YES(?,O(n^1)) 0.00/0.29 YES(?,O(n^1)) 0.00/0.29 0.00/0.29 We are left with following problem, upon which TcT provides the 0.00/0.29 certificate YES(?,O(n^1)). 0.00/0.29 0.00/0.29 Strict Trs: 0.00/0.29 { a__g(X) -> a__h(X) 0.00/0.29 , a__g(X) -> g(X) 0.00/0.29 , a__h(X) -> h(X) 0.00/0.29 , a__h(d()) -> a__g(c()) 0.00/0.29 , a__c() -> d() 0.00/0.29 , a__c() -> c() 0.00/0.29 , mark(d()) -> d() 0.00/0.29 , mark(c()) -> a__c() 0.00/0.29 , mark(g(X)) -> a__g(X) 0.00/0.29 , mark(h(X)) -> a__h(X) } 0.00/0.29 Obligation: 0.00/0.29 runtime complexity 0.00/0.29 Answer: 0.00/0.29 YES(?,O(n^1)) 0.00/0.29 0.00/0.29 The input is overlay and right-linear. Switching to innermost 0.00/0.29 rewriting. 0.00/0.29 0.00/0.29 We are left with following problem, upon which TcT provides the 0.00/0.29 certificate YES(?,O(n^1)). 0.00/0.29 0.00/0.29 Strict Trs: 0.00/0.29 { a__g(X) -> a__h(X) 0.00/0.29 , a__g(X) -> g(X) 0.00/0.29 , a__h(X) -> h(X) 0.00/0.29 , a__h(d()) -> a__g(c()) 0.00/0.29 , a__c() -> d() 0.00/0.29 , a__c() -> c() 0.00/0.29 , mark(d()) -> d() 0.00/0.29 , mark(c()) -> a__c() 0.00/0.29 , mark(g(X)) -> a__g(X) 0.00/0.29 , mark(h(X)) -> a__h(X) } 0.00/0.29 Obligation: 0.00/0.29 innermost runtime complexity 0.00/0.29 Answer: 0.00/0.29 YES(?,O(n^1)) 0.00/0.29 0.00/0.29 The problem is match-bounded by 3. The enriched problem is 0.00/0.29 compatible with the following automaton. 0.00/0.29 { a__g_0(2) -> 1 0.00/0.29 , a__g_1(2) -> 1 0.00/0.29 , a__g_1(3) -> 1 0.00/0.29 , a__h_0(2) -> 1 0.00/0.29 , a__h_1(2) -> 1 0.00/0.29 , a__h_2(2) -> 1 0.00/0.29 , a__h_2(3) -> 1 0.00/0.29 , a__c_0() -> 1 0.00/0.29 , a__c_1() -> 1 0.00/0.29 , d_0() -> 2 0.00/0.29 , d_1() -> 1 0.00/0.29 , d_2() -> 1 0.00/0.29 , c_0() -> 2 0.00/0.29 , c_1() -> 1 0.00/0.29 , c_1() -> 3 0.00/0.29 , c_2() -> 1 0.00/0.29 , mark_0(2) -> 1 0.00/0.29 , g_0(2) -> 2 0.00/0.29 , g_1(2) -> 1 0.00/0.29 , g_2(2) -> 1 0.00/0.29 , g_2(3) -> 1 0.00/0.29 , h_0(2) -> 2 0.00/0.29 , h_1(2) -> 1 0.00/0.29 , h_2(2) -> 1 0.00/0.29 , h_3(2) -> 1 0.00/0.29 , h_3(3) -> 1 } 0.00/0.29 0.00/0.29 Hurray, we answered YES(?,O(n^1)) 0.00/0.29 EOF