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