YES(?,O(n^1)) 4.41/1.25 YES(?,O(n^1)) 4.41/1.25 4.41/1.25 We are left with following problem, upon which TcT provides the 4.41/1.25 certificate YES(?,O(n^1)). 4.41/1.25 4.41/1.25 Strict Trs: 4.41/1.25 { f(f(x)) -> f(c(f(x))) 4.41/1.25 , f(f(x)) -> f(d(f(x))) 4.41/1.25 , g(c(x)) -> x 4.41/1.25 , g(c(0())) -> g(d(1())) 4.41/1.25 , g(c(1())) -> g(d(0())) 4.41/1.25 , g(d(x)) -> x } 4.41/1.25 Obligation: 4.41/1.25 runtime complexity 4.41/1.25 Answer: 4.41/1.25 YES(?,O(n^1)) 4.41/1.25 4.41/1.25 The problem is match-bounded by 1. The enriched problem is 4.41/1.25 compatible with the following automaton. 4.41/1.25 { f_0(2) -> 1 4.41/1.25 , c_0(2) -> 1 4.41/1.25 , c_0(2) -> 2 4.41/1.25 , d_0(2) -> 1 4.41/1.25 , d_0(2) -> 2 4.41/1.25 , d_1(4) -> 3 4.41/1.25 , g_0(2) -> 1 4.41/1.25 , g_1(3) -> 1 4.41/1.25 , 0_0() -> 1 4.41/1.25 , 0_0() -> 2 4.41/1.25 , 0_1() -> 1 4.41/1.25 , 0_1() -> 4 4.41/1.25 , 1_0() -> 1 4.41/1.25 , 1_0() -> 2 4.41/1.25 , 1_1() -> 1 4.41/1.25 , 1_1() -> 4 } 4.41/1.25 4.41/1.25 Hurray, we answered YES(?,O(n^1)) 4.41/1.26 EOF