YES(?,O(n^1)) 14.23/4.50 YES(?,O(n^1)) 14.23/4.50 14.23/4.50 We are left with following problem, upon which TcT provides the 14.23/4.50 certificate YES(?,O(n^1)). 14.23/4.50 14.23/4.50 Strict Trs: 14.23/4.50 { h(x, c(y, z)) -> h(c(s(y), x), z) 14.23/4.50 , h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z))) } 14.23/4.50 Obligation: 14.23/4.50 runtime complexity 14.23/4.50 Answer: 14.23/4.50 YES(?,O(n^1)) 14.23/4.50 14.23/4.50 The input is overlay and right-linear. Switching to innermost 14.23/4.50 rewriting. 14.23/4.50 14.23/4.50 We are left with following problem, upon which TcT provides the 14.23/4.50 certificate YES(?,O(n^1)). 14.23/4.50 14.23/4.50 Strict Trs: 14.23/4.50 { h(x, c(y, z)) -> h(c(s(y), x), z) 14.23/4.50 , h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z))) } 14.23/4.50 Obligation: 14.23/4.50 innermost runtime complexity 14.23/4.50 Answer: 14.23/4.50 YES(?,O(n^1)) 14.23/4.50 14.23/4.50 The problem is match-bounded by 2. The enriched problem is 14.23/4.50 compatible with the following automaton. 14.23/4.50 { h_0(2, 2) -> 1 14.23/4.50 , h_1(2, 5) -> 1 14.23/4.50 , h_1(3, 2) -> 1 14.23/4.50 , h_1(3, 5) -> 1 14.23/4.50 , h_1(9, 5) -> 1 14.23/4.50 , h_1(11, 5) -> 1 14.23/4.50 , h_2(9, 5) -> 1 14.23/4.50 , h_2(9, 7) -> 1 14.23/4.50 , h_2(11, 2) -> 1 14.23/4.50 , h_2(11, 5) -> 1 14.23/4.50 , c_0(2, 2) -> 2 14.23/4.50 , c_1(2, 2) -> 7 14.23/4.50 , c_1(2, 5) -> 7 14.23/4.50 , c_1(4, 2) -> 3 14.23/4.50 , c_1(4, 3) -> 3 14.23/4.50 , c_1(4, 11) -> 3 14.23/4.50 , c_1(6, 5) -> 5 14.23/4.50 , c_1(6, 7) -> 5 14.23/4.51 , c_2(10, 2) -> 9 14.23/4.51 , c_2(10, 3) -> 9 14.23/4.51 , c_2(10, 9) -> 9 14.23/4.51 , c_2(10, 11) -> 9 14.23/4.51 , c_2(12, 9) -> 11 14.23/4.51 , s_0(2) -> 2 14.23/4.51 , s_1(2) -> 4 14.23/4.51 , s_1(8) -> 6 14.23/4.51 , s_2(2) -> 12 14.23/4.51 , s_2(6) -> 10 14.23/4.51 , 0_0() -> 2 14.23/4.51 , 0_1() -> 8 } 14.23/4.51 14.23/4.51 Hurray, we answered YES(?,O(n^1)) 14.23/4.53 EOF