- : 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))
[4] +(x,0) -> x
[5] +(x,s(y)) -> s(+(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_fib(s(s(x))) , Marked_+(fib(s(x)),fib(x))>
<Marked_fib(s(s(x))) , Marked_fib(s(x))>
<Marked_fib(s(s(x))) , Marked_fib(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 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))>
}

{  <Marked_+(x,s(y)) , Marked_+(x,y)> --> <Marked_+(x,s(y)) , Marked_+(x,y)>
}
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)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  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
=== 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 ===
=== STOPING TIMER virtual ===
constraint: fib(0) >= 0
constraint: fib(s(0)) >= s(0)
constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_fib(s(s(x))) >= Marked_fib(s(x))
constraint: Marked_fib(s(s(x))) >= Marked_fib(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)) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  Marked_+(x,s(y)) >= Marked_+(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_+(x,s(y)) > Marked_+(x,y) ;
 }
 } 
=== 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 ===
=== STOPING TIMER virtual ===
constraint: fib(0) >= 0
constraint: fib(s(0)) >= s(0)
constraint: fib(s(s(x))) >= +(fib(s(x)),fib(x))
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_+(x,s(y)) >= Marked_+(x,y)
APPLY CRITERIA (Graph splitting)
Found 0 components:
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))
[4] +(x,0) -> x
[5] +(x,s(y)) -> s(+(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fib(s(s(x))) , Marked_+(fib(s(x)),fib(x))>
<Marked_fib(s(s(x))) , Marked_fib(s(x))>
<Marked_fib(s(s(x))) , Marked_fib(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 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:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { fib  >  s ; fib  >  + ; s  <  fib ;
                                   s  <  + ; +  <  fib ; +  >  s ; }

 ]} 
{
 
DP termination of:
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { fib  >  s ; fib  >  + ; s  <  fib ;
                                   s  <  + ; +  <  fib ; +  >  s ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.056937 seconds (real time)
Cime Exit Status: 0