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

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


Sub problem: 
guided: 

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

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

{  <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))> 
      --> <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_b -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
[2] c(f(f(c(x,a,z))),a,y) -> b(y,f(b(a,z)))
[3] b(b(c(b(a,a),a,z),f(a)),y) -> z
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))>
<Marked_b(f(b(x,z)),y) , Marked_b(y,z)>
<Marked_c(f(f(c(x,a,z))),a,y) , Marked_b(y,f(b(a,z)))>
<Marked_c(f(f(c(x,a,z))),a,y) , Marked_b(a,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))>
<Marked_b(f(b(x,z)),y) , Marked_b(y,z)>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ f ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 1 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ Marked_b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 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 ] ]; 
 [ a ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ b ] (X0,X1) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ c ] (X0,X1,X2) = [ [ 0 , 0 , 1 ] [ 0 , 0 , 1 ] [ 1 , 1 , 1 ] ]*X2 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] [ 0 , 1 , 1 ] ]*X0 + 
[ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 removing <Marked_b(f(b(x,z)),y),Marked_b(y,z)>
 [ {
      
     DP termination of:
     <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_b(f(b(x,z)),y) , Marked_b(z,b(y,z))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 4.306317 seconds (real time)
Cime Exit Status: 0