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

TRS termination of:
[1] active(f(a,X,X)) -> mark(f(X,b,b))
[2] active(b) -> mark(a)
[3] mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
[4] mark(a) -> active(a)
[5] mark(b) -> active(b)
[6] f(mark(X1),X2,X3) -> f(X1,X2,X3)
[7] f(X1,mark(X2),X3) -> f(X1,X2,X3)
[8] f(X1,X2,mark(X3)) -> f(X1,X2,X3)
[9] f(active(X1),X2,X3) -> f(X1,X2,X3)
[10] f(X1,active(X2),X3) -> f(X1,X2,X3)
[11] f(X1,X2,active(X3)) -> f(X1,X2,X3)


Sub problem: 
guided: 

DP termination of:
<Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
<Marked_active(f(a,X,X)) , Marked_f(X,b,b)>
<Marked_active(b) , Marked_mark(a)>
<Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
<Marked_mark(f(X1,X2,X3)) , Marked_f(X1,mark(X2),X3)>
<Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
<Marked_mark(a) , Marked_active(a)>
<Marked_mark(b) , Marked_active(b)>
<Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
<Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)> 
      --> <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)> 
     --> <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
  <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))> 
     --> <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
  <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))> 
     --> <Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
  <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))> 
     --> <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
}

{  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
      --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ;
  mark(b) >= active(b) ;
  mark(a) >= active(a) ;
  f(mark(X1),X2,X3) >= f(X1,X2,X3) ;
  f(active(X1),X2,X3) >= f(X1,X2,X3) ;
  f(X1,mark(X2),X3) >= f(X1,X2,X3) ;
  f(X1,active(X2),X3) >= f(X1,X2,X3) ;
  f(X1,X2,mark(X3)) >= f(X1,X2,X3) ;
  f(X1,X2,active(X3)) >= f(X1,X2,X3) ;
  active(f(a,X,X)) >= mark(f(X,b,b)) ;
  active(b) >= mark(a) ;
  Marked_mark(f(X1,X2,X3)) >= Marked_mark(X2) ;
  Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) ;
  Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(f(X1,X2,X3)) > Marked_mark(X2) ;
 }
{
  Marked_mark(f(X1,X2,X3)) > Marked_active(f(X1,mark(X2),X3)) ;
 }
{
  Marked_active(f(a,X,X)) > Marked_mark(f(X,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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3))
constraint: mark(b) >= active(b)
constraint: mark(a) >= active(a)
constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(active(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,active(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3)
constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3)
constraint: active(f(a,X,X)) >= mark(f(X,b,b))
constraint: active(b) >= mark(a)
constraint: Marked_mark(f(X1,X2,X3)) >= Marked_mark(X2)
constraint: Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3))
constraint: Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ;
  mark(b) >= active(b) ;
  mark(a) >= active(a) ;
  f(mark(X1),X2,X3) >= f(X1,X2,X3) ;
  f(active(X1),X2,X3) >= f(X1,X2,X3) ;
  f(X1,mark(X2),X3) >= f(X1,X2,X3) ;
  f(X1,active(X2),X3) >= f(X1,X2,X3) ;
  f(X1,X2,mark(X3)) >= f(X1,X2,X3) ;
  f(X1,X2,active(X3)) >= f(X1,X2,X3) ;
  active(f(a,X,X)) >= mark(f(X,b,b)) ;
  active(b) >= mark(a) ;
  Marked_f(mark(X1),X2,X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,X2,mark(X3)) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) ;
 }
 + Disjunctions:{ 
{
  Marked_f(mark(X1),X2,X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(active(X1),X2,X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,mark(X2),X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,active(X2),X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,X2,mark(X3)) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,X2,active(X3)) > Marked_f(X1,X2,X3) ;
 }
 } 
=== 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3))
constraint: mark(b) >= active(b)
constraint: mark(a) >= active(a)
constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(active(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,active(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3)
constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3)
constraint: active(f(a,X,X)) >= mark(f(X,b,b))
constraint: active(b) >= mark(a)
constraint: Marked_f(mark(X1),X2,X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,mark(X2),X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,X2,mark(X3)) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3)
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))> 
      --> <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
  <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))> 
     --> <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ;
  mark(b) >= active(b) ;
  mark(a) >= active(a) ;
  f(mark(X1),X2,X3) >= f(X1,X2,X3) ;
  f(active(X1),X2,X3) >= f(X1,X2,X3) ;
  f(X1,mark(X2),X3) >= f(X1,X2,X3) ;
  f(X1,active(X2),X3) >= f(X1,X2,X3) ;
  f(X1,X2,mark(X3)) >= f(X1,X2,X3) ;
  f(X1,X2,active(X3)) >= f(X1,X2,X3) ;
  active(f(a,X,X)) >= mark(f(X,b,b)) ;
  active(b) >= mark(a) ;
  Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3)) ;
  Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b)) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(f(X1,X2,X3)) > Marked_active(f(X1,mark(X2),X3)) ;
 }
{
  Marked_active(f(a,X,X)) > Marked_mark(f(X,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 : 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3))
constraint: mark(b) >= active(b)
constraint: mark(a) >= active(a)
constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(active(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,active(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3)
constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3)
constraint: active(f(a,X,X)) >= mark(f(X,b,b))
constraint: active(b) >= mark(a)
constraint: Marked_mark(f(X1,X2,X3)) >= Marked_active(f(X1,mark(X2),X3))
constraint: Marked_active(f(a,X,X)) >= Marked_mark(f(X,b,b))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
      --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
  <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)> 
     --> <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3)) ;
  mark(b) >= active(b) ;
  mark(a) >= active(a) ;
  f(mark(X1),X2,X3) >= f(X1,X2,X3) ;
  f(active(X1),X2,X3) >= f(X1,X2,X3) ;
  f(X1,mark(X2),X3) >= f(X1,X2,X3) ;
  f(X1,active(X2),X3) >= f(X1,X2,X3) ;
  f(X1,X2,mark(X3)) >= f(X1,X2,X3) ;
  f(X1,X2,active(X3)) >= f(X1,X2,X3) ;
  active(f(a,X,X)) >= mark(f(X,b,b)) ;
  active(b) >= mark(a) ;
  Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3) ;
  Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3) ;
 }
 + Disjunctions:{ 
{
  Marked_f(active(X1),X2,X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,active(X2),X3) > Marked_f(X1,X2,X3) ;
 }
{
  Marked_f(X1,X2,active(X3)) > Marked_f(X1,X2,X3) ;
 }
 } 
=== 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: mark(f(X1,X2,X3)) >= active(f(X1,mark(X2),X3))
constraint: mark(b) >= active(b)
constraint: mark(a) >= active(a)
constraint: f(mark(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(active(X1),X2,X3) >= f(X1,X2,X3)
constraint: f(X1,mark(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,active(X2),X3) >= f(X1,X2,X3)
constraint: f(X1,X2,mark(X3)) >= f(X1,X2,X3)
constraint: f(X1,X2,active(X3)) >= f(X1,X2,X3)
constraint: active(f(a,X,X)) >= mark(f(X,b,b))
constraint: active(b) >= mark(a)
constraint: Marked_f(active(X1),X2,X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,active(X2),X3) >= Marked_f(X1,X2,X3)
constraint: Marked_f(X1,X2,active(X3)) >= Marked_f(X1,X2,X3)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(f(a,X,X)) -> mark(f(X,b,b))
[2] active(b) -> mark(a)
[3] mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
[4] mark(a) -> active(a)
[5] mark(b) -> active(b)
[6] f(mark(X1),X2,X3) -> f(X1,X2,X3)
[7] f(X1,mark(X2),X3) -> f(X1,X2,X3)
[8] f(X1,X2,mark(X3)) -> f(X1,X2,X3)
[9] f(active(X1),X2,X3) -> f(X1,X2,X3)
[10] f(X1,active(X2),X3) -> f(X1,X2,X3)
[11] f(X1,X2,active(X3)) -> f(X1,X2,X3)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
<Marked_active(f(a,X,X)) , Marked_f(X,b,b)>
<Marked_active(b) , Marked_mark(a)>
<Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
<Marked_mark(f(X1,X2,X3)) , Marked_f(X1,mark(X2),X3)>
<Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
<Marked_mark(a) , Marked_active(a)>
<Marked_mark(b) , Marked_active(b)>
<Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
<Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
<Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
<Marked_mark(f(X1,X2,X3)) , Marked_mark(X2)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ a ] () = 0; 
 [ b ] () = 0; 
 [ Marked_mark ] (X0) = 1*X0; 
 [ f ] (X0,X1,X2) = 2*X1 + 2; 
 [ active ] (X0) = 1*X0; 
 [ Marked_active ] (X0) = 2; 
 removing <Marked_mark(f(X1,X2,X3)),Marked_mark(X2)>
 [ {
      
