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__c() -> a__f(g(c())) 0.00/0.48 , a__c() -> c() 0.00/0.48 , a__f(X) -> f(X) 0.00/0.48 , a__f(g(X)) -> g(X) 0.00/0.48 , mark(g(X)) -> g(X) 0.00/0.48 , mark(c()) -> a__c() 0.00/0.48 , mark(f(X)) -> a__f(X) } 0.00/0.48 Obligation: 0.00/0.48 derivational 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__c_0() -> 1 0.00/0.48 , a__c_1() -> 1 0.00/0.48 , a__f_0(1) -> 1 0.00/0.48 , a__f_1(1) -> 1 0.00/0.48 , a__f_1(2) -> 1 0.00/0.48 , a__f_1(4) -> 1 0.00/0.48 , a__f_2(4) -> 1 0.00/0.48 , g_0(1) -> 1 0.00/0.48 , g_1(1) -> 1 0.00/0.48 , g_1(3) -> 1 0.00/0.48 , g_1(3) -> 2 0.00/0.48 , g_1(5) -> 1 0.00/0.48 , g_2(1) -> 1 0.00/0.48 , g_2(3) -> 1 0.00/0.48 , g_2(5) -> 1 0.00/0.48 , g_2(5) -> 4 0.00/0.48 , g_3(5) -> 1 0.00/0.48 , c_0() -> 1 0.00/0.48 , c_1() -> 1 0.00/0.48 , c_1() -> 3 0.00/0.48 , c_2() -> 1 0.00/0.48 , c_2() -> 5 0.00/0.48 , mark_0(1) -> 1 0.00/0.48 , f_0(1) -> 1 0.00/0.48 , f_1(1) -> 1 0.00/0.48 , f_2(1) -> 1 0.00/0.48 , f_2(2) -> 1 0.00/0.48 , f_2(4) -> 1 0.00/0.48 , f_3(4) -> 1 } 0.00/0.48 0.00/0.48 Hurray, we answered YES(?,O(n^1)) 0.00/0.48 EOF