MAYBE

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

Strict Trs:
  { f(0()) -> 0()
  , f(s(0())) -> s(0())
  , f(s(s(x))) -> p(h(g(x)))
  , f(s(s(x))) -> +(p(g(x)), q(g(x)))
  , p(pair(x, y)) -> x
  , h(x) -> pair(+(p(x), q(x)), p(x))
  , g(0()) -> pair(s(0()), s(0()))
  , g(s(x)) -> h(g(x))
  , g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y))
  , q(pair(x, y)) -> y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..