YES(?,O(n^1)) 1128.53/297.05 YES(?,O(n^1)) 1128.53/297.05 1128.53/297.05 We are left with following problem, upon which TcT provides the 1128.53/297.05 certificate YES(?,O(n^1)). 1128.53/297.05 1128.53/297.05 Strict Trs: 1128.53/297.05 { a(b(a(a(x1)))) -> c(b(a(b(a(x1))))) 1128.53/297.05 , a(c(b(x1))) -> a(a(b(c(b(a(x1)))))) } 1128.53/297.05 Obligation: 1128.53/297.05 derivational complexity 1128.53/297.05 Answer: 1128.53/297.05 YES(?,O(n^1)) 1128.53/297.05 1128.53/297.05 The problem is match-bounded by 3. The enriched problem is 1128.53/297.05 compatible with the following automaton. 1128.53/297.05 { a_0(1) -> 1 1128.53/297.05 , a_1(1) -> 5 1128.53/297.05 , a_1(3) -> 5 1128.53/297.05 , a_1(4) -> 3 1128.53/297.05 , a_1(6) -> 1 1128.53/297.05 , a_1(6) -> 5 1128.53/297.05 , a_1(7) -> 6 1128.53/297.05 , a_2(3) -> 13 1128.53/297.05 , a_2(4) -> 17 1128.53/297.05 , a_2(6) -> 17 1128.53/297.05 , a_2(7) -> 17 1128.53/297.05 , a_2(9) -> 5 1128.53/297.05 , a_2(9) -> 13 1128.53/297.05 , a_2(10) -> 9 1128.53/297.05 , a_2(15) -> 13 1128.53/297.05 , a_2(16) -> 15 1128.53/297.05 , a_3(15) -> 22 1128.53/297.05 , a_3(18) -> 13 1128.53/297.05 , a_3(18) -> 22 1128.53/297.05 , a_3(19) -> 18 1128.53/297.05 , b_0(1) -> 1 1128.53/297.05 , b_1(3) -> 2 1128.53/297.05 , b_1(5) -> 4 1128.53/297.05 , b_1(6) -> 4 1128.53/297.05 , b_1(8) -> 7 1128.53/297.05 , b_2(9) -> 16 1128.53/297.05 , b_2(11) -> 10 1128.53/297.05 , b_2(13) -> 12 1128.53/297.05 , b_2(15) -> 14 1128.53/297.05 , b_2(17) -> 16 1128.53/297.05 , b_3(20) -> 19 1128.53/297.05 , b_3(22) -> 21 1128.53/297.05 , c_0(1) -> 1 1128.53/297.05 , c_1(2) -> 1 1128.53/297.05 , c_1(2) -> 3 1128.53/297.05 , c_1(2) -> 5 1128.53/297.05 , c_1(2) -> 17 1128.53/297.05 , c_1(4) -> 8 1128.53/297.05 , c_2(12) -> 11 1128.53/297.05 , c_2(14) -> 3 1128.53/297.05 , c_2(14) -> 15 1128.53/297.05 , c_2(14) -> 17 1128.53/297.05 , c_3(21) -> 20 } 1128.53/297.05 1128.53/297.05 Hurray, we answered YES(?,O(n^1)) 1128.89/297.35 EOF