MAYBE

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

Strict Trs:
  { fib(0()) -> 0()
  , fib(s(0())) -> s(0())
  , fib(s(s(x))) -> sp(g(x))
  , fib(s(s(0()))) -> s(0())
  , sp(pair(x, y)) -> +(x, y)
  , g(0()) -> pair(s(0()), 0())
  , g(s(x)) -> np(g(x))
  , g(s(0())) -> pair(s(0()), s(0()))
  , np(pair(x, y)) -> pair(+(x, y), x)
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y)) }
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:
     { fib^#(0()) -> c_1()
     , fib^#(s(0())) -> c_2()
     , fib^#(s(s(x))) -> c_3(sp^#(g(x)))
     , fib^#(s(s(0()))) -> c_4()
     , sp^#(pair(x, y)) -> c_5(+^#(x, y))
     , +^#(x, 0()) -> c_10(x)
     , +^#(x, s(y)) -> c_11(+^#(x, y))
     , g^#(0()) -> c_6()
     , g^#(s(x)) -> c_7(np^#(g(x)))
     , g^#(s(0())) -> c_8()
     , np^#(pair(x, y)) -> c_9(+^#(x, y), x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { fib^#(0()) -> c_1()
     , fib^#(s(0())) -> c_2()
     , fib^#(s(s(x))) -> c_3(sp^#(g(x)))
     , fib^#(s(s(0()))) -> c_4()
     , sp^#(pair(x, y)) -> c_5(+^#(x, y))
     , +^#(x, 0()) -> c_10(x)
     , +^#(x, s(y)) -> c_11(+^#(x, y))
     , g^#(0()) -> c_6()
     , g^#(s(x)) -> c_7(np^#(g(x)))
     , g^#(s(0())) -> c_8()
     , np^#(pair(x, y)) -> c_9(+^#(x, y), x) }
   Strict Trs:
     { fib(0()) -> 0()
     , fib(s(0())) -> s(0())
     , fib(s(s(x))) -> sp(g(x))
     , fib(s(s(0()))) -> s(0())
     , sp(pair(x, y)) -> +(x, y)
     , g(0()) -> pair(s(0()), 0())
     , g(s(x)) -> np(g(x))
     , g(s(0())) -> pair(s(0()), s(0()))
     , np(pair(x, y)) -> pair(+(x, y), x)
     , +(x, 0()) -> x
     , +(x, s(y)) -> s(+(x, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,4,8,10} by
   applications of Pre({1,2,4,8,10}) = {6,11}. Here rules are labeled
   as follows:
   
     DPs:
       { 1: fib^#(0()) -> c_1()
       , 2: fib^#(s(0())) -> c_2()
       , 3: fib^#(s(s(x))) -> c_3(sp^#(g(x)))
       , 4: fib^#(s(s(0()))) -> c_4()
       , 5: sp^#(pair(x, y)) -> c_5(+^#(x, y))
       , 6: +^#(x, 0()) -> c_10(x)
       , 7: +^#(x, s(y)) -> c_11(+^#(x, y))
       , 8: g^#(0()) -> c_6()
       , 9: g^#(s(x)) -> c_7(np^#(g(x)))
       , 10: g^#(s(0())) -> c_8()
       , 11: np^#(pair(x, y)) -> c_9(+^#(x, y), x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { fib^#(s(s(x))) -> c_3(sp^#(g(x)))
     , sp^#(pair(x, y)) -> c_5(+^#(x, y))
     , +^#(x, 0()) -> c_10(x)
     , +^#(x, s(y)) -> c_11(+^#(x, y))
     , g^#(s(x)) -> c_7(np^#(g(x)))
     , np^#(pair(x, y)) -> c_9(+^#(x, y), x) }
   Strict Trs:
     { fib(0()) -> 0()
     , fib(s(0())) -> s(0())
     , fib(s(s(x))) -> sp(g(x))
     , fib(s(s(0()))) -> s(0())
     , sp(pair(x, y)) -> +(x, y)
     , g(0()) -> pair(s(0()), 0())
     , g(s(x)) -> np(g(x))
     , g(s(0())) -> pair(s(0()), s(0()))
     , np(pair(x, y)) -> pair(+(x, y), x)
     , +(x, 0()) -> x
     , +(x, s(y)) -> s(+(x, y)) }
   Weak DPs:
     { fib^#(0()) -> c_1()
     , fib^#(s(0())) -> c_2()
     , fib^#(s(s(0()))) -> c_4()
     , g^#(0()) -> c_6()
     , g^#(s(0())) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..