YES(?,O(n^1)) 0.00/0.48 YES(?,O(n^1)) 0.00/0.48 0.00/0.48 We are left with following problem, upon which TcT provides the 0.00/0.48 certificate YES(?,O(n^1)). 0.00/0.48 0.00/0.48 Strict Trs: 0.00/0.48 { a__f(X) -> f(X) 0.00/0.48 , a__f(f(a())) -> a__f(g(f(a()))) 0.00/0.48 , mark(f(X)) -> a__f(mark(X)) 0.00/0.48 , mark(a()) -> a() 0.00/0.48 , mark(g(X)) -> g(X) } 0.00/0.48 Obligation: 0.00/0.48 innermost runtime complexity 0.00/0.48 Answer: 0.00/0.48 YES(?,O(n^1)) 0.00/0.48 0.00/0.48 The problem is match-bounded by 3. The enriched problem is 0.00/0.48 compatible with the following automaton. 0.00/0.48 { a__f_0(2) -> 1 0.00/0.48 , a__f_1(3) -> 1 0.00/0.48 , a__f_1(3) -> 3 0.00/0.48 , a__f_2(6) -> 1 0.00/0.48 , a__f_2(6) -> 3 0.00/0.48 , f_0(2) -> 2 0.00/0.48 , f_1(2) -> 1 0.00/0.48 , f_1(5) -> 4 0.00/0.48 , f_2(3) -> 1 0.00/0.48 , f_2(3) -> 3 0.00/0.48 , f_2(8) -> 7 0.00/0.48 , f_3(6) -> 1 0.00/0.48 , f_3(6) -> 3 0.00/0.48 , a_0() -> 2 0.00/0.48 , a_1() -> 1 0.00/0.48 , a_1() -> 3 0.00/0.48 , a_1() -> 5 0.00/0.48 , a_2() -> 8 0.00/0.48 , g_0(2) -> 2 0.00/0.48 , g_1(2) -> 1 0.00/0.48 , g_1(2) -> 3 0.00/0.48 , g_1(4) -> 3 0.00/0.48 , g_2(7) -> 6 0.00/0.48 , mark_0(2) -> 1 0.00/0.48 , mark_1(2) -> 3 } 0.00/0.48 0.00/0.48 Hurray, we answered YES(?,O(n^1)) 0.00/0.49 EOF