MAYBE

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

Strict Trs:
  { battle(H(H(H(0(), x), y), z), n) ->
    battle(H(f(x, y, n), z), s(n))
  , battle(H(H(0(), x), y), n) -> battle(f(x, y, n), s(n))
  , battle(H(0(), x), n) -> battle(x, s(n))
  , f(x, y, s(n)) -> H(x, f(x, y, n))
  , f(x, y, o()) -> y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..