YES(?,O(n^1)) 6.94/1.83 YES(?,O(n^1)) 6.94/1.83 6.94/1.83 We are left with following problem, upon which TcT provides the 6.94/1.83 certificate YES(?,O(n^1)). 6.94/1.83 6.94/1.83 Strict Trs: 6.94/1.83 { f(f(x)) -> f(c(f(x))) 6.94/1.83 , f(f(x)) -> f(d(f(x))) 6.94/1.83 , g(c(x)) -> x 6.94/1.83 , g(c(h(0()))) -> g(d(1())) 6.94/1.83 , g(c(1())) -> g(d(h(0()))) 6.94/1.83 , g(d(x)) -> x 6.94/1.83 , g(h(x)) -> g(x) } 6.94/1.83 Obligation: 6.94/1.83 runtime complexity 6.94/1.83 Answer: 6.94/1.83 YES(?,O(n^1)) 6.94/1.83 6.94/1.83 The problem is match-bounded by 1. The enriched problem is 6.94/1.83 compatible with the following automaton. 6.94/1.83 { f_0(2) -> 1 6.94/1.83 , c_0(2) -> 1 6.94/1.83 , c_0(2) -> 2 6.94/1.83 , d_0(2) -> 1 6.94/1.83 , d_0(2) -> 2 6.94/1.83 , d_1(4) -> 3 6.94/1.83 , g_0(2) -> 1 6.94/1.83 , g_1(2) -> 1 6.94/1.83 , g_1(3) -> 1 6.94/1.83 , h_0(2) -> 1 6.94/1.83 , h_0(2) -> 2 6.94/1.83 , h_1(5) -> 1 6.94/1.83 , h_1(5) -> 4 6.94/1.83 , 0_0() -> 1 6.94/1.83 , 0_0() -> 2 6.94/1.83 , 0_1() -> 5 6.94/1.83 , 1_0() -> 1 6.94/1.83 , 1_0() -> 2 6.94/1.83 , 1_1() -> 1 6.94/1.83 , 1_1() -> 4 } 6.94/1.83 6.94/1.83 Hurray, we answered YES(?,O(n^1)) 6.94/1.83 EOF