YES(?,O(n^1)) 21.59/8.91 YES(?,O(n^1)) 21.59/8.91 21.59/8.91 We are left with following problem, upon which TcT provides the 21.59/8.91 certificate YES(?,O(n^1)). 21.59/8.91 21.59/8.91 Strict Trs: 21.59/8.91 { a(a(x1)) -> a(b(c(a(x1)))) 21.59/8.91 , a(c(b(x1))) -> b(a(b(a(x1)))) 21.59/8.91 , b(x1) -> c(a(c(x1))) } 21.59/8.91 Obligation: 21.59/8.91 derivational complexity 21.59/8.91 Answer: 21.59/8.91 YES(?,O(n^1)) 21.59/8.91 21.59/8.91 The problem is match-bounded by 5. The enriched problem is 21.59/8.91 compatible with the following automaton. 21.59/8.91 { a_0(1) -> 1 21.59/8.91 , a_1(1) -> 4 21.59/8.91 , a_1(2) -> 1 21.59/8.91 , a_1(2) -> 4 21.59/8.91 , a_1(5) -> 4 21.59/8.91 , a_1(6) -> 5 21.59/8.91 , a_1(8) -> 7 21.59/8.91 , a_1(18) -> 4 21.59/8.91 , a_1(27) -> 4 21.59/8.91 , a_2(2) -> 17 21.59/8.91 , a_2(5) -> 20 21.59/8.91 , a_2(6) -> 17 21.59/8.91 , a_2(10) -> 9 21.59/8.91 , a_2(12) -> 11 21.59/8.91 , a_2(14) -> 13 21.59/8.91 , a_2(15) -> 4 21.59/8.91 , a_2(15) -> 20 21.59/8.91 , a_2(18) -> 20 21.59/8.91 , a_2(19) -> 18 21.59/8.91 , a_2(27) -> 20 21.59/8.91 , a_2(28) -> 17 21.59/8.91 , a_3(18) -> 29 21.59/8.91 , a_3(19) -> 36 21.59/8.91 , a_3(22) -> 21 21.59/8.91 , a_3(24) -> 23 21.59/8.91 , a_3(26) -> 25 21.59/8.91 , a_3(27) -> 29 21.59/8.91 , a_3(28) -> 27 21.59/8.91 , a_3(34) -> 20 21.59/8.91 , a_3(34) -> 29 21.59/8.91 , a_4(28) -> 41 21.59/8.91 , a_4(31) -> 30 21.59/8.91 , a_4(33) -> 32 21.59/8.91 , a_4(38) -> 37 21.59/8.91 , a_4(39) -> 29 21.59/8.91 , a_5(43) -> 42 21.59/8.91 , c_0(1) -> 1 21.59/8.91 , c_1(1) -> 8 21.59/8.91 , c_1(4) -> 3 21.59/8.91 , c_1(7) -> 1 21.59/8.91 , c_2(3) -> 10 21.59/8.91 , c_2(4) -> 12 21.59/8.91 , c_2(5) -> 14 21.59/8.91 , c_2(9) -> 2 21.59/8.91 , c_2(11) -> 6 21.59/8.91 , c_2(13) -> 1 21.59/8.91 , c_2(13) -> 4 21.59/8.91 , c_2(13) -> 7 21.59/8.91 , c_2(17) -> 16 21.59/8.91 , c_2(18) -> 16 21.59/8.91 , c_3(16) -> 22 21.59/8.91 , c_3(18) -> 24 21.59/8.91 , c_3(20) -> 26 21.59/8.91 , c_3(21) -> 15 21.59/8.91 , c_3(23) -> 4 21.59/8.91 , c_3(23) -> 5 21.59/8.91 , c_3(23) -> 7 21.59/8.91 , c_3(23) -> 11 21.59/8.91 , c_3(25) -> 19 21.59/8.91 , c_3(27) -> 35 21.59/8.91 , c_3(36) -> 35 21.59/8.91 , c_4(27) -> 31 21.59/8.91 , c_4(29) -> 33 21.59/8.91 , c_4(30) -> 11 21.59/8.91 , c_4(30) -> 13 21.59/8.91 , c_4(30) -> 17 21.59/8.91 , c_4(32) -> 28 21.59/8.91 , c_4(35) -> 38 21.59/8.91 , c_4(37) -> 34 21.59/8.91 , c_4(41) -> 40 21.59/8.91 , c_5(40) -> 43 21.59/8.91 , c_5(42) -> 39 21.59/8.91 , b_0(1) -> 1 21.59/8.91 , b_1(3) -> 2 21.59/8.91 , b_1(4) -> 6 21.59/8.91 , b_1(5) -> 1 21.59/8.91 , b_1(5) -> 4 21.59/8.91 , b_1(5) -> 7 21.59/8.91 , b_2(16) -> 15 21.59/8.91 , b_2(18) -> 4 21.59/8.91 , b_2(18) -> 5 21.59/8.91 , b_2(18) -> 7 21.59/8.91 , b_2(18) -> 11 21.59/8.91 , b_2(20) -> 19 21.59/8.91 , b_3(27) -> 11 21.59/8.91 , b_3(27) -> 13 21.59/8.91 , b_3(27) -> 17 21.59/8.91 , b_3(29) -> 28 21.59/8.91 , b_3(35) -> 34 21.59/8.91 , b_4(40) -> 39 } 21.59/8.91 21.59/8.91 Hurray, we answered YES(?,O(n^1)) 21.59/8.93 EOF