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

TRS termination of:
[1] a__f(f(a)) -> a__f(g(f(a)))
[2] mark(f(X)) -> a__f(mark(X))
[3] mark(a) -> a
[4] mark(g(X)) -> g(X)
[5] a__f(X) -> f(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__f(f(a)) , Marked_a__f(g(f(a)))>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(f(X)) , Marked_mark(X)> 
      --> <Marked_mark(f(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__f(f(a)) >= a__f(g(f(a))) ;
  a__f(X) >= f(X) ;
  mark(g(X)) >= g(X) ;
  mark(f(X)) >= a__f(mark(X)) ;
  mark(a) >= a ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(f(X)) > Marked_mark(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: a__f(f(a)) >= a__f(g(f(a)))
constraint: a__f(X) >= f(X)
constraint: mark(g(X)) >= g(X)
constraint: mark(f(X)) >= a__f(mark(X))
constraint: mark(a) >= a
constraint: Marked_mark(f(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__f(f(a)) -> a__f(g(f(a)))
[2] mark(f(X)) -> a__f(mark(X))
[3] mark(a) -> a
[4] mark(g(X)) -> g(X)
[5] a__f(X) -> f(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__f(f(a)) , Marked_a__f(g(f(a)))>
<Marked_mark(f(X)) , Marked_a__f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(f(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a__f ] (X0) = 2 + 3*X0 + 0; 
 [ mark ] (X0) = 2*X0 + 0; 
 [ f ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ g ] (X0) = 0; 
 [ a ] () = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.021661 seconds (real time)
Cime Exit Status: 0