YES(?,O(n^1)) 13.98/4.47 YES(?,O(n^1)) 13.98/4.47 13.98/4.47 We are left with following problem, upon which TcT provides the 13.98/4.47 certificate YES(?,O(n^1)). 13.98/4.47 13.98/4.47 Strict Trs: 13.98/4.47 { h(x, c(y, z)) -> h(c(s(y), x), z) 13.98/4.47 , h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z))) } 13.98/4.47 Obligation: 13.98/4.47 innermost runtime complexity 13.98/4.47 Answer: 13.98/4.47 YES(?,O(n^1)) 13.98/4.47 13.98/4.47 The problem is match-bounded by 2. The enriched problem is 13.98/4.47 compatible with the following automaton. 13.98/4.47 { h_0(2, 2) -> 1 13.98/4.47 , h_0(2, 3) -> 1 13.98/4.47 , h_0(2, 4) -> 1 13.98/4.47 , h_0(3, 2) -> 1 13.98/4.47 , h_0(3, 3) -> 1 13.98/4.47 , h_0(3, 4) -> 1 13.98/4.47 , h_0(4, 2) -> 1 13.98/4.47 , h_0(4, 3) -> 1 13.98/4.47 , h_0(4, 4) -> 1 13.98/4.47 , h_1(2, 7) -> 1 13.98/4.47 , h_1(3, 7) -> 1 13.98/4.47 , h_1(4, 7) -> 1 13.98/4.47 , h_1(5, 2) -> 1 13.98/4.47 , h_1(5, 3) -> 1 13.98/4.47 , h_1(5, 4) -> 1 13.98/4.47 , h_1(5, 7) -> 1 13.98/4.47 , h_1(11, 7) -> 1 13.98/4.47 , h_1(13, 7) -> 1 13.98/4.47 , h_2(11, 7) -> 1 13.98/4.47 , h_2(11, 9) -> 1 13.98/4.47 , h_2(13, 2) -> 1 13.98/4.47 , h_2(13, 3) -> 1 13.98/4.47 , h_2(13, 4) -> 1 13.98/4.47 , h_2(13, 7) -> 1 13.98/4.47 , c_0(2, 2) -> 2 13.98/4.47 , c_0(2, 3) -> 2 13.98/4.47 , c_0(2, 4) -> 2 13.98/4.47 , c_0(3, 2) -> 2 13.98/4.47 , c_0(3, 3) -> 2 13.98/4.47 , c_0(3, 4) -> 2 13.98/4.47 , c_0(4, 2) -> 2 13.98/4.47 , c_0(4, 3) -> 2 13.98/4.47 , c_0(4, 4) -> 2 13.98/4.47 , c_1(2, 2) -> 9 13.98/4.47 , c_1(2, 3) -> 9 13.98/4.47 , c_1(2, 4) -> 9 13.98/4.47 , c_1(2, 7) -> 9 13.98/4.47 , c_1(3, 2) -> 9 13.98/4.47 , c_1(3, 3) -> 9 13.98/4.47 , c_1(3, 4) -> 9 13.98/4.47 , c_1(3, 7) -> 9 13.98/4.47 , c_1(4, 2) -> 9 13.98/4.47 , c_1(4, 3) -> 9 13.98/4.47 , c_1(4, 4) -> 9 13.98/4.47 , c_1(4, 7) -> 9 13.98/4.47 , c_1(6, 2) -> 5 13.98/4.47 , c_1(6, 3) -> 5 13.98/4.47 , c_1(6, 4) -> 5 13.98/4.47 , c_1(6, 5) -> 5 13.98/4.47 , c_1(6, 13) -> 5 13.98/4.47 , c_1(8, 7) -> 7 13.98/4.47 , c_1(8, 9) -> 7 13.98/4.47 , c_2(12, 2) -> 11 13.98/4.47 , c_2(12, 3) -> 11 13.98/4.47 , c_2(12, 4) -> 11 13.98/4.47 , c_2(12, 5) -> 11 13.98/4.47 , c_2(12, 11) -> 11 13.98/4.47 , c_2(12, 13) -> 11 13.98/4.47 , c_2(14, 11) -> 13 13.98/4.47 , s_0(2) -> 3 13.98/4.47 , s_0(3) -> 3 13.98/4.47 , s_0(4) -> 3 13.98/4.47 , s_1(2) -> 6 13.98/4.47 , s_1(3) -> 6 13.98/4.47 , s_1(4) -> 6 13.98/4.47 , s_1(10) -> 8 13.98/4.47 , s_2(2) -> 14 13.98/4.47 , s_2(3) -> 14 13.98/4.47 , s_2(4) -> 14 13.98/4.47 , s_2(8) -> 12 13.98/4.47 , 0_0() -> 4 13.98/4.47 , 0_1() -> 10 } 13.98/4.47 13.98/4.47 Hurray, we answered YES(?,O(n^1)) 13.98/4.49 EOF