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

TRS termination of:
[1] f(a) -> g(h(a))
[2] h(g(x)) -> g(h(f(x)))
[3] k(x,h(x),a) -> h(x)
[4] k(f(x),y,x) -> f(x)


Sub problem: 
guided: 

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

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

Cime worked for 0.205780 seconds (real time)
Cime Exit Status: 0