YES(?,O(n^1)) 11.73/4.94 YES(?,O(n^1)) 11.73/4.94 11.73/4.94 We are left with following problem, upon which TcT provides the 11.73/4.94 certificate YES(?,O(n^1)). 11.73/4.94 11.73/4.94 Strict Trs: 11.73/4.94 { a(x, y) -> b(x, b(0(), c(y))) 11.73/4.94 , b(y, 0()) -> y 11.73/4.94 , c(b(y, c(x))) -> c(c(b(a(0(), 0()), y))) } 11.73/4.94 Obligation: 11.73/4.94 derivational complexity 11.73/4.94 Answer: 11.73/4.94 YES(?,O(n^1)) 11.73/4.94 11.73/4.94 The problem is match-bounded by 3. The enriched problem is 11.73/4.94 compatible with the following automaton. 11.73/4.94 { a_0(1, 1) -> 1 11.73/4.94 , a_1(3, 3) -> 6 11.73/4.94 , a_1(3, 3) -> 7 11.73/4.94 , a_2(9, 9) -> 14 11.73/4.94 , b_0(1, 1) -> 1 11.73/4.94 , b_1(1, 2) -> 1 11.73/4.94 , b_1(3, 4) -> 2 11.73/4.94 , b_1(7, 1) -> 6 11.73/4.94 , b_1(7, 7) -> 11 11.73/4.94 , b_2(3, 8) -> 6 11.73/4.94 , b_2(3, 8) -> 7 11.73/4.94 , b_2(9, 10) -> 8 11.73/4.94 , b_2(14, 7) -> 13 11.73/4.94 , b_3(9, 15) -> 14 11.73/4.94 , b_3(16, 17) -> 15 11.73/4.94 , 0_0() -> 1 11.73/4.94 , 0_1() -> 3 11.73/4.94 , 0_2() -> 9 11.73/4.94 , 0_3() -> 16 11.73/4.94 , c_0(1) -> 1 11.73/4.94 , c_1(1) -> 4 11.73/4.94 , c_1(5) -> 1 11.73/4.94 , c_1(5) -> 4 11.73/4.94 , c_1(6) -> 5 11.73/4.94 , c_1(11) -> 6 11.73/4.94 , c_2(3) -> 10 11.73/4.94 , c_2(12) -> 5 11.73/4.94 , c_2(13) -> 12 11.73/4.94 , c_3(9) -> 17 } 11.73/4.94 11.73/4.94 Hurray, we answered YES(?,O(n^1)) 11.73/4.95 EOF