YES(?,O(n^1)) 0.00/0.50 YES(?,O(n^1)) 0.00/0.50 0.00/0.50 We are left with following problem, upon which TcT provides the 0.00/0.50 certificate YES(?,O(n^1)). 0.00/0.50 0.00/0.50 Strict Trs: 0.00/0.50 { f(c(X, s(Y))) -> f(c(s(X), Y)) 0.00/0.50 , g(c(s(X), Y)) -> f(c(X, s(Y))) } 0.00/0.50 Obligation: 0.00/0.50 innermost runtime complexity 0.00/0.50 Answer: 0.00/0.50 YES(?,O(n^1)) 0.00/0.50 0.00/0.50 The problem is match-bounded by 2. The enriched problem is 0.00/0.50 compatible with the following automaton. 0.00/0.50 { f_0(2) -> 1 0.00/0.50 , f_0(3) -> 1 0.00/0.50 , f_1(5) -> 1 0.00/0.50 , f_1(7) -> 4 0.00/0.50 , f_2(8) -> 4 0.00/0.50 , c_0(2, 2) -> 2 0.00/0.50 , c_0(2, 3) -> 2 0.00/0.50 , c_0(3, 2) -> 2 0.00/0.50 , c_0(3, 3) -> 2 0.00/0.50 , c_1(2, 6) -> 7 0.00/0.50 , c_1(3, 6) -> 7 0.00/0.50 , c_1(6, 2) -> 5 0.00/0.50 , c_1(6, 3) -> 5 0.00/0.50 , c_1(10, 2) -> 7 0.00/0.50 , c_1(10, 3) -> 7 0.00/0.50 , c_2(9, 2) -> 8 0.00/0.50 , c_2(9, 3) -> 8 0.00/0.50 , c_2(9, 6) -> 8 0.00/0.50 , s_0(2) -> 3 0.00/0.50 , s_0(3) -> 3 0.00/0.50 , s_1(2) -> 6 0.00/0.50 , s_1(3) -> 6 0.00/0.50 , s_1(6) -> 6 0.00/0.50 , s_1(9) -> 10 0.00/0.50 , s_1(10) -> 10 0.00/0.50 , s_2(2) -> 9 0.00/0.50 , s_2(3) -> 9 0.00/0.50 , s_2(9) -> 9 0.00/0.50 , g_0(2) -> 4 0.00/0.50 , g_0(3) -> 4 } 0.00/0.50 0.00/0.50 Hurray, we answered YES(?,O(n^1)) 0.00/0.51 EOF