YES(?,O(n^1)) 0.00/0.72 YES(?,O(n^1)) 0.00/0.72 0.00/0.72 We are left with following problem, upon which TcT provides the 0.00/0.72 certificate YES(?,O(n^1)). 0.00/0.72 0.00/0.72 Strict Trs: 0.00/0.72 { f(a()) -> f(c(a())) 0.00/0.72 , f(a()) -> f(d(a())) 0.00/0.72 , f(c(X)) -> X 0.00/0.72 , f(c(a())) -> f(d(b())) 0.00/0.72 , f(c(b())) -> f(d(a())) 0.00/0.72 , f(d(X)) -> X 0.00/0.72 , e(g(X)) -> e(X) } 0.00/0.72 Obligation: 0.00/0.72 innermost runtime complexity 0.00/0.72 Answer: 0.00/0.72 YES(?,O(n^1)) 0.00/0.72 0.00/0.72 The problem is match-bounded by 2. The enriched problem is 0.00/0.72 compatible with the following automaton. 0.00/0.72 { f_0(2) -> 1 0.00/0.72 , f_1(3) -> 1 0.00/0.72 , f_2(5) -> 1 0.00/0.72 , a_0() -> 1 0.00/0.72 , a_0() -> 2 0.00/0.72 , a_1() -> 1 0.00/0.72 , a_1() -> 4 0.00/0.72 , a_2() -> 1 0.00/0.72 , a_2() -> 6 0.00/0.72 , c_0(2) -> 1 0.00/0.72 , c_0(2) -> 2 0.00/0.72 , c_1(4) -> 3 0.00/0.72 , d_0(2) -> 1 0.00/0.72 , d_0(2) -> 2 0.00/0.72 , d_1(4) -> 3 0.00/0.72 , d_2(6) -> 5 0.00/0.72 , b_0() -> 1 0.00/0.72 , b_0() -> 2 0.00/0.72 , b_1() -> 1 0.00/0.72 , b_1() -> 4 0.00/0.72 , b_2() -> 1 0.00/0.72 , b_2() -> 6 0.00/0.72 , e_0(2) -> 1 0.00/0.72 , e_1(2) -> 1 0.00/0.72 , g_0(2) -> 1 0.00/0.72 , g_0(2) -> 2 } 0.00/0.72 0.00/0.72 Hurray, we answered YES(?,O(n^1)) 0.00/0.73 EOF