YES(?,O(n^1)) 0.00/0.26 YES(?,O(n^1)) 0.00/0.26 0.00/0.26 We are left with following problem, upon which TcT provides the 0.00/0.26 certificate YES(?,O(n^1)). 0.00/0.26 0.00/0.26 Strict Trs: 0.00/0.26 { a__g(X) -> a__h(X) 0.00/0.26 , a__g(X) -> g(X) 0.00/0.26 , a__h(X) -> h(X) 0.00/0.26 , a__h(d()) -> a__g(c()) 0.00/0.26 , a__c() -> d() 0.00/0.26 , a__c() -> c() 0.00/0.26 , mark(d()) -> d() 0.00/0.26 , mark(c()) -> a__c() 0.00/0.26 , mark(g(X)) -> a__g(X) 0.00/0.26 , mark(h(X)) -> a__h(X) } 0.00/0.26 Obligation: 0.00/0.26 innermost runtime complexity 0.00/0.26 Answer: 0.00/0.26 YES(?,O(n^1)) 0.00/0.26 0.00/0.26 The problem is match-bounded by 3. The enriched problem is 0.00/0.26 compatible with the following automaton. 0.00/0.26 { a__g_0(4) -> 1 0.00/0.26 , a__g_0(5) -> 1 0.00/0.26 , a__g_0(7) -> 1 0.00/0.26 , a__g_0(8) -> 1 0.00/0.26 , a__g_1(4) -> 6 0.00/0.26 , a__g_1(5) -> 6 0.00/0.26 , a__g_1(7) -> 6 0.00/0.26 , a__g_1(8) -> 6 0.00/0.26 , a__g_1(9) -> 1 0.00/0.26 , a__g_1(9) -> 2 0.00/0.26 , a__g_1(9) -> 6 0.00/0.26 , a__h_0(4) -> 2 0.00/0.26 , a__h_0(5) -> 2 0.00/0.26 , a__h_0(7) -> 2 0.00/0.26 , a__h_0(8) -> 2 0.00/0.26 , a__h_1(4) -> 1 0.00/0.26 , a__h_1(4) -> 6 0.00/0.26 , a__h_1(5) -> 1 0.00/0.26 , a__h_1(5) -> 6 0.00/0.26 , a__h_1(7) -> 1 0.00/0.26 , a__h_1(7) -> 6 0.00/0.26 , a__h_1(8) -> 1 0.00/0.26 , a__h_1(8) -> 6 0.00/0.26 , a__h_2(4) -> 6 0.00/0.26 , a__h_2(5) -> 6 0.00/0.26 , a__h_2(7) -> 6 0.00/0.26 , a__h_2(8) -> 6 0.00/0.26 , a__h_2(9) -> 1 0.00/0.26 , a__h_2(9) -> 2 0.00/0.26 , a__h_2(9) -> 6 0.00/0.26 , a__c_0() -> 3 0.00/0.26 , a__c_1() -> 6 0.00/0.26 , d_0() -> 4 0.00/0.26 , d_1() -> 3 0.00/0.26 , d_1() -> 6 0.00/0.26 , d_2() -> 6 0.00/0.26 , c_0() -> 5 0.00/0.26 , c_1() -> 3 0.00/0.26 , c_1() -> 9 0.00/0.26 , c_2() -> 6 0.00/0.26 , mark_0(4) -> 6 0.00/0.26 , mark_0(5) -> 6 0.00/0.26 , mark_0(7) -> 6 0.00/0.26 , mark_0(8) -> 6 0.00/0.26 , g_0(4) -> 7 0.00/0.26 , g_0(5) -> 7 0.00/0.26 , g_0(7) -> 7 0.00/0.26 , g_0(8) -> 7 0.00/0.26 , g_1(4) -> 1 0.00/0.26 , g_1(5) -> 1 0.00/0.26 , g_1(7) -> 1 0.00/0.26 , g_1(8) -> 1 0.00/0.26 , g_2(4) -> 6 0.00/0.26 , g_2(5) -> 6 0.00/0.26 , g_2(7) -> 6 0.00/0.26 , g_2(8) -> 6 0.00/0.26 , g_2(9) -> 1 0.00/0.26 , g_2(9) -> 2 0.00/0.26 , g_2(9) -> 6 0.00/0.26 , h_0(4) -> 8 0.00/0.26 , h_0(5) -> 8 0.00/0.26 , h_0(7) -> 8 0.00/0.26 , h_0(8) -> 8 0.00/0.26 , h_1(4) -> 2 0.00/0.26 , h_1(5) -> 2 0.00/0.26 , h_1(7) -> 2 0.00/0.26 , h_1(8) -> 2 0.00/0.26 , h_2(4) -> 1 0.00/0.26 , h_2(4) -> 6 0.00/0.26 , h_2(5) -> 1 0.00/0.26 , h_2(5) -> 6 0.00/0.26 , h_2(7) -> 1 0.00/0.26 , h_2(7) -> 6 0.00/0.26 , h_2(8) -> 1 0.00/0.26 , h_2(8) -> 6 0.00/0.26 , h_3(4) -> 6 0.00/0.26 , h_3(5) -> 6 0.00/0.26 , h_3(7) -> 6 0.00/0.26 , h_3(8) -> 6 0.00/0.26 , h_3(9) -> 1 0.00/0.26 , h_3(9) -> 2 0.00/0.26 , h_3(9) -> 6 } 0.00/0.26 0.00/0.26 Hurray, we answered YES(?,O(n^1)) 0.00/0.27 EOF