2(x,y,z)
[22] f2(x,1,z) -> f0(x,z,z)
[23] f0(x,y,z) -> d
[24] f1(x,y,z) -> c


Sub problem: 
guided: 

DP termination of:
<Marked_plus(x,y) , Marked_ifPlus(isZero(x),x,inc(y))>
<Marked_plus(x,y) , Marked_isZero(x)>
<Marked_plus(x,y) , Marked_inc(y)>
<Marked_ifPlus(true,x,y) , Marked_p(y)>
<Marked_ifPlus(false,x,y) , Marked_plus(p(x),y)>
<Marked_ifPlus(false,x,y) , Marked_p(x)>
<Marked_times(x,y) , Marked_timesIter(0,x,y,0)>
<Marked_timesIter(i,x,y,z) , Marked_ifTimes(ge(i,x),i,x,y,z)>
<Marked_timesIter(i,x,y,z) , Marked_ge(i,x)>
<Marked_ifTimes(false,i,x,y,z) , Marked_timesIter(inc(i),x,y,plus(z,y))>
<Marked_ifTimes(false,i,x,y,z) , Marked_inc(i)>
<Marked_ifTimes(false,i,x,y,z) , Marked_plus(z,y)>
<Marked_isZero(s(s(x))) , Marked_isZero(s(x))>
<Marked_inc(s(x)) , Marked_inc(x)>
<Marked_p(s(s(x))) , Marked_p(s(x))>
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
<Marked_f0(0,y,x) , Marked_f1(x,y,x)>
<Marked_f1(x,y,z) , Marked_f2(x,y,z)>
<Marked_f2(x,1,z) , Marked_f0(x,z,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_ifTimes(false,i,x,y,z) , Marked_timesIter(inc(i),x,y,plus(z,y))> 
      --> <Marked_timesIter(i,x,y,z) , Marked_ifTimes(ge(i,x),i,x,y,z)>
  <Marked_timesIter(i,x,y,z) , Marked_ifTimes(ge(i,x),i,x,y,z)> 
     --> <Marked_ifTimes(false,i,x,y,z) , Marked_timesIter(inc(i),x,y,
                                           plus(z,y))>
}

{  <Marked_ifPlus(false,x,y) , Marked_plus(p(x),y)> 
      --> <Marked_plus(x,y) , Marked_ifPlus(isZero(x),x,inc(y))>
  <Marked_plus(x,y) , Marked_ifPlus(isZero(x),x,inc(y))> 
     --> <Marked_ifPlus(false,x,y) , Marked_plus(p(x),y)>
}

{  <Marked_isZero(s(s(x))) , Marked_isZero(s(x))> 
      --> <Marked_isZero(s(s(x))) , Marked_isZero(s(x))>
}

{  <Marked_inc(s(x)) , Marked_inc(x)> --> <Marked_inc(s(x)) , Marked_inc(x)>
}

{  <Marked_p(s(s(x))) , Marked_p(s(x))> 
      --> <Marked_p(s(s(x))) , Marked_p(s(x))>
}

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

{  <Marked_f2(x,1,z) , Marked_f0(x,z,z)> 
      --> <Marked_f0(0,y,x) , Marked_f1(x,y,x)>
  <Marked_f1(x,y,z) , Marked_f2(x,y,z)> 
     --> <Marked_f2(x,1,z) , Marked_f0(x,z,z)>
  <Marked_f0(0,y,x) , Marked_f1(x,y,x)> 
     --> <Marked_f1(x,y,z) , Marked_f2(x,y,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ifPlus(true,x,y) >= p(y) ;
  ifPlus(false,x,y) >= plus(p(x),y) ;
  isZero(0) >= true ;
  isZero(s(0)) >= false ;
  isZero(s(s(x))) >= isZero(s(x)) ;
  inc(0) >= s(0) ;
  inc(s(x)) >= s(inc(x)) ;
  inc(x) >= s(x) ;
  plus(x,y) >= ifPlus(isZero(x),x,inc(y)) ;
  p(0) >= 0 ;
  p(s(s(x))) >= s(p(s(x))) ;
  p(s(x)) >= x ;
  timesIter(i,x,y,z) >= ifTimes(ge(i,x),i,x,y,z) ;
  times(x,y) >= timesIter(0,x,y,0) ;
  ifTimes(true,i,x,y,z) >= z ;
  ifTimes(false,i,x,y,z) >= timesIter(inc(i),x,y,plus(z,y)) ;
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  f1(x,y,z) >= f2(x,y,z) ;
  f1(x,y,z) >= c ;
  f0(0,y,x) >= f1(x,y,x) ;
  f0(x,y,z) >= d ;
  f2(x,1,z) >= f0(x,z,z) ;
  Marked_ifTimes(false,i,x,y,z) >= Marked_timesIter(inc(i),x,y,plus(z,y)) ;
  Marked_timesIter(i,x,y,z) >= Marked_ifTimes(ge(i,x),i,x,y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_ifTimes(false,i,x,y,z) > Marked_timesIter(inc(i),x,y,plus(z,y)) ;
 }
{
  Marked_timesIter(i,x,y,z) > Marked_ifTimes(ge(i,x),i,x,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
=== 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 ===
Time out for these parameters.
=== 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 25.916999 seconds (real time)
Cime Exit Status: 0