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

TRS termination of:
[1] tower(x) -> f(a,x,s(0))
[2] f(a,0,y) -> y
[3] f(a,s(x),y) -> f(b,y,s(x))
[4] f(b,y,x) -> f(a,half(x),exp(y))
[5] exp(0) -> s(0)
[6] exp(s(x)) -> double(exp(x))
[7] double(0) -> 0
[8] double(s(x)) -> s(s(double(x)))
[9] half(0) -> double(0)
[10] half(s(0)) -> half(0)
[11] half(s(s(x))) -> s(half(x))


Sub problem: 
guided: 

DP termination of:
<Marked_tower(x) , Marked_f(a,x,s(0))>
<Marked_f(a,s(x),y) , Marked_f(b,y,s(x))>
<Marked_f(b,y,x) , Marked_f(a,half(x),exp(y))>
<Marked_f(b,y,x) , Marked_half(x)>
<Marked_f(b,y,x) , Marked_exp(y)>
<Marked_exp(s(x)) , Marked_double(exp(x))>
<Marked_exp(s(x)) , Marked_exp(x)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_half(0) , Marked_double(0)>
<Marked_half(s(0)) , Marked_half(0)>
<Marked_half(s(s(x))) , Marked_half(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_f(b,y,x) , Marked_f(a,half(x),exp(y))> 
      --> <Marked_f(a,s(x),y) , Marked_f(b,y,s(x))>
  <Marked_f(a,s(x),y) , Marked_f(b,y,s(x))> 
     --> <Marked_f(b,y,x) , Marked_f(a,half(x),exp(y))>
}

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

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

{  <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:
{
  f(a,s(x),y) >= f(b,y,s(x)) ;
  f(a,0,y) >= y ;
  f(b,y,x) >= f(a,half(x),exp(y)) ;
  tower(x) >= f(a,x,s(0)) ;
  half(s(s(x))) >= s(half(x)) ;
  half(s(0)) >= half(0) ;
  half(0) >= double(0) ;
  exp(s(x)) >= double(exp(x)) ;
  exp(0) >= s(0) ;
  double(s(x)) >= s(s(double(x))) ;
  double(0) >= 0 ;
  Marked_f(a,s(x),y) >= Marked_f(b,y,s(x)) ;
  Marked_f(b,y,x) >= Marked_f(a,half(x),exp(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(a,s(x),y) > Marked_f(b,y,s(x)) ;
 }
{
  Marked_f(b,y,x) > Marked_f(a,half(x),exp(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 (Simple graph)
Found the following constraints:
{
  f(a,s(x),y) >= f(b,y,s(x)) ;
  f(a,0,y) >= y ;
  f(b,y,x) >= f(a,half(x),exp(y)) ;
  tower(x) >= f(a,x,s(0)) ;
  half(s(s(x))) >= s(half(x)) ;
  half(s(0)) >= half(0) ;
  half(0) >= double(0) ;
  exp(s(x)) >= double(exp(x)) ;
  exp(0) >= s(0) ;
  double(s(x)) >= s(s(double(x))) ;
  double(0) >= 0 ;
  Marked_f(a,s(x),y) > Marked_f(b,y,s(x)) ;
  Marked_f(b,y,x) >= Marked_f(a,half(x),exp(y)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  f(a,s(x),y) >= f(b,y,s(x)) ;
  f(a,0,y) >= y ;
  f(b,y,x) >= f(a,half(x),exp(y)) ;
  tower(x) >= f(a,x,s(0)) ;
  half(s(s(x))) >= s(half(x)) ;
  half(s(0)) >= half(0) ;
  half(0) >= double(0) ;
  exp(s(x)) >= double(exp(x)) ;
  exp(0) >= s(0) ;
  double(s(x)) >= s(s(double(x))) ;
  double(0) >= 0 ;
  Marked_f(a,s(x),y) > Marked_f(b,y,s(x)) ;
  Marked_f(b,y,x) >= Marked_f(a,half(x),exp(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.(1087 bt (933) [207])
=== 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 1.557554 seconds (real time)
Cime Exit Status: 0