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

TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(0)
[3] f(s(s(x))) -> f(f(s(x)))


Sub problem: 
guided: 

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

{  <Marked_f(s(s(x))) , Marked_f(s(x))> 
      --> <Marked_f(s(s(x))) , Marked_f(s(x))>
  <Marked_f(s(s(x))) , Marked_f(s(x))> 
     --> <Marked_f(s(s(x))) , Marked_f(f(s(x)))>
  <Marked_f(s(s(x))) , Marked_f(f(s(x)))> 
     --> <Marked_f(s(s(x))) , Marked_f(s(x))>
  <Marked_f(s(s(x))) , Marked_f(f(s(x)))> 
     --> <Marked_f(s(s(x))) , Marked_f(f(s(x)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(s(s(x))) >= f(f(s(x))) ;
  f(s(0)) >= s(0) ;
  f(0) >= s(0) ;
  Marked_f(s(s(x))) >= Marked_f(s(x)) ;
  Marked_f(s(s(x))) >= Marked_f(f(s(x))) ;
 }
 + Disjunctions:{ 
{
  Marked_f(s(s(x))) > Marked_f(s(x)) ;
 }
{
  Marked_f(s(s(x))) > Marked_f(f(s(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: f(s(s(x))) >= f(f(s(x)))
constraint: f(s(0)) >= s(0)
constraint: f(0) >= s(0)
constraint: Marked_f(s(s(x))) >= Marked_f(s(x))
constraint: Marked_f(s(s(x))) >= Marked_f(f(s(x)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(0)
[3] f(s(s(x))) -> f(f(s(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(s(x))) , Marked_f(f(s(x)))>
<Marked_f(s(s(x))) , Marked_f(s(x))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(s(x))) , Marked_f(f(s(x)))>
<Marked_f(s(s(x))) , Marked_f(s(x))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ s ] (X0) = 2 + 2*X0 + 0; 
 [ f ] (X0) = 3 + 1*X0 + 0; 
 [ 0 ] () = 1 + 0; 
 [ Marked_f ] (X0) = 2*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.034306 seconds (real time)
Cime Exit Status: 0