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

TRS termination of:
[1] check(0) -> zero
[2] check(s(0)) -> odd
[3] check(s(s(0))) -> even
[4] check(s(s(s(x)))) -> check(s(x))
[5] half(0) -> 0
[6] half(s(0)) -> 0
[7] half(s(s(x))) -> s(half(x))
[8] plus(0,y) -> y
[9] plus(s(x),y) -> s(plus(x,y))
[10] times(x,y) -> timesIter(x,y,0)
[11] timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
[12] p(s(x)) -> x
[13] p(0) -> 0
[14] if(zero,x,y,z,u) -> z
[15] if(odd,x,y,z,u) -> timesIter(p(x),y,u)
[16] if(even,x,y,z,u) ->
 plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))


Sub problem: 
guided: 

DP termination of:
<Marked_check(s(s(s(x)))) , Marked_check(s(x))>
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_plus(s(x),y) , Marked_plus(x,y)>
<Marked_times(x,y) , Marked_timesIter(x,y,0)>
<Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))>
<Marked_timesIter(x,y,z) , Marked_check(x)>
<Marked_timesIter(x,y,z) , Marked_plus(z,y)>
<Marked_if(odd,x,y,z,u) , Marked_timesIter(p(x),y,u)>
<Marked_if(odd,x,y,z,u) , Marked_p(x)>
<Marked_if(even,x,y,z,u) , Marked_plus(timesIter(half(x),y,half(z)),
                            timesIter(half(x),y,half(s(z))))>
<Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(z))>
<Marked_if(even,x,y,z,u) , Marked_half(x)>
<Marked_if(even,x,y,z,u) , Marked_half(z)>
<Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(s(z)))>
<Marked_if(even,x,y,z,u) , Marked_half(x)>
<Marked_if(even,x,y,z,u) , Marked_half(s(z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(s(z)))> 
      --> <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))>
  <Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(z))> 
     --> <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))>
  <Marked_if(odd,x,y,z,u) , Marked_timesIter(p(x),y,u)> 
     --> <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))>
  <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))> 
     --> <Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(s(z)))>
  <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))> 
     --> <Marked_if(even,x,y,z,u) , Marked_timesIter(half(x),y,half(z))>
  <Marked_timesIter(x,y,z) , Marked_if(check(x),x,y,z,plus(z,y))> 
     --> <Marked_if(odd,x,y,z,u) , Marked_timesIter(p(x),y,u)>
}

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

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

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  check(0) >= zero ;
  check(s(0)) >= odd ;
  check(s(s(0))) >= even ;
  check(s(s(s(x)))) >= check(s(x)) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(x,y)) ;
  timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ;
  times(x,y) >= timesIter(x,y,0) ;
  if(zero,x,y,z,u) >= z ;
  if(odd,x,y,z,u) >= timesIter(p(x),y,u) ;
  if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)),
                       timesIter(half(x),y,half(s(z)))) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_if(odd,x,y,z,u) >= Marked_timesIter(p(x),y,u) ;
  Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ;
  Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(z)) ;
  Marked_timesIter(x,y,z) >= Marked_if(check(x),x,y,z,plus(z,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ;
 }
{
  Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(s(z))) ;
 }
{
  Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ;
 }
{
  Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,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 : 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 (Simple graph)
Found the following constraints:
{
  check(0) >= zero ;
  check(s(0)) >= odd ;
  check(s(s(0))) >= even ;
  check(s(s(s(x)))) >= check(s(x)) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(x,y)) ;
  timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ;
  times(x,y) >= timesIter(x,y,0) ;
  if(zero,x,y,z,u) >= z ;
  if(odd,x,y,z,u) >= timesIter(p(x),y,u) ;
  if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)),
                       timesIter(half(x),y,half(s(z)))) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ;
  Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ;
  Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ;
  Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,y)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  check(0) >= zero ;
  check(s(0)) >= odd ;
  check(s(s(0))) >= even ;
  check(s(s(s(x)))) >= check(s(x)) ;
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  plus(0,y) >= y ;
  plus(s(x),y) >= s(plus(x,y)) ;
  timesIter(x,y,z) >= if(check(x),x,y,z,plus(z,y)) ;
  times(x,y) >= timesIter(x,y,0) ;
  if(zero,x,y,z,u) >= z ;
  if(odd,x,y,z,u) >= timesIter(p(x),y,u) ;
  if(even,x,y,z,u) >= plus(timesIter(half(x),y,half(z)),
                       timesIter(half(x),y,half(s(z)))) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_if(odd,x,y,z,u) > Marked_timesIter(p(x),y,u) ;
  Marked_if(even,x,y,z,u) >= Marked_timesIter(half(x),y,half(s(z))) ;
  Marked_if(even,x,y,z,u) > Marked_timesIter(half(x),y,half(z)) ;
  Marked_timesIter(x,y,z) > Marked_if(check(x),x,y,z,plus(z,y)) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(66608 bt (67788) [4984])
=== 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 17.279973 seconds (real time)
Cime Exit Status: 0