YES(?,O(n^1)) 4.08/1.26 YES(?,O(n^1)) 4.08/1.26 4.08/1.26 We are left with following problem, upon which TcT provides the 4.08/1.26 certificate YES(?,O(n^1)). 4.08/1.26 4.08/1.26 Strict Trs: 4.08/1.26 { f(a()) -> g(h(a())) 4.08/1.26 , h(g(x)) -> g(h(f(x))) 4.08/1.26 , k(x, h(x), a()) -> h(x) 4.08/1.26 , k(f(x), y, x) -> f(x) } 4.08/1.26 Obligation: 4.08/1.26 innermost runtime complexity 4.08/1.26 Answer: 4.08/1.26 YES(?,O(n^1)) 4.08/1.26 4.08/1.26 The problem is match-bounded by 2. The enriched problem is 4.08/1.26 compatible with the following automaton. 4.08/1.26 { f_0(2) -> 1 4.08/1.26 , f_0(3) -> 1 4.08/1.26 , f_1(2) -> 9 4.08/1.26 , f_1(3) -> 9 4.08/1.26 , f_2(6) -> 11 4.08/1.26 , a_0() -> 2 4.08/1.26 , a_1() -> 7 4.08/1.26 , g_0(2) -> 3 4.08/1.26 , g_0(3) -> 3 4.08/1.26 , g_1(6) -> 1 4.08/1.26 , g_1(6) -> 9 4.08/1.26 , g_1(8) -> 4 4.08/1.26 , g_2(10) -> 8 4.08/1.26 , h_0(2) -> 4 4.08/1.26 , h_0(3) -> 4 4.08/1.26 , h_1(7) -> 6 4.08/1.26 , h_1(9) -> 8 4.08/1.26 , h_2(11) -> 10 4.08/1.26 , k_0(2, 2, 2) -> 5 4.08/1.26 , k_0(2, 2, 3) -> 5 4.08/1.26 , k_0(2, 3, 2) -> 5 4.08/1.26 , k_0(2, 3, 3) -> 5 4.08/1.26 , k_0(3, 2, 2) -> 5 4.08/1.26 , k_0(3, 2, 3) -> 5 4.08/1.26 , k_0(3, 3, 2) -> 5 4.08/1.26 , k_0(3, 3, 3) -> 5 } 4.08/1.26 4.08/1.26 Hurray, we answered YES(?,O(n^1)) 4.08/1.26 EOF