MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { cond1(true(), x, y) -> cond2(gr(x, 0()), x, y) , cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y) , cond2(false(), x, y) -> cond3(gr(y, 0()), x, y) , gr(0(), x) -> false() , gr(s(x), 0()) -> true() , gr(s(x), s(y)) -> gr(x, y) , add(0(), x) -> x , add(s(x), y) -> s(add(x, y)) , p(0()) -> 0() , p(s(x)) -> x , cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)) , cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..