We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { f(0()) -> s(0()) , f(s(0())) -> s(0()) , f(s(s(x))) -> f(f(s(x))) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 2. The enriched problem is compatible with the following automaton. { f_0(2) -> 1 , f_1(4) -> 1 , f_1(4) -> 4 , f_1(5) -> 4 , 0_0() -> 2 , 0_1() -> 3 , 0_2() -> 6 , s_0(2) -> 2 , s_1(2) -> 5 , s_1(3) -> 1 , s_1(3) -> 4 , s_2(6) -> 1 , s_2(6) -> 4 } Hurray, we answered YES(?,O(n^1))