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

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


Sub problem: 
guided: 

DP termination of:
<Marked_-(s(x),s(y)) , Marked_-(x,y)>
<Marked_min(s(x),s(y)) , Marked_min(x,y)>
<Marked_twice(s(x)) , Marked_twice(x)>
<Marked_f(s(x),s(y)) , Marked_f(-(y,min(x,y)),s(twice(min(x,y))))>
<Marked_f(s(x),s(y)) , Marked_-(y,min(x,y))>
<Marked_f(s(x),s(y)) , Marked_min(x,y)>
<Marked_f(s(x),s(y)) , Marked_twice(min(x,y))>
<Marked_f(s(x),s(y)) , Marked_min(x,y)>
<Marked_f(s(x),s(y)) , Marked_f(-(x,min(x,y)),s(twice(min(x,y))))>
<Marked_f(s(x),s(y)) , Marked_-(x,min(x,y))>
<Marked_f(s(x),s(y)) , Marked_min(x,y)>
<Marked_f(s(x),s(y)) , Marked_twice(min(x,y))>
<Marked_f(s(x),s(y)) , Marked_min(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_f(s(x),s(y)) , Marked_f(-(x,min(x,y)),s(twice(min(x,y))))> 
      --> <Marked_f(s(x),s(y)) , Marked_f(-(x,min(x,y)),s(twice(min(x,y))))>
  <Marked_f(s(x),s(y)) , Marked_f(-(x,min(x,y)),s(twice(min(x,y))))> 
     --> <Marked_f(s(x),s(y)) , Marked_f(-(y,min(x,y)),s(twice(min(x,y))))>
  <Marked_f(s(x),s(y)) , Marked_f(-(y,min(x,y)),s(twice(min(x,y))))> 
     --> <Marked_f(s(x),s(y)) , Marked_f(-(x,min(x,y)),s(twice(min(x,y))))>
  <Marked_f(s(x),s(y)) , Marked_f(-(y,min(x,y)),s(twice(min(x,y))))> 
     --> <Marked_f(s(x),s(y)) , Marked_f(-(y,min(x,y)),s(twice(min(x,y))))>
}

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

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

{  <Marked_min(s(x),s(y)) , Marked_min(x,y)> 
      --> <Marked_min(s(x),s(y)) , Marked_min(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  min(0,y) >= 0 ;
  min(s(x),s(y)) >= s(min(x,y)) ;
  min(x,0) >= 0 ;
  twice(0) >= 0 ;
  twice(s(x)) >= s(s(twice(x))) ;
  f(s(x),s(y)) >= f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  f(s(x),s(y)) >= f(-(y,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) >= Marked_f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) >= Marked_f(-(y,min(x,y)),s(twice(min(x,y)))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(x),s(y)) > Marked_f(-(x,min(x,y)),s(twice(min(x,y)))) ;
 }
{
  Marked_f(s(x),s(y)) > Marked_f(-(y,min(x,y)),s(twice(min(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 : 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:
{
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  min(0,y) >= 0 ;
  min(s(x),s(y)) >= s(min(x,y)) ;
  min(x,0) >= 0 ;
  twice(0) >= 0 ;
  twice(s(x)) >= s(s(twice(x))) ;
  f(s(x),s(y)) >= f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  f(s(x),s(y)) >= f(-(y,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) > Marked_f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) > Marked_f(-(y,min(x,y)),s(twice(min(x,y)))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  -(s(x),s(y)) >= -(x,y) ;
  -(x,0) >= x ;
  min(0,y) >= 0 ;
  min(s(x),s(y)) >= s(min(x,y)) ;
  min(x,0) >= 0 ;
  twice(0) >= 0 ;
  twice(s(x)) >= s(s(twice(x))) ;
  f(s(x),s(y)) >= f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  f(s(x),s(y)) >= f(-(y,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) > Marked_f(-(x,min(x,y)),s(twice(min(x,y)))) ;
  Marked_f(s(x),s(y)) > Marked_f(-(y,min(x,y)),s(twice(min(x,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.(340 bt (351) [48])
=== 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 20.124033 seconds (real time)
Cime Exit Status: 0