YES(?,O(n^2)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^2)). Strict Trs: { p(0()) -> 0() , p(s(x)) -> x , minus(x, 0()) -> x , minus(x, s(y)) -> minus(p(x), y) } Obligation: innermost runtime complexity Answer: YES(?,O(n^2)) The input was oriented with the instance of 'Small Polynomial Path Order (PS)' as induced by the safe mapping safe(p) = {1}, safe(0) = {}, safe(s) = {1}, safe(minus) = {1} and precedence minus > p . Following symbols are considered recursive: {p, minus} The recursion depth is 2. For your convenience, here are the satisfied ordering constraints: p(; 0()) > 0() p(; s(; x)) > x minus(0(); x) > x minus(s(; y); x) > minus(y; p(; x)) Hurray, we answered YES(?,O(n^2))