MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { a__from(X) -> cons(mark(X), from(s(X))) , a__from(X) -> from(X) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(from(X)) -> a__from(mark(X)) , mark(s(X)) -> s(mark(X)) , mark(0()) -> 0() , mark(nil()) -> nil() , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2)) , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2)) , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2)) , a__sel(X1, X2) -> sel(X1, X2) , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS)) , a__sel(0(), cons(X, XS)) -> mark(X) , a__minus(X1, X2) -> minus(X1, X2) , a__minus(X, 0()) -> 0() , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y)) , a__quot(X1, X2) -> quot(X1, X2) , a__quot(s(X), s(Y)) -> s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y)))) , a__quot(0(), s(Y)) -> 0() , a__zWquot(X1, X2) -> zWquot(X1, X2) , a__zWquot(XS, nil()) -> nil() , a__zWquot(cons(X, XS), cons(Y, YS)) -> cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS)) , a__zWquot(nil(), XS) -> nil() } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..