YES(?,O(n^1)) 5.23/1.49 YES(?,O(n^1)) 5.23/1.49 5.23/1.49 We are left with following problem, upon which TcT provides the 5.23/1.49 certificate YES(?,O(n^1)). 5.23/1.49 5.23/1.49 Strict Trs: 5.23/1.49 { f(f(X)) -> f(a(b(f(X)))) 5.23/1.49 , f(a(g(X))) -> b(X) 5.23/1.49 , b(X) -> a(X) } 5.23/1.49 Obligation: 5.23/1.49 runtime complexity 5.23/1.49 Answer: 5.23/1.49 YES(?,O(n^1)) 5.23/1.49 5.23/1.49 The problem is match-bounded by 2. The enriched problem is 5.23/1.49 compatible with the following automaton. 5.23/1.49 { f_0(2) -> 1 5.23/1.49 , f_0(4) -> 1 5.23/1.49 , a_0(2) -> 2 5.23/1.49 , a_0(4) -> 2 5.23/1.49 , a_1(2) -> 3 5.23/1.49 , a_1(4) -> 3 5.23/1.49 , a_2(2) -> 1 5.23/1.49 , a_2(4) -> 1 5.23/1.49 , b_0(2) -> 3 5.23/1.49 , b_0(4) -> 3 5.23/1.49 , b_1(2) -> 1 5.23/1.49 , b_1(4) -> 1 5.23/1.49 , g_0(2) -> 4 5.23/1.49 , g_0(4) -> 4 } 5.23/1.49 5.23/1.49 Hurray, we answered YES(?,O(n^1)) 5.23/1.49 EOF