MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { acka(y(), n) -> s(n) , acka(a(m), y()) -> acka(m, s(0())) , acka(a(m), a(n)) -> acka(m, ackb(s(m), n)) , s(n) -> a(n) , s(n) -> b(n) , 0() -> y() , 0() -> z() , ackb(z(), n) -> s(n) , ackb(b(m), z()) -> ackb(m, s(0())) , ackb(b(m), b(n)) -> acka(m, ackb(s(m), n)) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..