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

TRS termination of:
[1] f(f(x)) -> f(g(f(x),x))
[2] f(f(x)) -> f(h(f(x),f(x)))
[3] g(x,y) -> y
[4] h(x,x) -> g(x,0)


Sub problem: 
guided: 

DP termination of:
<Marked_f(f(x)) , Marked_f(g(f(x),x))>
<Marked_f(f(x)) , Marked_g(f(x),x)>
<Marked_f(f(x)) , Marked_f(h(f(x),f(x)))>
<Marked_f(f(x)) , Marked_h(f(x),f(x))>
<Marked_h(x,x) , Marked_g(x,0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

Cime worked for 0.050540 seconds (real time)
Cime Exit Status: 0