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

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


Sub problem: 
guided: 

DP termination of:
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
<Marked_f(s(x),y) , Marked_f(x,s(x))>
<Marked_f(x,s(y)) , Marked_f(y,x)>
<Marked_f(x,y) , Marked_ack(x,y)>
<Marked_ack(s(x),y) , Marked_f(x,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),y) >= f(x,x) ;
  ack(0,y) >= s(y) ;
  f(s(x),y) >= f(x,s(x)) ;
  f(x,s(y)) >= f(y,x) ;
  f(x,y) >= ack(x,y) ;
  Marked_ack(s(x),s(y)) > Marked_ack(s(x),y) ;
  Marked_ack(s(x),s(y)) > Marked_ack(x,ack(s(x),y)) ;
  Marked_ack(s(x),0) > Marked_ack(x,s(0)) ;
  Marked_ack(s(x),y) >= Marked_f(x,x) ;
  Marked_f(s(x),y) > Marked_f(x,s(x)) ;
  Marked_f(x,s(y)) > Marked_f(y,x) ;
  Marked_f(x,y) > Marked_ack(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.(27 bt (28) [10])
=== 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 0.928538 seconds (real time)
Cime Exit Status: 0