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

TRS termination of:
[1] inc(s(x)) -> s(inc(x))
[2] inc(0) -> s(0)
[3] plus(x,y) -> ifPlus(eq(x,0),minus(x,s(0)),x,inc(x))
[4] ifPlus(false,x,y,z) -> plus(x,z)
[5] ifPlus(true,x,y,z) -> y
[6] minus(s(x),s(y)) -> minus(x,y)
[7] minus(0,x) -> 0
[8] minus(x,0) -> x
[9] minus(x,x) -> 0
[10] eq(s(x),s(y)) -> eq(x,y)
[11] eq(0,s(x)) -> false
[12] eq(s(x),0) -> false
[13] eq(0,0) -> true
[14] eq(x,x) -> true
[15] times(x,y) -> timesIter(x,y,0)
[16] timesIter(x,y,z) -> ifTimes(eq(x,0),minus(x,s(0)),y,z,plus(y,z))
[17] ifTimes(true,x,y,z,u) -> z
[18] ifTimes(false,x,y,z,u) -> timesIter(x,y,u)
[19] f -> g
[20] f -> h


Sub problem: 
guided: 

DP termination of:
<Marked_inc(s(x)) , Marked_inc(x)>
<Marked_plus(x,y) , Marked_ifPlus(eq(x,0),minus(x,s(0)),x,inc(x))>
<Marked_plus(x,y) , Marked_eq(x,0)>
<Marked_plus(x,y) , Marked_minus(x,s(0))>
<Marked_plus(x,y) , Marked_inc(x)>
<Marked_ifPlus(false,x,y,z) , Marked_plus(x,z)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_times(x,y) , Marked_timesIter(x,y,0)>
<Marked_timesIter(x,y,z) , Marked_ifTimes(eq(x,0),minus(x,s(0)),y,z,plus(y,z))>
<Marked_timesIter(x,y,z) , Marked_eq(x,0)>
<Marked_timesIter(x,y,z) , Marked_minus(x,s(0))>
<Marked_timesIter(x,y,z) , Marked_plus(y,z)>
<Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,u)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

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

{  <Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,u)> 
      --> <Marked_timesIter(x,y,z) , Marked_ifTimes(eq(x,0),minus(x,s(0)),
                                      y,z,plus(y,z))>
  <Marked_timesIter(x,y,z) , Marked_ifTimes(eq(x,0),minus(x,s(0)),y,z,
                              plus(y,z))> 
     --> <Marked_ifTimes(false,x,y,z,u) , Marked_timesIter(x,y,u)>
}

{  <Marked_ifPlus(false,x,y,z) , Marked_plus(x,z)> 
      --> <Marked_plus(x,y) , Marked_ifPlus(eq(x,0),minus(x,s(0)),x,inc(x))>
  <Marked_plus(x,y) , Marked_ifPlus(eq(x,0),minus(x,s(0)),x,inc(x))> 
     --> <Marked_ifPlus(false,x,y,z) , Marked_plus(x,z)>
}

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

{  <Marked_inc(s(x)) , Marked_inc(x)> --> <Marked_inc(s(x)) , Marked_inc(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  inc(s(x)) >= s(inc(x)) ;
  inc(0) >= s(0) ;
  ifPlus(false,x,y,z) >= plus(x,z) ;
  ifPlus(true,x,y,z) >= y ;
  eq(s(x),s(y)) >= eq(x,y) ;
  eq(s(x),0) >= false ;
  eq(0,s(x)) >= false ;
  eq(0,0) >= true ;
  eq(x,x) >= true ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(0,x) >= 0 ;
  minus(x,0) >= x ;
  minus(x,x) >= 0 ;
  plus(x,y) >= ifPlus(eq(x,0),minus(x,s(0)),x,inc(x)) ;
  timesIter(x,y,z) >= ifTimes(eq(x,0),minus(x,s(0)),y,z,plus(y,z)) ;
  times(x,y) >= timesIter(x,y,0) ;
  ifTimes(false,x,y,z,u) >= timesIter(x,y,u) ;
  ifTimes(true,x,y,z,u) >= z ;
  f >= g ;
  f >= h ;
  Marked_eq(s(x),s(y)) >= Marked_eq(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_eq(s(x),s(y)) > Marked_eq(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 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 15.004321 seconds (real time)
Cime Exit Status: 0