YES(?,O(n^3)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^3)). Strict Trs: { d(x) -> e(u(x)) , d(u(x)) -> c(x) , c(u(x)) -> b(x) , b(u(x)) -> a(e(x)) , v(e(x)) -> x } Obligation: innermost runtime complexity Answer: YES(?,O(n^3)) The input was oriented with the instance of 'Small Polynomial Path Order (PS)' as induced by the safe mapping safe(d) = {1}, safe(e) = {1}, safe(u) = {1}, safe(c) = {1}, safe(b) = {1}, safe(v) = {}, safe(a) = {1} and precedence d > c, d > b, c > b, v > c, v > b, d ~ v . Following symbols are considered recursive: {d, c, b} The recursion depth is 3. For your convenience, here are the satisfied ordering constraints: d(; x) > e(; u(; x)) d(; u(; x)) > c(; x) c(; u(; x)) > b(; x) b(; u(; x)) > a(; e(; x)) v(e(; x);) > x Hurray, we answered YES(?,O(n^3))