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

TRS termination of:
[1] f(x,f(y,a)) -> f(f(f(f(a,x),y),a),h(a))


Sub problem: 
guided: 

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

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

{  <Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)> 
      --> <Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(x,f(y,a)) -> f(f(f(f(a,x),y),a),h(a))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(x,f(y,a)) , Marked_f(f(f(f(a,x),y),a),h(a))>
<Marked_f(x,f(y,a)) , Marked_f(f(f(a,x),y),a)>
<Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)>
<Marked_f(x,f(y,a)) , Marked_f(a,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)>
<Marked_f(x,f(y,a)) , Marked_f(a,x)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1) = 2*X1*X0 + 2; 
 [ h ] (X0) = 0; 
 [ a ] () = 1; 
 [ Marked_f ] (X0,X1) = 1*X1*X0 + 2*X1 + 2*X0; 
 removing <Marked_f(x,f(y,a)),Marked_f(a,x)>
 [ {
      
     DP termination of:
     <Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(x,f(y,a)) , Marked_f(f(a,x),y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.473683 seconds (real time)
Cime Exit Status: 0