MAYBE

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
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Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  lt(0(), s(x)) -> true()
     , lt(x, 0()) -> false()
     , 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())
     , 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))
     , sum(x, 0()) -> x
     , sum(x, s(y)) -> s(sum(x, y))}

Proof Output:    
  The input cannot be shown compatible