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

TRS termination of:
[1] app(app(F,app(app(F,f),x)),x) ->
 app(app(F,app(G,app(app(F,f),x))),app(f,x))


Sub problem: 
guided: 

DP termination of:
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                    app(G,app(app(F,f),x))),
                                         app(f,x))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(F,app(G,app(app(F,f),x)))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(G,app(app(F,f),x))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)> 
      --> <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)>
  <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)> 
     --> <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                             app(G,
                                                              app(app(F,f),x))),
                                                  app(f,x))>
  <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                      app(G,app(app(F,f),x))),
                                           app(f,x))> 
     --> <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)>
  <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                      app(G,app(app(F,f),x))),
                                           app(f,x))> 
     --> <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                             app(G,
                                                              app(app(F,f),x))),
                                                  app(f,x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  app(app(F,app(app(F,f),x)),x) >= app(app(F,app(G,app(app(F,f),x))),app(f,x)) ;
  Marked_app(app(F,app(app(F,f),x)),x) >= Marked_app(app(F,
                                                      app(G,app(app(F,f),x))),
                                           app(f,x)) ;
  Marked_app(app(F,app(app(F,f),x)),x) >= Marked_app(f,x) ;
 }
 + Disjunctions:{ 
{
  Marked_app(app(F,app(app(F,f),x)),x) > Marked_app(app(F,
                                                     app(G,app(app(F,f),x))),
                                          app(f,x)) ;
 }
{
  Marked_app(app(F,app(app(F,f),x)),x) > Marked_app(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 : 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: app(app(F,app(app(F,f),x)),x) >= app(app(F,app(G,app(app(F,f),x))),
                                              app(f,x))
constraint: Marked_app(app(F,app(app(F,f),x)),x) >= Marked_app(app(F,
                                                                app(G,
                                                                 app(
                                                                  app(F,f),
                                                                  x))),
                                                     app(f,x))
constraint: Marked_app(app(F,app(app(F,f),x)),x) >= Marked_app(f,x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] app(app(F,app(app(F,f),x)),x) ->
 app(app(F,app(G,app(app(F,f),x))),app(f,x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                         app(G,app(app(F,f),x))),
                                              app(f,x))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(F,app(G,app(app(F,f),x)))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(G,app(app(F,f),x))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(app(F,
                                                         app(G,app(app(F,f),x))),
                                              app(f,x))>
<Marked_app(app(F,app(app(F,f),x)),x) , Marked_app(f,x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ app ] (X0,X1) = 2*X0 + 2*X1*X0 + 0; 
 [ G ] () = 0; 
 [ F ] () = 1 + 0; 
 [ Marked_app ] (X0,X1) = 1*X0 + 2*X1*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 3.939687 seconds (real time)
Cime Exit Status: 0