YES(?,O(n^1)) 1179.77/297.06 YES(?,O(n^1)) 1179.77/297.06 1179.77/297.06 We are left with following problem, upon which TcT provides the 1179.77/297.06 certificate YES(?,O(n^1)). 1179.77/297.06 1179.77/297.06 Strict Trs: 1179.77/297.06 { a(a(a(b(b(x1))))) -> b(b(b(b(b(a(a(a(a(a(x1)))))))))) } 1179.77/297.06 Obligation: 1179.77/297.06 derivational complexity 1179.77/297.06 Answer: 1179.77/297.06 YES(?,O(n^1)) 1179.77/297.06 1179.77/297.06 The problem is match-bounded by 5. The enriched problem is 1179.77/297.06 compatible with the following automaton. 1179.77/297.06 { a_0(1) -> 1 1179.77/297.06 , a_1(1) -> 10 1179.77/297.06 , a_1(2) -> 10 1179.77/297.06 , a_1(3) -> 10 1179.77/297.06 , a_1(7) -> 6 1179.77/297.06 , a_1(8) -> 7 1179.77/297.06 , a_1(9) -> 8 1179.77/297.06 , a_1(10) -> 9 1179.77/297.06 , a_2(3) -> 19 1179.77/297.06 , a_2(4) -> 19 1179.77/297.06 , a_2(5) -> 19 1179.77/297.06 , a_2(6) -> 19 1179.77/297.06 , a_2(11) -> 19 1179.77/297.06 , a_2(12) -> 28 1179.77/297.06 , a_2(16) -> 15 1179.77/297.06 , a_2(17) -> 16 1179.77/297.06 , a_2(18) -> 17 1179.77/297.06 , a_2(19) -> 18 1179.77/297.06 , a_2(25) -> 24 1179.77/297.06 , a_2(26) -> 25 1179.77/297.06 , a_2(27) -> 26 1179.77/297.06 , a_2(28) -> 27 1179.77/297.06 , a_3(12) -> 37 1179.77/297.06 , a_3(13) -> 37 1179.77/297.06 , a_3(14) -> 46 1179.77/297.06 , a_3(15) -> 46 1179.77/297.06 , a_3(21) -> 55 1179.77/297.06 , a_3(23) -> 64 1179.77/297.06 , a_3(30) -> 73 1179.77/297.06 , a_3(34) -> 33 1179.77/297.06 , a_3(35) -> 34 1179.77/297.06 , a_3(36) -> 35 1179.77/297.06 , a_3(37) -> 36 1179.77/297.06 , a_3(43) -> 42 1179.77/297.06 , a_3(44) -> 43 1179.77/297.06 , a_3(45) -> 44 1179.77/297.06 , a_3(46) -> 45 1179.77/297.06 , a_3(47) -> 82 1179.77/297.06 , a_3(48) -> 73 1179.77/297.06 , a_3(52) -> 51 1179.77/297.06 , a_3(53) -> 52 1179.77/297.06 , a_3(54) -> 53 1179.77/297.06 , a_3(55) -> 54 1179.77/297.06 , a_3(61) -> 60 1179.77/297.06 , a_3(62) -> 61 1179.77/297.06 , a_3(63) -> 62 1179.77/297.06 , a_3(64) -> 63 1179.77/297.06 , a_3(70) -> 69 1179.77/297.06 , a_3(71) -> 70 1179.77/297.06 , a_3(72) -> 71 1179.77/297.06 , a_3(73) -> 72 1179.77/297.06 , a_3(79) -> 78 1179.77/297.06 , a_3(80) -> 79 1179.77/297.06 , a_3(81) -> 80 1179.77/297.06 , a_3(82) -> 81 1179.77/297.06 , a_4(30) -> 100 1179.77/297.06 , a_4(32) -> 109 1179.77/297.06 , a_4(48) -> 91 1179.77/297.06 , a_4(49) -> 118 1179.77/297.06 , a_4(50) -> 109 1179.77/297.06 , a_4(51) -> 136 1179.77/297.06 , a_4(57) -> 154 1179.77/297.06 , a_4(59) -> 163 1179.77/297.06 , a_4(66) -> 127 1179.77/297.06 , a_4(68) -> 145 1179.77/297.06 , a_4(88) -> 87 1179.77/297.06 , a_4(89) -> 88 1179.77/297.06 , a_4(90) -> 89 1179.77/297.06 , a_4(91) -> 90 1179.77/297.06 , a_4(97) -> 96 1179.77/297.06 , a_4(98) -> 97 1179.77/297.06 , a_4(99) -> 98 1179.77/297.06 , a_4(100) -> 99 1179.77/297.06 , a_4(106) -> 105 1179.77/297.06 , a_4(107) -> 106 1179.77/297.06 , a_4(108) -> 107 1179.77/297.06 , a_4(109) -> 108 1179.77/297.06 , a_4(115) -> 114 1179.77/297.06 , a_4(116) -> 115 1179.77/297.06 , a_4(117) -> 116 1179.77/297.06 , a_4(118) -> 117 1179.77/297.06 , a_4(124) -> 123 1179.77/297.06 , a_4(125) -> 124 1179.77/297.06 , a_4(126) -> 125 1179.77/297.06 , a_4(127) -> 126 1179.77/297.06 , a_4(133) -> 132 1179.77/297.06 , a_4(134) -> 133 1179.77/297.06 , a_4(135) -> 134 1179.77/297.06 , a_4(136) -> 135 1179.77/297.06 , a_4(142) -> 141 1179.77/297.06 , a_4(143) -> 142 1179.77/297.06 , a_4(144) -> 143 1179.77/297.06 , a_4(145) -> 144 1179.77/297.06 , a_4(151) -> 150 1179.77/297.06 , a_4(152) -> 151 1179.77/297.06 , a_4(153) -> 152 1179.77/297.06 , a_4(154) -> 153 1179.77/297.06 , a_4(160) -> 159 1179.77/297.06 , a_4(161) -> 160 1179.77/297.06 , a_4(162) -> 161 1179.77/297.06 , a_4(163) -> 162 1179.77/297.06 , a_5(147) -> 172 1179.77/297.06 , a_5(149) -> 181 1179.77/297.06 , a_5(169) -> 168 1179.77/297.07 , a_5(170) -> 169 1179.77/297.07 , a_5(171) -> 170 1179.77/297.07 , a_5(172) -> 171 1179.77/297.07 , a_5(178) -> 177 1179.77/297.07 , a_5(179) -> 178 1179.77/297.07 , a_5(180) -> 179 1179.77/297.07 , a_5(181) -> 180 1179.77/297.07 , b_0(1) -> 1 1179.77/297.07 , b_1(2) -> 1 1179.77/297.07 , b_1(2) -> 8 1179.77/297.07 , b_1(2) -> 9 1179.77/297.07 , b_1(2) -> 10 1179.77/297.07 , b_1(3) -> 2 1179.77/297.07 , b_1(4) -> 3 1179.77/297.07 , b_1(5) -> 4 1179.77/297.07 , b_1(6) -> 5 1179.77/297.07 , b_2(11) -> 6 1179.77/297.07 , b_2(11) -> 7 1179.77/297.07 , b_2(11) -> 8 1179.77/297.07 , b_2(11) -> 17 1179.77/297.07 , b_2(11) -> 19 1179.77/297.07 , b_2(12) -> 11 1179.77/297.07 , b_2(13) -> 12 1179.77/297.07 , b_2(14) -> 13 1179.77/297.07 , b_2(15) -> 14 1179.77/297.07 , b_2(20) -> 18 1179.77/297.07 , b_2(20) -> 19 1179.77/297.07 , b_2(21) -> 20 1179.77/297.07 , b_2(22) -> 21 1179.77/297.07 , b_2(23) -> 22 1179.77/297.07 , b_2(24) -> 23 1179.77/297.07 , b_3(29) -> 16 1179.77/297.07 , b_3(29) -> 17 1179.77/297.07 , b_3(29) -> 46 1179.77/297.07 , b_3(30) -> 29 1179.77/297.07 , b_3(31) -> 30 1179.77/297.07 , b_3(32) -> 31 1179.77/297.07 , b_3(33) -> 32 1179.77/297.07 , b_3(38) -> 26 1179.77/297.07 , b_3(38) -> 35 1179.77/297.07 , b_3(39) -> 38 1179.77/297.07 , b_3(40) -> 39 1179.77/297.07 , b_3(41) -> 40 1179.77/297.07 , b_3(42) -> 41 1179.77/297.07 , b_3(47) -> 15 