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

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


Sub problem: 
guided: 

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

{  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
      --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)>
  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))> 
     --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ;
  c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ;
  f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(b(z,z),f(b(y,b(x,a))))) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(y,b(x,a))) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) ;
  Marked_f(c(a,b(b(z,a),y),x)) >= Marked_c(x,b(z,x),y) ;
  Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) ;
  Marked_f(c(a,b(b(z,a),y),x)) >= Marked_b(z,x) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) ;
 }
 + Disjunctions:{ 
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_f(b(b(z,z),f(b(y,b(x,a))))) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_f(b(y,b(x,a))) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(b(z,z),f(b(y,b(x,a)))) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(y,b(x,a)) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(z,z) ;
 }
{
  Marked_f(c(a,b(b(z,a),y),x)) > Marked_c(x,b(z,x),y) ;
 }
{
  Marked_f(c(a,b(b(z,a),y),x)) > Marked_f(c(x,b(z,x),y)) ;
 }
{
  Marked_f(c(a,b(b(z,a),y),x)) > Marked_b(z,x) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_c(y,z,a) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_b(b(z,c(y,z,a)),x) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_b(z,c(y,z,a)) ;
 }
 } 
=== 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x)
constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a)))))
constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(b(z,z),f(b(y,b(x,a)))))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_f(b(y,b(x,a)))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a))))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z)
constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_c(x,b(z,x),y)
constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y))
constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_b(z,x)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a))
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))> 
      --> <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
}

{  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
      --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)> 
     --> <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
  <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)> 
     --> <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ;
  c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ;
  f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ;
  Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(c(a,b(b(z,a),y),x)) > Marked_f(c(x,b(z,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 : 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x)
constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a)))))
constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y))
constraint: Marked_f(c(a,b(b(z,a),y),x)) >= Marked_f(c(x,b(z,x),y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x) ;
  c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a))))) ;
  f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y)) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a)))) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a)) ;
  Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x) ;
  Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a)) ;
 }
 + Disjunctions:{ 
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(b(z,z),f(b(y,b(x,a)))) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(y,b(x,a)) ;
 }
{
  Marked_c(f(c(a,y,a)),x,z) > Marked_b(z,z) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_c(y,z,a) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_b(b(z,c(y,z,a)),x) ;
 }
{
  Marked_b(a,b(c(z,x,y),a)) > Marked_b(z,c(y,z,a)) ;
 }
 } 
=== 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: b(a,b(c(z,x,y),a)) >= b(b(z,c(y,z,a)),x)
constraint: c(f(c(a,y,a)),x,z) >= f(b(b(z,z),f(b(y,b(x,a)))))
constraint: f(c(a,b(b(z,a),y),x)) >= f(c(x,b(z,x),y))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(b(z,z),f(b(y,b(x,a))))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(y,b(x,a))
constraint: Marked_c(f(c(a,y,a)),x,z) >= Marked_b(z,z)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_c(y,z,a)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(b(z,c(y,z,a)),x)
constraint: Marked_b(a,b(c(z,x,y),a)) >= Marked_b(z,c(y,z,a))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] b(a,b(c(z,x,y),a)) -> b(b(z,c(y,z,a)),x)
[2] f(c(a,b(b(z,a),y),x)) -> f(c(x,b(z,x),y))
[3] c(f(c(a,y,a)),x,z) -> f(b(b(z,z),f(b(y,b(x,a)))))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
<Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
<Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(x,a)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
<Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
<Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_c(x,b(z,x),y)>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_b(z,x)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(b(z,z),f(b(y,b(x,a)))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_f(b(y,b(x,a)))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ b ] (X0,X1) = 0; 
 [ Marked_c ] (X0,X1,X2) = 1; 
 [ a ] () = 0; 
 [ Marked_b ] (X0,X1) = 1; 
 [ c ] (X0,X1,X2) = 2; 
 [ Marked_f ] (X0) = 2*X0; 
 [ f ] (X0) = 2; 
 removing <Marked_f(c(a,b(b(z,a),y),x)),Marked_c(x,b(z,x),y)><Marked_f(
                                                               c(a,b(b(z,a),y),
                                                                x)),Marked_b(
                                                                    z,
                                                                    x)><
Marked_c(f(c(a,y,a)),x,z),Marked_f(b(b(z,z),f(b(y,b(x,a)))))><Marked_c(
                                                               f(c(a,y,a)),
                                                               x,z),Marked_f(
                                                                    b(
                                                                    y,
                                                                    b(x,a)))>
 [ {
      
     DP termination of:
     <Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
<Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
<Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
<Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(c(a,b(b(z,a),y),x)) , Marked_f(c(x,b(z,x),y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
      [ b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X1 + 
     [ [ 0 , 1 , 1 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] () = [ [ 0 , 0 , 0 ] [ 1 , 1 , 1 ] [ 1 , 1 , 1 ] ]; 
 [ c ] (X0,X1,X2) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] ]*X2 + 
[ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 1 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 1 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 ]} 
{
 
DP termination of:
<Marked_b(a,b(c(z,x,y),a)) , Marked_b(b(z,c(y,z,a)),x)>
<Marked_b(a,b(c(z,x,y),a)) , Marked_b(z,c(y,z,a))>
<Marked_b(a,b(c(z,x,y),a)) , Marked_c(y,z,a)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ b ] (X0,X1) = 1*X1 + 2*X0; 
 [ Marked_c ] (X0,X1,X2) = 2*X2 + 2*X1; 
 [ a ] () = 0; 
 [ Marked_b ] (X0,X1) = 1*X1; 
 [ c ] (X0,X1,X2) = 3*X2 + 1*X1 + 3*X0 + 2; 
 [ f ] (X0) = 0; 
 removing <Marked_b(a,b(c(z,x,y),a)),Marked_b(b(z,c(y,z,a)),x)><Marked_b(
                                                                 a,
                                                                 b(c(z,x,y),a)),
Marked_b(z,c(y,z,a))><Marked_b(a,b(c(z,x,y),a)),Marked_c(y,z,a)>
 [ {
      
     DP termination of:
     <Marked_c(f(c(a,y,a)),x,z) , Marked_b(b(z,z),f(b(y,b(x,a))))>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(z,z)>
<Marked_c(f(c(a,y,a)),x,z) , Marked_b(y,b(x,a))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 8.983031 seconds (real time)
Cime Exit Status: 0