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

TRS termination of:
[1] even(0) -> true
[2] even(s(0)) -> false
[3] even(s(s(x))) -> even(x)
[4] half(0) -> 0
[5] half(s(s(x))) -> s(half(x))
[6] plus(0,y) -> y
[7] plus(s(x),y) -> s(plus(x,y))
[8] times(0,y) -> 0
[9] times(s(x),y) -> if_times(even(s(x)),s(x),y)
[10] if_times(true,s(x),y) -> plus(times(half(s(x)),y),times(half(s(x)),y))
[11] if_times(false,s(x),y) -> plus(y,times(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_even(s(s(x))) , Marked_even(x)>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)>
<Marked_times(s(x),y) , Marked_even(s(x))>
<Marked_if_times(true,s(x),y) , Marked_plus(times(half(s(x)),y),
                                 times(half(s(x)),y))>
<Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)>
<Marked_if_times(true,s(x),y) , Marked_half(s(x))>
<Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)>
<Marked_if_times(true,s(x),y) , Marked_half(s(x))>
<Marked_if_times(false,s(x),y) , Marked_plus(y,times(x,y))>
<Marked_if_times(false,s(x),y) , Marked_times(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if_times(false,s(x),y) , Marked_times(x,y)> 
      --> <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)>
  <Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)> 
     --> <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)>
  <Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)> 
     --> <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)>
  <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)> 
     --> <Marked_if_times(false,s(x),y) , Marked_times(x,y)>
  <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)> 
     --> <Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)>
  <Marked_times(s(x),y) , Marked_if_times(even(s(x)),s(x),y)> 
     --> <Marked_if_times(true,s(x),y) , Marked_times(half(s(x)),y)>
}

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

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

{  <Marked_even(s(s(x))) , Marked_even(x)> 
      --> <Marked_even(s(s(x))) , Marked_even(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  even(0) >= true ;
  even(s(0)) >= false ;
  even(s(s(x))) >= even(x) ;
  half(0) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(x,y)) ;
  times(0,y) >= 0 ;
  times(s(x),y) >= if_times(even(s(x)),s(x),y) ;
  if_times(true,s(x),y) >= plus(times(half(s(x)),y),times(half(s(x)),y)) ;
  if_times(false,s(x),y) >= plus(y,times(x,y)) ;
  Marked_if_times(true,s(x),y) >= Marked_times(half(s(x)),y) ;
  Marked_if_times(false,s(x),y) >= Marked_times(x,y) ;
  Marked_times(s(x),y) >= Marked_if_times(even(s(x)),s(x),y) ;
 }
 + Disjunctions:{ 
{
  Marked_if_times(true,s(x),y) > Marked_times(half(s(x)),y) ;
 }
{
  Marked_if_times(false,s(x),y) > Marked_times(x,y) ;
 }
{
  Marked_times(s(x),y) > Marked_if_times(even(s(x)),s(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 : 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 3.448108 seconds (real time)
Cime Exit Status: 0