YES(?,O(n^1)) 726.28/297.10 YES(?,O(n^1)) 726.28/297.10 726.28/297.10 We are left with following problem, upon which TcT provides the 726.28/297.10 certificate YES(?,O(n^1)). 726.28/297.10 726.28/297.10 Strict Trs: 726.28/297.10 { f(f(x, a()), a()) -> f(f(f(a(), f(a(), a())), a()), x) } 726.28/297.10 Obligation: 726.28/297.10 derivational complexity 726.28/297.10 Answer: 726.28/297.10 YES(?,O(n^1)) 726.28/297.10 726.28/297.10 The problem is match-bounded by 1. The enriched problem is 726.28/297.10 compatible with the following automaton. 726.28/297.10 { f_0(1, 1) -> 1 726.28/297.10 , f_0(1, 2) -> 1 726.28/297.10 , f_0(2, 1) -> 1 726.28/297.10 , f_0(2, 2) -> 1 726.28/297.10 , f_1(3, 1) -> 1 726.28/297.10 , f_1(3, 2) -> 1 726.28/297.10 , f_1(3, 3) -> 1 726.28/297.10 , f_1(3, 4) -> 1 726.28/297.10 , f_1(4, 5) -> 3 726.28/297.10 , f_1(6, 7) -> 4 726.28/297.10 , f_1(8, 9) -> 7 726.28/297.10 , a_0() -> 2 726.28/297.10 , a_1() -> 5 726.28/297.10 , a_1() -> 6 726.28/297.10 , a_1() -> 8 726.28/297.10 , a_1() -> 9 } 726.28/297.10 726.28/297.10 Hurray, we answered YES(?,O(n^1)) 726.28/297.18 EOF