MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { nats() -> adx(zeros()) , adx(X) -> n__adx(X) , adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) , zeros() -> cons(n__0(), n__zeros()) , zeros() -> n__zeros() , incr(X) -> n__incr(X) , incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) , activate(X) -> X , activate(n__0()) -> 0() , activate(n__zeros()) -> zeros() , activate(n__s(X)) -> s(X) , activate(n__incr(X)) -> incr(X) , activate(n__adx(X)) -> adx(X) , hd(cons(X, Y)) -> activate(X) , tl(cons(X, Y)) -> activate(Y) , 0() -> n__0() , s(X) -> n__s(X) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..