YES(?,O(n^1)) 31.64/12.71 YES(?,O(n^1)) 31.64/12.71 31.64/12.71 We are left with following problem, upon which TcT provides the 31.64/12.71 certificate YES(?,O(n^1)). 31.64/12.71 31.64/12.71 Strict Trs: 31.64/12.71 { f(f(x)) -> f(c(f(x))) 31.64/12.71 , f(f(x)) -> f(d(f(x))) 31.64/12.71 , g(c(x)) -> x 31.64/12.71 , g(c(h(0()))) -> g(d(1())) 31.64/12.71 , g(c(1())) -> g(d(h(0()))) 31.64/12.71 , g(d(x)) -> x 31.64/12.71 , g(h(x)) -> g(x) } 31.64/12.71 Obligation: 31.64/12.71 derivational complexity 31.64/12.71 Answer: 31.64/12.71 YES(?,O(n^1)) 31.64/12.71 31.64/12.71 The problem is match-bounded by 2. The enriched problem is 31.64/12.71 compatible with the following automaton. 31.64/12.71 { f_0(1) -> 1 31.64/12.71 , f_1(1) -> 3 31.64/12.71 , f_1(2) -> 1 31.64/12.71 , f_1(2) -> 3 31.64/12.71 , f_2(2) -> 5 31.64/12.71 , f_2(4) -> 3 31.64/12.71 , c_0(1) -> 1 31.64/12.71 , c_1(3) -> 2 31.64/12.71 , c_2(5) -> 4 31.64/12.71 , d_0(1) -> 1 31.64/12.71 , d_1(3) -> 2 31.64/12.71 , d_1(7) -> 6 31.64/12.71 , d_2(5) -> 4 31.64/12.71 , g_0(1) -> 1 31.64/12.71 , g_1(1) -> 1 31.64/12.71 , g_1(6) -> 1 31.64/12.71 , g_1(8) -> 1 31.64/12.71 , g_2(8) -> 1 31.64/12.71 , h_0(1) -> 1 31.64/12.71 , h_1(8) -> 1 31.64/12.71 , h_1(8) -> 7 31.64/12.71 , 0_0() -> 1 31.64/12.71 , 0_1() -> 8 31.64/12.71 , 1_0() -> 1 31.64/12.71 , 1_1() -> 1 31.64/12.71 , 1_1() -> 7 } 31.64/12.71 31.64/12.71 Hurray, we answered YES(?,O(n^1)) 31.64/12.73 EOF