MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { lt(x, 0()) -> false()
  , lt(0(), s(x)) -> true()
  , lt(s(x), s(y)) -> lt(x, y)
  , fibo(0()) -> fib(0())
  , fibo(s(0())) -> fib(s(0()))
  , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
  , fib(0()) -> s(0())
  , fib(s(0())) -> s(0())
  , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
  , 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)) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { lt^#(x, 0()) -> c_1()
     , lt^#(0(), s(x)) -> c_2()
     , lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
     , fibo^#(0()) -> c_4(fib^#(0()))
     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
     , fib^#(0()) -> c_7()
     , fib^#(s(0())) -> c_8()
     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
     , sum^#(x, 0()) -> c_10(x)
     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
     , if^#(true(), c, s(s(x)), a, b) ->
       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
     , if^#(false(), c, s(s(x)), a, b) ->
       c_13(sum^#(fibo(a), fibo(b))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { lt^#(x, 0()) -> c_1()
     , lt^#(0(), s(x)) -> c_2()
     , lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
     , fibo^#(0()) -> c_4(fib^#(0()))
     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
     , fib^#(0()) -> c_7()
     , fib^#(s(0())) -> c_8()
     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
     , sum^#(x, 0()) -> c_10(x)
     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
     , if^#(true(), c, s(s(x)), a, b) ->
       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
     , if^#(false(), c, s(s(x)), a, b) ->
       c_13(sum^#(fibo(a), fibo(b))) }
   Strict Trs:
     { lt(x, 0()) -> false()
     , lt(0(), s(x)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , fibo(0()) -> fib(0())
     , fibo(s(0())) -> fib(s(0()))
     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
     , fib(0()) -> s(0())
     , fib(s(0())) -> s(0())
     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
     , 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)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,7,8} by applications
   of Pre({1,2,7,8}) = {3,4,5,10}. Here rules are labeled as follows:
   
     DPs:
       { 1: lt^#(x, 0()) -> c_1()
       , 2: lt^#(0(), s(x)) -> c_2()
       , 3: lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
       , 4: fibo^#(0()) -> c_4(fib^#(0()))
       , 5: fibo^#(s(0())) -> c_5(fib^#(s(0())))
       , 6: fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
       , 7: fib^#(0()) -> c_7()
       , 8: fib^#(s(0())) -> c_8()
       , 9: fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
       , 10: sum^#(x, 0()) -> c_10(x)
       , 11: sum^#(x, s(y)) -> c_11(sum^#(x, y))
       , 12: if^#(true(), c, s(s(x)), a, b) ->
             c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
       , 13: if^#(false(), c, s(s(x)), a, b) ->
             c_13(sum^#(fibo(a), fibo(b))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
     , fibo^#(0()) -> c_4(fib^#(0()))
     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
     , sum^#(x, 0()) -> c_10(x)
     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
     , if^#(true(), c, s(s(x)), a, b) ->
       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
     , if^#(false(), c, s(s(x)), a, b) ->
       c_13(sum^#(fibo(a), fibo(b))) }
   Strict Trs:
     { lt(x, 0()) -> false()
     , lt(0(), s(x)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , fibo(0()) -> fib(0())
     , fibo(s(0())) -> fib(s(0()))
     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
     , fib(0()) -> s(0())
     , fib(s(0())) -> s(0())
     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
     , 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)) }
   Weak DPs:
     { lt^#(x, 0()) -> c_1()
     , lt^#(0(), s(x)) -> c_2()
     , fib^#(0()) -> c_7()
     , fib^#(s(0())) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,3} by applications of
   Pre({2,3}) = {6}. Here rules are labeled as follows:
   
     DPs:
       { 1: lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
       , 2: fibo^#(0()) -> c_4(fib^#(0()))
       , 3: fibo^#(s(0())) -> c_5(fib^#(s(0())))
       , 4: fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
       , 5: fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
       , 6: sum^#(x, 0()) -> c_10(x)
       , 7: sum^#(x, s(y)) -> c_11(sum^#(x, y))
       , 8: if^#(true(), c, s(s(x)), a, b) ->
            c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
       , 9: if^#(false(), c, s(s(x)), a, b) ->
            c_13(sum^#(fibo(a), fibo(b)))
       , 10: lt^#(x, 0()) -> c_1()
       , 11: lt^#(0(), s(x)) -> c_2()
       , 12: fib^#(0()) -> c_7()
       , 13: fib^#(s(0())) -> c_8() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { lt^#(s(x), s(y)) -> c_3(lt^#(x, y))
     , fibo^#(s(s(x))) -> c_6(sum^#(fibo(s(x)), fibo(x)))
     , fib^#(s(s(x))) -> c_9(if^#(true(), 0(), s(s(x)), 0(), 0()))
     , sum^#(x, 0()) -> c_10(x)
     , sum^#(x, s(y)) -> c_11(sum^#(x, y))
     , if^#(true(), c, s(s(x)), a, b) ->
       c_12(if^#(lt(s(c), s(s(x))), s(c), s(s(x)), b, c))
     , if^#(false(), c, s(s(x)), a, b) ->
       c_13(sum^#(fibo(a), fibo(b))) }
   Strict Trs:
     { lt(x, 0()) -> false()
     , lt(0(), s(x)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , fibo(0()) -> fib(0())
     , fibo(s(0())) -> fib(s(0()))
     , fibo(s(s(x))) -> sum(fibo(s(x)), fibo(x))
     , fib(0()) -> s(0())
     , fib(s(0())) -> s(0())
     , fib(s(s(x))) -> if(true(), 0(), s(s(x)), 0(), 0())
     , 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)) }
   Weak DPs:
     { lt^#(x, 0()) -> c_1()
     , lt^#(0(), s(x)) -> c_2()
     , fibo^#(0()) -> c_4(fib^#(0()))
     , fibo^#(s(0())) -> c_5(fib^#(s(0())))
     , fib^#(0()) -> c_7()
     , fib^#(s(0())) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..