- : 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(0))) -> s(0)
[4] fib(s(s(x))) -> sp(g(x))
[5] g(0) -> pair(s(0),0)
[6] g(s(0)) -> pair(s(0),s(0))
[7] g(s(x)) -> np(g(x))
[8] sp(pair(x,y)) -> +(x,y)
[9] np(pair(x,y)) -> pair(+(x,y),x)
[10] +(x,0) -> x
[11] +(x,s(y)) -> s(+(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_fib(s(s(x))) , Marked_sp(g(x))>
<Marked_fib(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_np(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_sp(pair(x,y)) , Marked_+(x,y)>
<Marked_np(pair(x,y)) , Marked_+(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_g(s(x)) , Marked_g(x)> --> <Marked_g(s(x)) , Marked_g(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(0))) >= s(0) ;
  fib(s(s(x))) >= sp(g(x)) ;
  sp(pair(x,y)) >= +(x,y) ;
  g(0) >= pair(s(0),0) ;
  g(s(0)) >= pair(s(0),s(0)) ;
  g(s(x)) >= np(g(x)) ;
  np(pair(x,y)) >= pair(+(x,y),x) ;
  +(x,0) >= x ;
  +(x,s(y)) >= s(+(x,y)) ;
  Marked_g(s(x)) >= Marked_g(x) ;
 }
 + Disjunctions:{ 
{
  Marked_g(s(x)) > Marked_g(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(0))) >= s(0)
constraint: fib(s(s(x))) >= sp(g(x))
constraint: sp(pair(x,y)) >= +(x,y)
constraint: g(0) >= pair(s(0),0)
constraint: g(s(0)) >= pair(s(0),s(0))
constraint: g(s(x)) >= np(g(x))
constraint: np(pair(x,y)) >= pair(+(x,y),x)
constraint: +(x,0) >= x
constraint: +(x,s(y)) >= s(+(x,y))
constraint: Marked_g(s(x)) >= Marked_g(x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  fib(0) >= 0 ;
  fib(s(0)) >= s(0) ;
  fib(s(s(0))) >= s(0) ;
  fib(s(s(x))) >= sp(g(x)) ;
  sp(pair(x,y)) >= +(x,y) ;
  g(0) >= pair(s(0),0) ;
  g(s(0)) >= pair(s(0),s(0)) ;
  g(s(x)) >= np(g(x)) ;
  np(pair(x,y)) >= pair(+(x,y),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(0))) >= s(0)
constraint: fib(s(s(x))) >= sp(g(x))
constraint: sp(pair(x,y)) >= +(x,y)
constraint: g(0) >= pair(s(0),0)
constraint: g(s(0)) >= pair(s(0),s(0))
constraint: g(s(x)) >= np(g(x))
constraint: np(pair(x,y)) >= pair(+(x,y),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(0))) -> s(0)
[4] fib(s(s(x))) -> sp(g(x))
[5] g(0) -> pair(s(0),0)
[6] g(s(0)) -> pair(s(0),s(0))
[7] g(s(x)) -> np(g(x))
[8] sp(pair(x,y)) -> +(x,y)
[9] np(pair(x,y)) -> pair(+(x,y),x)
[10] +(x,0) -> x
[11] +(x,s(y)) -> s(+(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fib(s(s(x))) , Marked_sp(g(x))>
<Marked_fib(s(s(x))) , Marked_g(x)>
<Marked_g(s(x)) , Marked_np(g(x))>
<Marked_g(s(x)) , Marked_g(x)>
<Marked_sp(pair(x,y)) , Marked_+(x,y)>
<Marked_np(pair(x,y)) , Marked_+(x,y)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(s(x)) , Marked_g(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { fib  >  s ; fib  >  sp ; fib  >  g ;
                                   fib  >  pair ; fib  >  np ; fib  >  + ;
                                   s  <  fib ; s  <  sp ; s  <  g ; s  <  np ;
                                   s  <  + ; sp  <  fib ; sp  >  s ; 
                                   sp  >  + ; g  <  fib ; g  >  s ;
                                   g  >  pair ; g  >  np ; g  >  + ;
                                   pair  <  fib ; pair  <  g ; pair  <  np ;
                                   np  <  fib ; np  >  s ; np  <  g ;
                                   np  >  pair ; np  >  + ; +  <  fib ;
                                   +  >  s ; +  <  sp ; +  <  g ; +  <  np ; }

 ]} 
{
 
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  >  sp ; fib  >  g ;
                                   fib  >  pair ; fib  >  np ; fib  >  + ;
                                   s  <  fib ; s  <  sp ; s  <  g ; s  <  np ;
                                   s  <  + ; sp  <  fib ; sp  >  s ; 
                                   sp  >  + ; g  <  fib ; g  >  s ;
                                   g  >  pair ; g  >  np ; g  >  + ;
                                   pair  <  fib ; pair  <  g ; pair  <  np ;
                                   np  <  fib ; np  >  s ; np  <  g ;
                                   np  >  pair ; np  >  + ; +  <  fib ;
                                   +  >  s ; +  <  sp ; +  <  g ; +  <  np ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.113965 seconds (real time)
Cime Exit Status: 0