YES(?,O(n^1)) 766.39/297.07 YES(?,O(n^1)) 766.39/297.07 766.39/297.07 We are left with following problem, upon which TcT provides the 766.39/297.07 certificate YES(?,O(n^1)). 766.39/297.07 766.39/297.07 Strict Trs: 766.39/297.07 { f(a(), f(x, a())) -> f(f(x, f(f(a(), a()), a())), a()) } 766.39/297.07 Obligation: 766.39/297.07 derivational complexity 766.39/297.07 Answer: 766.39/297.07 YES(?,O(n^1)) 766.39/297.07 766.39/297.07 The problem is match-bounded by 1. The enriched problem is 766.39/297.07 compatible with the following automaton. 766.39/297.07 { f_0(1, 1) -> 1 766.39/297.07 , f_0(1, 2) -> 1 766.39/297.07 , f_0(2, 1) -> 1 766.39/297.07 , f_0(2, 2) -> 1 766.39/297.07 , f_1(1, 5) -> 3 766.39/297.07 , f_1(2, 5) -> 3 766.39/297.07 , f_1(3, 4) -> 1 766.39/297.07 , f_1(3, 5) -> 3 766.39/297.07 , f_1(6, 5) -> 10 766.39/297.07 , f_1(6, 7) -> 5 766.39/297.07 , f_1(8, 9) -> 6 766.39/297.07 , f_1(10, 9) -> 3 766.39/297.07 , a_0() -> 2 766.39/297.07 , a_1() -> 4 766.39/297.07 , a_1() -> 7 766.39/297.07 , a_1() -> 8 766.39/297.07 , a_1() -> 9 } 766.39/297.07 766.39/297.07 Hurray, we answered YES(?,O(n^1)) 766.51/297.17 EOF