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

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


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(s(x)),y) , Marked_plus(x,s(y))>
<Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,plus(y,ack(s(x),y)))>
<Marked_ack(s(x),s(y)) , Marked_plus(y,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <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,plus(y,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,plus(y,ack(s(x),y)))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,plus(y,ack(s(x),y)))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,plus(y,ack(s(x),y)))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,plus(y,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),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,plus(y,ack(s(x),y)))>
}

{  <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)> 
      --> <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
  <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)> 
     --> <Marked_plus(s(s(x)),y) , Marked_plus(x,s(y))>
  <Marked_plus(s(s(x)),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(x,s(s(y))) , Marked_plus(s(x),y)>
  <Marked_plus(s(s(x)),y) , Marked_plus(x,s(y))> 
     --> <Marked_plus(s(s(x)),y) , Marked_plus(x,s(y))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_ack -> 1

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

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  plus(s(s(x)),y) >= s(plus(x,s(y))) ;
  plus(s(0),y) >= s(y) ;
  plus(0,y) >= y ;
  plus(x,s(s(y))) >= s(plus(s(x),y)) ;
  ack(s(x),s(y)) >= ack(x,plus(y,ack(s(x),y))) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(0,y) >= s(y) ;
  Marked_plus(s(s(x)),y) > Marked_plus(x,s(y)) ;
  Marked_plus(x,s(s(y))) > Marked_plus(s(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.(13 bt (16) [3])
=== 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 2.451200 seconds (real time)
Cime Exit Status: 0