We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) , revapp(Nil(), rest) -> rest , goal(xs, ys) -> revapp(xs, ys) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The input was oriented with the instance of 'Small Polynomial Path Order (PS,1-bounded)' as induced by the safe mapping safe(revapp) = {2}, safe(Cons) = {1, 2}, safe(Nil) = {}, safe(goal) = {} and precedence goal > revapp . Following symbols are considered recursive: {revapp} The recursion depth is 1. For your convenience, here are the satisfied ordering constraints: revapp(Cons(; x, xs); rest) > revapp(xs; Cons(; x, rest)) revapp(Nil(); rest) > rest goal(xs, ys;) > revapp(xs; ys) Hurray, we answered YES(?,O(n^1))