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

TRS termination of:
[1] half(0) -> 0
[2] half(s(0)) -> 0
[3] half(s(s(x))) -> s(half(x))
[4] inc(0) -> 0
[5] inc(s(x)) -> s(inc(x))
[6] zero(0) -> true
[7] zero(s(x)) -> false
[8] p(0) -> 0
[9] p(s(x)) -> x
[10] bits(x) -> bitIter(x,0)
[11] bitIter(x,y) -> if(zero(x),x,inc(y))
[12] if(true,x,y) -> p(y)
[13] if(false,x,y) -> bitIter(half(x),y)


Sub problem: 
guided: 

DP termination of:
<Marked_half(s(s(x))) , Marked_half(x)>
<Marked_inc(s(x)) , Marked_inc(x)>
<Marked_bits(x) , Marked_bitIter(x,0)>
<Marked_bitIter(x,y) , Marked_if(zero(x),x,inc(y))>
<Marked_bitIter(x,y) , Marked_zero(x)>
<Marked_bitIter(x,y) , Marked_inc(y)>
<Marked_if(true,x,y) , Marked_p(y)>
<Marked_if(false,x,y) , Marked_bitIter(half(x),y)>
<Marked_if(false,x,y) , Marked_half(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(false,x,y) , Marked_bitIter(half(x),y)> 
      --> <Marked_bitIter(x,y) , Marked_if(zero(x),x,inc(y))>
  <Marked_bitIter(x,y) , Marked_if(zero(x),x,inc(y))> 
     --> <Marked_if(false,x,y) , Marked_bitIter(half(x),y)>
}

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

{  <Marked_half(s(s(x))) , Marked_half(x)> 
      --> <Marked_half(s(s(x))) , Marked_half(x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  half(0) >= 0 ;
  half(s(0)) >= 0 ;
  half(s(s(x))) >= s(half(x)) ;
  inc(0) >= 0 ;
  inc(s(x)) >= s(inc(x)) ;
  zero(0) >= true ;
  zero(s(x)) >= false ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  bitIter(x,y) >= if(zero(x),x,inc(y)) ;
  bits(x) >= bitIter(x,0) ;
  if(true,x,y) >= p(y) ;
  if(false,x,y) >= bitIter(half(x),y) ;
  Marked_if(false,x,y) >= Marked_bitIter(half(x),y) ;
  Marked_bitIter(x,y) >= Marked_if(zero(x),x,inc(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,x,y) > Marked_bitIter(half(x),y) ;
 }
{
  Marked_bitIter(x,y) > Marked_if(zero(x),x,inc(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 : 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 2.084860 seconds (real time)
Cime Exit Status: 0