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