YES(?,O(n^1)) 0.00/0.28 YES(?,O(n^1)) 0.00/0.28 0.00/0.28 We are left with following problem, upon which TcT provides the 0.00/0.28 certificate YES(?,O(n^1)). 0.00/0.28 0.00/0.28 Strict Trs: 0.00/0.28 { f(X) -> n__f(X) 0.00/0.28 , f(f(a())) -> c(n__f(g(f(a())))) 0.00/0.28 , activate(X) -> X 0.00/0.28 , activate(n__f(X)) -> f(X) } 0.00/0.28 Obligation: 0.00/0.28 runtime complexity 0.00/0.28 Answer: 0.00/0.28 YES(?,O(n^1)) 0.00/0.28 0.00/0.28 The problem is match-bounded by 2. The enriched problem is 0.00/0.28 compatible with the following automaton. 0.00/0.28 { f_0(2) -> 1 0.00/0.28 , f_0(3) -> 1 0.00/0.28 , f_0(4) -> 1 0.00/0.28 , f_0(5) -> 1 0.00/0.28 , f_1(2) -> 6 0.00/0.28 , f_1(3) -> 6 0.00/0.28 , f_1(4) -> 6 0.00/0.28 , f_1(5) -> 6 0.00/0.28 , a_0() -> 2 0.00/0.28 , a_0() -> 6 0.00/0.28 , c_0(2) -> 3 0.00/0.28 , c_0(2) -> 6 0.00/0.28 , c_0(3) -> 3 0.00/0.28 , c_0(3) -> 6 0.00/0.28 , c_0(4) -> 3 0.00/0.28 , c_0(4) -> 6 0.00/0.28 , c_0(5) -> 3 0.00/0.28 , c_0(5) -> 6 0.00/0.28 , n__f_0(2) -> 4 0.00/0.28 , n__f_0(2) -> 6 0.00/0.28 , n__f_0(3) -> 4 0.00/0.28 , n__f_0(3) -> 6 0.00/0.28 , n__f_0(4) -> 4 0.00/0.28 , n__f_0(4) -> 6 0.00/0.28 , n__f_0(5) -> 4 0.00/0.28 , n__f_0(5) -> 6 0.00/0.28 , n__f_1(2) -> 1 0.00/0.28 , n__f_1(3) -> 1 0.00/0.28 , n__f_1(4) -> 1 0.00/0.28 , n__f_1(5) -> 1 0.00/0.28 , n__f_2(2) -> 6 0.00/0.28 , n__f_2(3) -> 6 0.00/0.28 , n__f_2(4) -> 6 0.00/0.28 , n__f_2(5) -> 6 0.00/0.28 , g_0(2) -> 5 0.00/0.28 , g_0(2) -> 6 0.00/0.28 , g_0(3) -> 5 0.00/0.28 , g_0(3) -> 6 0.00/0.28 , g_0(4) -> 5 0.00/0.28 , g_0(4) -> 6 0.00/0.28 , g_0(5) -> 5 0.00/0.28 , g_0(5) -> 6 0.00/0.28 , activate_0(2) -> 6 0.00/0.28 , activate_0(3) -> 6 0.00/0.28 , activate_0(4) -> 6 0.00/0.28 , activate_0(5) -> 6 } 0.00/0.28 0.00/0.28 Hurray, we answered YES(?,O(n^1)) 0.00/0.28 EOF