YES(?,O(n^1)) 743.78/297.02 YES(?,O(n^1)) 743.78/297.02 743.78/297.02 We are left with following problem, upon which TcT provides the 743.78/297.02 certificate YES(?,O(n^1)). 743.78/297.02 743.78/297.02 Strict Trs: 743.78/297.02 { f(f(x, a()), a()) -> f(f(f(x, a()), f(a(), a())), a()) } 743.78/297.02 Obligation: 743.78/297.02 derivational complexity 743.78/297.02 Answer: 743.78/297.02 YES(?,O(n^1)) 743.78/297.02 743.78/297.02 The problem is match-bounded by 2. The enriched problem is 743.78/297.02 compatible with the following automaton. 743.78/297.02 { f_0(1, 1) -> 1 743.78/297.02 , f_0(1, 2) -> 1 743.78/297.02 , f_0(2, 1) -> 1 743.78/297.02 , f_0(2, 2) -> 1 743.78/297.02 , f_1(1, 9) -> 5 743.78/297.02 , f_1(2, 9) -> 5 743.78/297.02 , f_1(3, 4) -> 1 743.78/297.02 , f_1(3, 9) -> 5 743.78/297.02 , f_1(5, 6) -> 3 743.78/297.02 , f_1(7, 8) -> 6 743.78/297.02 , f_2(3, 16) -> 12 743.78/297.02 , f_2(10, 11) -> 5 743.78/297.02 , f_2(12, 13) -> 10 743.78/297.02 , f_2(14, 15) -> 13 743.78/297.02 , a_0() -> 2 743.78/297.02 , a_1() -> 4 743.78/297.02 , a_1() -> 7 743.78/297.02 , a_1() -> 8 743.78/297.02 , a_1() -> 9 743.78/297.02 , a_2() -> 11 743.78/297.02 , a_2() -> 14 743.78/297.02 , a_2() -> 15 743.78/297.02 , a_2() -> 16 } 743.78/297.02 743.78/297.02 Hurray, we answered YES(?,O(n^1)) 743.91/297.15 EOF