YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { f(s(X), Y) -> h(s(f(h(Y), X))) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 1. The enriched problem is compatible with the following automaton. { f_0(2, 2) -> 1 , f_1(5, 2) -> 4 , s_0(2) -> 2 , s_1(4) -> 3 , h_0(2) -> 2 , h_1(2) -> 5 , h_1(3) -> 1 } Hurray, we answered YES(?,O(n^1))