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

TRS termination of:
[1] f(a,f(a,f(a,f(x,b)))) -> f(f(a,f(a,f(a,x))),b)
[2] f(f(f(a,x),b),b) -> f(f(a,f(f(x,b),b)),b)


Sub problem: 
guided: 

DP termination of:
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)> 
      --> <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ;
  f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(f(x,b),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(x,b) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,x)) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,x) ;
 }
 + Disjunctions:{ 
{
  Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),b)),b) ;
 }
{
  Marked_f(f(f(a,x),b),b) > Marked_f(f(x,b),b) ;
 }
{
  Marked_f(f(f(a,x),b),b) > Marked_f(a,f(f(x,b),b)) ;
 }
{
  Marked_f(f(f(a,x),b),b) > Marked_f(x,b) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(f(a,f(a,f(a,x))),b) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(a,x))) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,x)) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,x) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b)
constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(x,b),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b))
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(x,b)
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x)))
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,x))
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,x)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
      --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
     --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)> 
     --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ;
  f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b)) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),b)),b) ;
 }
{
  Marked_f(f(f(a,x),b),b) > Marked_f(a,f(f(x,b),b)) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(f(a,f(a,f(a,x))),b) ;
 }
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(a,x))) ;
 }
 } 
=== 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 : 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b)
constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(a,f(f(x,b),b))
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x)))
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))> 
      --> <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
}

{  <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)> 
      --> <Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ;
  f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ;
  Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(a,f(a,f(a,f(x,b)))) > Marked_f(a,f(a,f(a,x))) ;
 }
 } 
=== 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 solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b)
constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(a,f(a,f(a,f(x,b)))) >= Marked_f(a,f(a,f(a,x)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b) ;
  f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b) ;
  Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b) ;
 }
 + Disjunctions:{ 
{
  Marked_f(f(f(a,x),b),b) > Marked_f(f(a,f(f(x,b),b)),b) ;
 }
 } 
=== 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 solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: f(f(f(a,x),b),b) >= f(f(a,f(f(x,b),b)),b)
constraint: f(a,f(a,f(a,f(x,b)))) >= f(f(a,f(a,f(a,x))),b)
constraint: Marked_f(f(f(a,x),b),b) >= Marked_f(f(a,f(f(x,b),b)),b)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(a,f(a,f(a,f(x,b)))) -> f(f(a,f(a,f(a,x))),b)
[2] f(f(f(a,x),b),b) -> f(f(a,f(f(x,b),b)),b)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,x))>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,x)>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(x,b),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(x,b)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1) = 1*X1 + 1*X0; 
 [ b ] () = 0; 
 [ a ] () = 1; 
 [ Marked_f ] (X0,X1) = 1*X1 + 1*X0; 
 removing <Marked_f(a,f(a,f(a,f(x,b)))),Marked_f(a,f(a,x))><Marked_f(
                                                             a,
                                                             f(a,f(a,f(x,b)))),
Marked_f(a,x)><Marked_f(f(f(a,x),b),b),Marked_f(f(x,b),b)><Marked_f(f(f(a,x),b),
                                                            b),Marked_f(x,b)>
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
<Marked_f(f(f(a,x),b),b) , Marked_f(a,f(f(x,b),b))>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ b ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_f ] (X0,X1) = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_f(f(f(a,x),b),b),Marked_f(a,f(f(x,b),b))>
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(f(a,f(a,f(a,x))),b)>
<Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(a,f(a,f(a,f(x,b)))) , Marked_f(a,f(a,f(a,x)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ f ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] ]*X1 + 
     [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ b ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0,X1) = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
{
 
DP termination of:
<Marked_f(f(f(a,x),b),b) , Marked_f(f(a,f(f(x,b),b)),b)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ f ] (X0,X1) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X1 + 
     [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ b ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 27.293653 seconds (real time)
Cime Exit Status: 0