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