TIMEOUT We are left with following problem, upon which TcT provides the certificate TIMEOUT. Strict Trs: { isEmpty(cons(x, xs)) -> false() , isEmpty(nil()) -> true() , isZero(0()) -> true() , isZero(s(x)) -> false() , head(cons(x, xs)) -> x , tail(cons(x, xs)) -> xs , tail(nil()) -> nil() , append(cons(y, ys), x) -> cons(y, append(ys, x)) , append(nil(), x) -> cons(x, nil()) , p(0()) -> 0() , p(s(0())) -> 0() , p(s(s(x))) -> s(p(s(x))) , inc(0()) -> s(0()) , inc(s(x)) -> s(inc(x)) , addLists(xs, ys, zs) -> if(isEmpty(xs), isEmpty(ys), isZero(head(xs)), tail(xs), tail(ys), cons(p(head(xs)), tail(xs)), cons(inc(head(ys)), tail(ys)), zs, append(zs, head(ys))) , if(false(), false(), false(), xs, ys, xs2, ys2, zs, zs2) -> addLists(xs2, ys2, zs) , if(false(), false(), true(), xs, ys, xs2, ys2, zs, zs2) -> addLists(xs, ys, zs2) , if(false(), true(), b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError() , if(true(), false(), b, xs, ys, xs2, ys2, zs, zs2) -> differentLengthError() , if(true(), true(), b, xs, ys, xs2, ys2, zs, zs2) -> zs , addList(xs, ys) -> addLists(xs, ys, nil()) } Obligation: innermost runtime complexity Answer: TIMEOUT Computation stopped due to timeout after 60.0 seconds. Arrrr..