MAYBE

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  double(x) -> permute(x, x, a())
     , permute(x, y, a()) -> permute(isZero(x), x, b())
     , permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
     , permute(true(), x, b()) -> 0()
     , permute(y, x, c()) -> s(s(permute(x, y, a())))
     , p(0()) -> 0()
     , p(s(x)) -> x
     , ack(0(), x) -> plus(x, s(0()))
     , ack(s(x), 0()) -> ack(x, s(0()))
     , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
     , plus(0(), y) -> y
     , plus(s(x), y) -> plus(x, s(y))
     , plus(x, s(s(y))) -> s(plus(s(x), y))
     , plus(x, s(0())) -> s(x)
     , plus(x, 0()) -> x
     , isZero(0()) -> true()
     , isZero(s(x)) -> false()}

Proof Output:    
  The input cannot be shown compatible