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

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


Sub problem: 
guided: 

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

{  <Marked_f(f(f(c(z,x,a)))) , Marked_f(x)> 
      --> <Marked_f(f(f(c(z,x,a)))) , Marked_f(x)>
  <Marked_f(f(f(c(z,x,a)))) , Marked_f(x)> 
     --> <Marked_f(f(f(c(z,x,a)))) , Marked_b(f(x),z)>
  <Marked_f(f(f(c(z,x,a)))) , Marked_b(f(x),z)> 
     --> <Marked_b(y,b(a,z)) , Marked_f(z)>
  <Marked_f(f(f(c(z,x,a)))) , Marked_b(f(x),z)> 
     --> <Marked_b(y,b(a,z)) , Marked_b(f(c(y,y,a)),b(f(z),a))>
  <Marked_b(y,b(a,z)) , Marked_f(z)> 
     --> <Marked_f(f(f(c(z,x,a)))) , Marked_f(x)>
  <Marked_b(y,b(a,z)) , Marked_f(z)> 
     --> <Marked_f(f(f(c(z,x,a)))) , Marked_b(f(x),z)>
  <Marked_b(y,b(a,z)) , Marked_b(f(c(y,y,a)),b(f(z),a))> 
     --> <Marked_b(y,b(a,z)) , Marked_f(z)>
  <Marked_b(y,b(a,z)) , Marked_b(f(c(y,y,a)),b(f(z),a))> 
     --> <Marked_b(y,b(a,z)) , Marked_b(f(c(y,y,a)),b(f(z),a))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(f(f(c(z,x,a)))) >= b(f(x),z) ;
  f(b(a,z)) >= z ;
  b(y,b(a,z)) >= b(f(c(y,y,a)),b(f(z),a)) ;
  Marked_f(f(f(c(z,x,a)))) >= Marked_f(x) ;
  Marked_f(f(f(c(z,x,a)))) >= Marked_b(f(x),z) ;
  Marked_b(y,b(a,z)) >= Marked_f(z) ;
  Marked_b(y,b(a,z)) >= Marked_b(f(c(y,y,a)),b(f(z),a)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(f(f(c(z,x,a)))) > Marked_f(x) ;
 }
{
  Marked_f(f(f(c(z,x,a)))) > Marked_b(f(x),z) ;
 }
{
  Marked_b(y,b(a,z)) > Marked_f(z) ;
 }
{
  Marked_b(y,b(a,z)) > Marked_b(f(c(y,y,a)),b(f(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: f(f(f(c(z,x,a)))) >= b(f(x),z)
constraint: f(b(a,z)) >= z
constraint: b(y,b(a,z)) >= b(f(c(y,y,a)),b(f(z),a))
constraint: Marked_f(f(f(c(z,x,a)))) >= Marked_f(x)
constraint: Marked_f(f(f(c(z,x,a)))) >= Marked_b(f(x),z)
constraint: Marked_b(y,b(a,z)) >= Marked_f(z)
constraint: Marked_b(y,b(a,z)) >= Marked_b(f(c(y,y,a)),b(f(z),a))
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 2.725265 seconds (real time)
Cime Exit Status: 0