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

TRS termination of:
[1] f(s(x)) -> f(id_inc(c(x,x)))
[2] f(c(s(x),y)) -> g(c(x,y))
[3] g(c(s(x),y)) -> g(c(y,x))
[4] g(c(x,s(y))) -> g(c(y,x))
[5] g(c(x,x)) -> f(x)
[6] id_inc(c(x,y)) -> c(id_inc(x),id_inc(y))
[7] id_inc(s(x)) -> s(id_inc(x))
[8] id_inc(0) -> 0
[9] id_inc(0) -> s(0)


Sub problem: 
guided: 

DP termination of:
<Marked_f(s(x)) , Marked_f(id_inc(c(x,x)))>
<Marked_f(s(x)) , Marked_id_inc(c(x,x))>
<Marked_f(c(s(x),y)) , Marked_g(c(x,y))>
<Marked_g(c(s(x),y)) , Marked_g(c(y,x))>
<Marked_g(c(x,s(y))) , Marked_g(c(y,x))>
<Marked_g(c(x,x)) , Marked_f(x)>
<Marked_id_inc(c(x,y)) , Marked_id_inc(x)>
<Marked_id_inc(c(x,y)) , Marked_id_inc(y)>
<Marked_id_inc(s(x)) , Marked_id_inc(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(c(x,x)) , Marked_f(x)> 
      --> <Marked_f(c(s(x),y)) , Marked_g(c(x,y))>
  <Marked_g(c(x,x)) , Marked_f(x)> 
     --> <Marked_f(s(x)) , Marked_f(id_inc(c(x,x)))>
  <Marked_g(c(x,s(y))) , Marked_g(c(y,x))> --> <Marked_g(c(x,x)) , Marked_f(x)>
  <Marked_g(c(x,s(y))) , Marked_g(c(y,x))> 
     --> <Marked_g(c(x,s(y))) , Marked_g(c(y,x))>
  <Marked_g(c(x,s(y))) , Marked_g(c(y,x))> 
     --> <Marked_g(c(s(x),y)) , Marked_g(c(y,x))>
  <Marked_g(c(s(x),y)) , Marked_g(c(y,x))> --> <Marked_g(c(x,x)) , Marked_f(x)>
  <Marked_g(c(s(x),y)) , Marked_g(c(y,x))> 
     --> <Marked_g(c(x,s(y))) , Marked_g(c(y,x))>
  <Marked_g(c(s(x),y)) , Marked_g(c(y,x))> 
     --> <Marked_g(c(s(x),y)) , Marked_g(c(y,x))>
  <Marked_f(c(s(x),y)) , Marked_g(c(x,y))> --> <Marked_g(c(x,x)) , Marked_f(x)>
  <Marked_f(c(s(x),y)) , Marked_g(c(x,y))> 
     --> <Marked_g(c(x,s(y))) , Marked_g(c(y,x))>
  <Marked_f(c(s(x),y)) , Marked_g(c(x,y))> 
     --> <Marked_g(c(s(x),y)) , Marked_g(c(y,x))>
  <Marked_f(s(x)) , Marked_f(id_inc(c(x,x)))> 
     --> <Marked_f(c(s(x),y)) , Marked_g(c(x,y))>
  <Marked_f(s(x)) , Marked_f(id_inc(c(x,x)))> 
     --> <Marked_f(s(x)) , Marked_f(id_inc(c(x,x)))>
}

{  <Marked_id_inc(s(x)) , Marked_id_inc(x)> 
      --> <Marked_id_inc(s(x)) , Marked_id_inc(x)>
  <Marked_id_inc(s(x)) , Marked_id_inc(x)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(y)>
  <Marked_id_inc(s(x)) , Marked_id_inc(x)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(x)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(y)> 
     --> <Marked_id_inc(s(x)) , Marked_id_inc(x)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(y)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(y)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(y)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(x)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(x)> 
     --> <Marked_id_inc(s(x)) , Marked_id_inc(x)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(x)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(y)>
  <Marked_id_inc(c(x,y)) , Marked_id_inc(x)> 
     --> <Marked_id_inc(c(x,y)) , Marked_id_inc(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(c(s(x),y)) >= g(c(x,y)) ;
  f(s(x)) >= f(id_inc(c(x,x))) ;
  id_inc(c(x,y)) >= c(id_inc(x),id_inc(y)) ;
  id_inc(s(x)) >= s(id_inc(x)) ;
  id_inc(0) >= s(0) ;
  id_inc(0) >= 0 ;
  g(c(s(x),y)) >= g(c(y,x)) ;
  g(c(x,s(y))) >= g(c(y,x)) ;
  g(c(x,x)) >= f(x) ;
  Marked_g(c(s(x),y)) >= Marked_g(c(y,x)) ;
  Marked_g(c(x,s(y))) >= Marked_g(c(y,x)) ;
  Marked_g(c(x,x)) >= Marked_f(x) ;
  Marked_f(c(s(x),y)) >= Marked_g(c(x,y)) ;
  Marked_f(s(x)) >= Marked_f(id_inc(c(x,x))) ;
 }
 + Disjunctions:{ 
{
  Marked_g(c(s(x),y)) > Marked_g(c(y,x)) ;
 }
{
  Marked_g(c(x,s(y))) > Marked_g(c(y,x)) ;
 }
{
  Marked_g(c(x,x)) > Marked_f(x) ;
 }
{
  Marked_f(c(s(x),y)) > Marked_g(c(x,y)) ;
 }
{
  Marked_f(s(x)) > Marked_f(id_inc(c(x,x))) ;
 }
 } 
=== 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 : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== 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 2.639567 seconds (real time)
Cime Exit Status: 0