     DP termination of:
     <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
<Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(a,X,X)) , Marked_mark(f(X,b,b))>
<Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ mark ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] () = [ [ 1 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ b ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] ]; 
 [ Marked_mark ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ f ] (X0,X1,X2) = [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X2 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ active ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_active ] (X0) = [ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + 
[ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 removing <Marked_active(f(a,X,X)),Marked_mark(f(X,b,b))>
 [ {
      
     DP termination of:
     <Marked_mark(f(X1,X2,X3)) , Marked_active(f(X1,mark(X2),X3))>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_f(mark(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,mark(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,mark(X3)) , Marked_f(X1,X2,X3)>
<Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 2*X0 + 2; 
 [ a ] () = 0; 
 [ b ] () = 1; 
 [ f ] (X0,X1,X2) = 2; 
 [ Marked_f ] (X0,X1,X2) = 3*X2 + 3*X1 + 3*X0; 
 [ active ] (X0) = 3*X0; 
 removing <Marked_f(mark(X1),X2,X3),Marked_f(X1,X2,X3)><Marked_f(X1,mark(X2),
                                                         X3),Marked_f(X1,X2,X3)><
Marked_f(X1,X2,mark(X3)),Marked_f(X1,X2,X3)>
 [ {
      
     DP termination of:
     <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(active(X1),X2,X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,active(X2),X3) , Marked_f(X1,X2,X3)>
<Marked_f(X1,X2,active(X3)) , Marked_f(X1,X2,X3)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1 + 0; 
 [ a ] () = 0; 
 [ b ] () = 0; 
 [ f ] (X0,X1,X2) = 0; 
 [ Marked_f ] (X0,X1,X2) = 3*X0 + 3*X1 + 3*X2 + 0; 
 [ active ] (X0) = 1 + 2*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.926881 seconds (real time)
Cime Exit Status: 0