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

TRS termination of:
[1] lt(0,s(x)) -> true
[2] lt(x,0) -> false
[3] lt(s(x),s(y)) -> lt(x,y)
[4] fibo(0) -> fib(0)
[5] fibo(s(0)) -> fib(s(0))
[6] fibo(s(s(x))) -> sum(fibo(s(x)),fibo(x))
[7] fib(0) -> s(0)
[8] fib(s(0)) -> s(0)
[9] fib(s(s(x))) -> if(true,0,s(s(x)),0,0)
[10] if(true,c,s(s(x)),a,b) -> if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)
[11] if(false,c,s(s(x)),a,b) -> sum(fibo(a),fibo(b))
[12] sum(x,0) -> x
[13] sum(x,s(y)) -> s(sum(x,y))


Sub problem: 
guided: 

DP termination of:
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_fibo(0) , Marked_fib(0)>
<Marked_fibo(s(0)) , Marked_fib(s(0))>
<Marked_fibo(s(s(x))) , Marked_sum(fibo(s(x)),fibo(x))>
<Marked_fibo(s(s(x))) , Marked_fibo(s(x))>
<Marked_fibo(s(s(x))) , Marked_fibo(x)>
<Marked_fib(s(s(x))) , Marked_if(true,0,s(s(x)),0,0)>
<Marked_if(true,c,s(s(x)),a,b) , Marked_if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)>
<Marked_if(true,c,s(s(x)),a,b) , Marked_lt(s(c),s(s(x)))>
<Marked_if(false,c,s(s(x)),a,b) , Marked_sum(fibo(a),fibo(b))>
<Marked_if(false,c,s(s(x)),a,b) , Marked_fibo(a)>
<Marked_if(false,c,s(s(x)),a,b) , Marked_fibo(b)>
<Marked_sum(x,s(y)) , Marked_sum(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if(true,c,s(s(x)),a,b) , Marked_if(lt(s(c),s(s(x))),s(c),s(s(x)),
                                     b,c)> 
      --> <Marked_if(true,c,s(s(x)),a,b) , Marked_if(lt(s(c),s(s(x))),
                                            s(c),s(s(x)),b,c)>
}

{  <Marked_lt(s(x),s(y)) , Marked_lt(x,y)> 
      --> <Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
}

{  <Marked_fibo(s(s(x))) , Marked_fibo(x)> 
      --> <Marked_fibo(s(s(x))) , Marked_fibo(x)>
  <Marked_fibo(s(s(x))) , Marked_fibo(x)> 
     --> <Marked_fibo(s(s(x))) , Marked_fibo(s(x))>
  <Marked_fibo(s(s(x))) , Marked_fibo(s(x))> 
     --> <Marked_fibo(s(s(x))) , Marked_fibo(x)>
  <Marked_fibo(s(s(x))) , Marked_fibo(s(x))> 
     --> <Marked_fibo(s(s(x))) , Marked_fibo(s(x))>
}

{  <Marked_sum(x,s(y)) , Marked_sum(x,y)> 
      --> <Marked_sum(x,s(y)) , Marked_sum(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  lt(0,s(x)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  fib(0) >= s(0) ;
  fib(s(0)) >= s(0) ;
  fib(s(s(x))) >= if(true,0,s(s(x)),0,0) ;
  fibo(0) >= fib(0) ;
  fibo(s(0)) >= fib(s(0)) ;
  fibo(s(s(x))) >= sum(fibo(s(x)),fibo(x)) ;
  sum(x,0) >= x ;
  sum(x,s(y)) >= s(sum(x,y)) ;
  if(true,c,s(s(x)),a,b) >= if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c) ;
  if(false,c,s(s(x)),a,b) >= sum(fibo(a),fibo(b)) ;
  Marked_if(true,c,s(s(x)),a,b) >= Marked_if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,c,s(s(x)),a,b) > Marked_if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c) ;
 }
 } 
=== 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 ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 9.528181 seconds (real time)
Cime Exit Status: 0