MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { plus(x, s(s(y))) -> s(plus(s(x), y)) , plus(s(s(x)), y) -> s(plus(x, s(y))) , plus(s(0()), y) -> s(y) , plus(0(), y) -> y , ack(s(x), s(y)) -> ack(x, plus(y, ack(s(x), y))) , ack(s(x), 0()) -> ack(x, s(0())) , ack(0(), y) -> s(y) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..