MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { lt(0(), s(X)) -> true() , lt(s(X), 0()) -> false() , lt(s(X), s(Y)) -> lt(X, Y) , append(nil(), Y) -> Y , append(add(N, X), Y) -> add(N, append(X, Y)) , split(N, nil()) -> pair(nil(), nil()) , split(N, add(M, Y)) -> f_1(split(N, Y), N, M, Y) , f_1(pair(X, Z), N, M, Y) -> f_2(lt(N, M), N, M, Y, X, Z) , f_2(true(), N, M, Y, X, Z) -> pair(X, add(M, Z)) , f_2(false(), N, M, Y, X, Z) -> pair(add(M, X), Z) , qsort(nil()) -> nil() , qsort(add(N, X)) -> f_3(split(N, X), N, X) , f_3(pair(Y, Z), N, X) -> append(qsort(Y), add(X, qsort(Z))) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..