YES(?,O(n^1)) 1181.43/297.05 YES(?,O(n^1)) 1181.43/297.05 1181.43/297.05 We are left with following problem, upon which TcT provides the 1181.43/297.05 certificate YES(?,O(n^1)). 1181.43/297.05 1181.43/297.05 Strict Trs: 1181.43/297.05 { b(a(b(a(a(a(x1)))))) -> a(a(a(a(b(a(b(a(b(x1))))))))) } 1181.43/297.05 Obligation: 1181.43/297.05 derivational complexity 1181.43/297.05 Answer: 1181.43/297.05 YES(?,O(n^1)) 1181.43/297.05 1181.43/297.05 The problem is match-bounded by 4. The enriched problem is 1181.43/297.05 compatible with the following automaton. 1181.43/297.05 { b_0(1) -> 1 1181.43/297.05 , b_1(1) -> 9 1181.43/297.05 , b_1(2) -> 9 1181.43/297.05 , b_1(3) -> 9 1181.43/297.05 , b_1(4) -> 9 1181.43/297.05 , b_1(6) -> 5 1181.43/297.05 , b_1(8) -> 7 1181.43/297.05 , b_2(3) -> 25 1181.43/297.05 , b_2(4) -> 17 1181.43/297.05 , b_2(5) -> 17 1181.43/297.05 , b_2(11) -> 25 1181.43/297.05 , b_2(14) -> 13 1181.43/297.05 , b_2(16) -> 15 1181.43/297.05 , b_2(18) -> 17 1181.43/297.05 , b_2(19) -> 25 1181.43/297.05 , b_2(22) -> 21 1181.43/297.05 , b_2(24) -> 23 1181.43/297.05 , b_3(11) -> 49 1181.43/297.05 , b_3(19) -> 33 1181.43/297.05 , b_3(20) -> 41 1181.43/297.05 , b_3(21) -> 41 1181.43/297.05 , b_3(26) -> 57 1181.43/297.05 , b_3(30) -> 29 1181.43/297.05 , b_3(32) -> 31 1181.43/297.05 , b_3(38) -> 37 1181.43/297.05 , b_3(40) -> 39 1181.43/297.05 , b_3(46) -> 45 1181.43/297.05 , b_3(48) -> 47 1181.43/297.05 , b_3(51) -> 49 1181.43/297.05 , b_3(54) -> 53 1181.43/297.05 , b_3(56) -> 55 1181.43/297.05 , b_4(29) -> 65 1181.43/297.05 , b_4(43) -> 73 1181.43/297.05 , b_4(62) -> 61 1181.43/297.05 , b_4(64) -> 63 1181.43/297.05 , b_4(70) -> 69 1181.43/297.05 , b_4(72) -> 71 1181.43/297.05 , a_0(1) -> 1 1181.43/297.05 , a_1(2) -> 1 1181.43/297.05 , a_1(2) -> 7 1181.43/297.05 , a_1(2) -> 9 1181.43/297.05 , a_1(3) -> 2 1181.43/297.05 , a_1(4) -> 3 1181.43/297.05 , a_1(5) -> 4 1181.43/297.05 , a_1(7) -> 6 1181.43/297.05 , a_1(9) -> 8 1181.43/297.05 , a_2(10) -> 7 1181.43/297.05 , a_2(10) -> 23 1181.43/297.05 , a_2(11) -> 10 1181.43/297.05 , a_2(12) -> 11 1181.43/297.05 , a_2(13) -> 12 1181.43/297.05 , a_2(15) -> 14 1181.43/297.05 , a_2(17) -> 16 1181.43/297.05 , a_2(18) -> 5 1181.43/297.05 , a_2(18) -> 7 1181.43/297.05 , a_2(18) -> 9 1181.43/297.05 , a_2(18) -> 15 1181.43/297.05 , a_2(18) -> 17 1181.43/297.05 , a_2(19) -> 18 1181.43/297.05 , a_2(20) -> 19 1181.43/297.05 , a_2(21) -> 20 1181.43/297.05 , a_2(23) -> 22 1181.43/297.05 , a_2(25) -> 24 1181.43/297.05 , a_3(26) -> 13 1181.43/297.05 , a_3(27) -> 26 1181.43/297.05 , a_3(28) -> 27 1181.43/297.05 , a_3(29) -> 28 1181.43/297.05 , a_3(31) -> 30 1181.43/297.05 , a_3(33) -> 32 1181.43/297.05 , a_3(34) -> 15 1181.43/297.05 , a_3(35) -> 34 1181.43/297.05 , a_3(36) -> 35 1181.43/297.05 , a_3(37) -> 36 1181.43/297.05 , a_3(39) -> 38 1181.43/297.05 , a_3(41) -> 40 1181.43/297.05 , a_3(42) -> 41 1181.43/297.05 , a_3(43) -> 42 1181.43/297.05 , a_3(44) -> 43 1181.43/297.05 , a_3(45) -> 44 1181.43/297.05 , a_3(47) -> 46 1181.43/297.05 , a_3(49) -> 48 1181.43/297.05 , a_3(50) -> 23 1181.43/297.05 , a_3(50) -> 47 1181.43/297.05 , a_3(51) -> 50 1181.43/297.05 , a_3(52) -> 51 1181.43/297.05 , a_3(53) -> 52 1181.43/297.05 , a_3(55) -> 54 1181.43/297.05 , a_3(57) -> 56 1181.43/297.05 , a_4(58) -> 55 1181.43/297.05 , a_4(59) -> 58 1181.43/297.05 , a_4(60) -> 59 1181.43/297.05 , a_4(61) -> 60 1181.43/297.05 , a_4(63) -> 62 1181.43/297.05 , a_4(65) -> 64 1181.43/297.05 , a_4(66) -> 37 1181.43/297.05 , a_4(67) -> 66 1181.43/297.05 , a_4(68) -> 67 1181.43/297.05 , a_4(69) -> 68 1181.43/297.05 , a_4(71) -> 70 1181.43/297.05 , a_4(73) -> 72 } 1181.43/297.05 1181.43/297.05 Hurray, we answered YES(?,O(n^1)) 1182.15/297.67 EOF