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

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


Sub problem: 
guided: 

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

{  <Marked_fib(s(s(x))) , Marked_fib(x)> 
      --> <Marked_fib(s(s(x))) , Marked_fib(x)>
  <Marked_fib(s(s(x))) , Marked_fib(x)> 
     --> <Marked_fib(s(s(x))) , Marked_fib(s(x))>
  <Marked_fib(s(s(x))) , Marked_fib(s(x))> 
     --> <Marked_fib(s(s(x))) , Marked_fib(x)>
  <Marked_fib(s(s(x))) , Marked_fib(s(x))> 
     --> <Marked_fib(s(s(x))) , Marked_fib(s(x))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  fib(0) >= 0 ;
  fib(s(0)) >= s(0) ;
  fib(s(s(x))) >= +(fib(s(x)),fib(x)) ;
  Marked_fib(s(s(x))) >= Marked_fib(s(x)) ;
  Marked_fib(s(s(x))) >= Marked_fib(x) ;
 }
 + Disjunctions:{ 
{
  Marked_fib(s(s(x))) > Marked_fib(s(x)) ;
 }
{
  Marked_fib(s(s(x))) > Marked_fib(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: fib(0) >= 0
constraint: fib(s(0)) >= s(0)
constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x))
constraint: Marked_fib(s(s(x))) >= Marked_fib(s(x))
constraint: Marked_fib(s(s(x))) >= Marked_fib(x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] fib(0) -> 0
[2] fib(s(0)) -> s(0)
[3] fib(s(s(x))) -> +(fib(s(x)),fib(x))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fib(s(s(x))) , Marked_fib(s(x))>
<Marked_fib(s(s(x))) , Marked_fib(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_fib(s(s(x))) , Marked_fib(s(x))>
<Marked_fib(s(s(x))) , Marked_fib(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ 0 ] () = 3 + 0; 
 [ Marked_fib ] (X0) = 1*X0 + 0; 
 [ s ] (X0) = 2 + 2*X0 + 0; 
 [ fib ] (X0) = 1*X0 + 0; 
 [ + ] (X0,X1) = 2*X1 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.030232 seconds (real time)
Cime Exit Status: 0