YES(?,POLY) We are left with following problem, upon which TcT provides the certificate YES(?,POLY). Strict Trs: { f(g(x), y, y) -> g(f(x, x, y)) } Obligation: innermost runtime complexity Answer: YES(?,POLY) The input was oriented with the instance of 'Polynomial Path Order' as induced by the safe mapping safe(f) = {3}, 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), y; y) > g(; f(x, x; y)) Hurray, we answered YES(?,POLY)