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

TRS termination of:
[1] f(x,f(s(s(y)),f(z,w))) -> f(s(x),f(y,f(s(z),w)))
[2] L(f(s(s(y)),f(z,w))) -> L(f(s(0),f(y,f(s(z),w))))
[3] f(x,f(s(s(y)),nil)) -> f(s(x),f(y,f(s(0),nil)))


Sub problem: 
guided: 

DP termination of:
<Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
<Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
<Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
<Marked_L(f(s(s(y)),f(z,w))) , Marked_L(f(s(0),f(y,f(s(z),w))))>
<Marked_L(f(s(s(y)),f(z,w))) , Marked_f(s(0),f(y,f(s(z),w)))>
<Marked_L(f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
<Marked_L(f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
<Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
<Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
<Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(0),nil)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_L(f(s(s(y)),f(z,w))) , Marked_L(f(s(0),f(y,f(s(z),w))))> 
      --> <Marked_L(f(s(s(y)),f(z,w))) , Marked_L(f(s(0),f(y,f(s(z),w))))>
}

{  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))> 
      --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
  <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(y,f(s(0),nil))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))> 
     --> <Marked_f(x,f(s(s(y)),nil)) , Marked_f(s(x),f(y,f(s(0),nil)))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(z),w)>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(y,f(s(z),w))>
  <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))> 
     --> <Marked_f(x,f(s(s(y)),f(z,w))) , Marked_f(s(x),f(y,f(s(z),w)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(x,f(s(s(y)),f(z,w))) >= f(s(x),f(y,f(s(z),w))) ;
  f(x,f(s(s(y)),nil)) >= f(s(x),f(y,f(s(0),nil))) ;
  L(f(s(s(y)),f(z,w))) >= L(f(s(0),f(y,f(s(z),w)))) ;
  Marked_L(f(s(s(y)),f(z,w))) >= Marked_L(f(s(0),f(y,f(s(z),w)))) ;
 }
 + Disjunctions:{ 
{
  Marked_L(f(s(s(y)),f(z,w))) > Marked_L(f(s(0),f(y,f(s(z),w)))) ;
 }
 } 
=== 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 : 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 timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  f(x,f(s(s(y)),f(z,w))) >= f(s(x),f(y,f(s(z),w))) ;
  f(x,f(s(s(y)),nil)) >= f(s(x),f(y,f(s(0),nil))) ;
  L(f(s(s(y)),f(z,w))) >= L(f(s(0),f(y,f(s(z),w)))) ;
  Marked_L(f(s(s(y)),f(z,w))) > Marked_L(f(s(0),f(y,f(s(z),w)))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  f(x,f(s(s(y)),f(z,w))) >= f(s(x),f(y,f(s(z),w))) ;
  f(x,f(s(s(y)),nil)) >= f(s(x),f(y,f(s(0),nil))) ;
  L(f(s(s(y)),f(z,w))) >= L(f(s(0),f(y,f(s(z),w)))) ;
  Marked_L(f(s(s(y)),f(z,w))) > Marked_L(f(s(0),f(y,f(s(z),w)))) ;
 }
 + 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.(46 bt (6) [45])
=== 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 timeout reached
=== 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 111.935037 seconds (real time)
Cime Exit Status: 0