1179.77/297.07 , b_3(47) -> 16 1179.77/297.07 , b_3(48) -> 47 1179.77/297.07 , b_3(49) -> 48 1179.77/297.07 , b_3(50) -> 49 1179.77/297.07 , b_3(51) -> 50 1179.77/297.07 , b_3(56) -> 53 1179.77/297.07 , b_3(57) -> 56 1179.77/297.07 , b_3(58) -> 57 1179.77/297.07 , b_3(59) -> 58 1179.77/297.07 , b_3(60) -> 59 1179.77/297.07 , b_3(65) -> 45 1179.77/297.07 , b_3(65) -> 46 1179.77/297.07 , b_3(66) -> 65 1179.77/297.07 , b_3(67) -> 66 1179.77/297.07 , b_3(68) -> 67 1179.77/297.07 , b_3(69) -> 68 1179.77/297.07 , b_3(74) -> 44 1179.77/297.07 , b_3(75) -> 74 1179.77/297.07 , b_3(76) -> 75 1179.77/297.07 , b_3(77) -> 76 1179.77/297.07 , b_3(78) -> 77 1179.77/297.07 , b_4(83) -> 44 1179.77/297.07 , b_4(84) -> 83 1179.77/297.07 , b_4(85) -> 84 1179.77/297.07 , b_4(86) -> 85 1179.77/297.07 , b_4(87) -> 86 1179.77/297.07 , b_4(92) -> 43 1179.77/297.07 , b_4(93) -> 92 1179.77/297.07 , b_4(94) -> 93 1179.77/297.07 , b_4(95) -> 94 1179.77/297.07 , b_4(96) -> 95 1179.77/297.07 , b_4(101) -> 71 1179.77/297.07 , b_4(101) -> 89 1179.77/297.07 , b_4(101) -> 98 1179.77/297.07 , b_4(102) -> 101 1179.77/297.07 , b_4(103) -> 102 1179.77/297.07 , b_4(104) -> 103 1179.77/297.07 , b_4(105) -> 104 1179.77/297.07 , b_4(110) -> 80 1179.77/297.07 , b_4(111) -> 110 1179.77/297.07 , b_4(112) -> 111 1179.77/297.07 , b_4(113) -> 112 1179.77/297.07 , b_4(114) -> 113 1179.77/297.07 , b_4(119) -> 42 1179.77/297.07 , b_4(119) -> 43 1179.77/297.07 , b_4(120) -> 119 1179.77/297.07 , b_4(121) -> 120 1179.77/297.07 , b_4(122) -> 121 1179.77/297.07 , b_4(123) -> 122 1179.77/297.07 , b_4(128) -> 116 1179.77/297.07 , b_4(129) -> 128 1179.77/297.07 , b_4(130) -> 129 1179.77/297.07 , b_4(131) -> 130 1179.77/297.07 , b_4(132) -> 131 1179.77/297.07 , b_4(137) -> 125 1179.77/297.07 , b_4(138) -> 137 1179.77/297.07 , b_4(139) -> 138 1179.77/297.07 , b_4(140) -> 139 1179.77/297.07 , b_4(141) -> 140 1179.77/297.07 , b_4(146) -> 136 1179.77/297.07 , b_4(147) -> 146 1179.77/297.07 , b_4(148) -> 147 1179.77/297.07 , b_4(149) -> 148 1179.77/297.07 , b_4(150) -> 149 1179.77/297.07 , b_4(155) -> 152 1179.77/297.07 , b_4(156) -> 155 1179.77/297.07 , b_4(157) -> 156 1179.77/297.07 , b_4(158) -> 157 1179.77/297.07 , b_4(159) -> 158 1179.77/297.07 , b_5(164) -> 133 1179.77/297.07 , b_5(165) -> 164 1179.77/297.07 , b_5(166) -> 165 1179.77/297.07 , b_5(167) -> 166 1179.77/297.07 , b_5(168) -> 167 1179.77/297.07 , b_5(173) -> 170 1179.77/297.07 , b_5(174) -> 173 1179.77/297.07 , b_5(175) -> 174 1179.77/297.07 , b_5(176) -> 175 1179.77/297.07 , b_5(177) -> 176 } 1179.77/297.07 1179.77/297.07 Hurray, we answered YES(?,O(n^1)) 1180.74/297.82 EOF