YES(?,O(n^1)) 1104.02/297.07 YES(?,O(n^1)) 1104.02/297.07 1104.02/297.07 We are left with following problem, upon which TcT provides the 1104.02/297.07 certificate YES(?,O(n^1)). 1104.02/297.07 1104.02/297.07 Strict Trs: 1104.02/297.07 { 0(0(3(2(5(3(2(0(x1)))))))) -> 0(3(0(1(5(4(3(x1))))))) 1104.02/297.07 , 0(1(0(5(3(0(3(4(x1)))))))) -> 1(5(3(1(1(5(4(x1))))))) 1104.02/297.07 , 0(1(1(5(0(1(5(5(4(5(5(4(x1)))))))))))) -> 1104.02/297.07 2(4(2(4(5(5(5(0(0(5(4(x1))))))))))) 1104.02/297.07 , 0(1(2(3(2(x1))))) -> 4(4(5(2(x1)))) 1104.02/297.07 , 0(4(4(5(5(3(2(2(2(5(3(x1))))))))))) -> 1104.02/297.07 2(4(1(1(0(0(5(4(4(3(x1)))))))))) 1104.02/297.07 , 1(0(2(1(5(5(5(1(5(3(0(5(2(4(3(4(0(5(2(x1))))))))))))))))))) -> 1104.02/297.07 1(1(3(3(0(1(5(0(0(4(1(2(2(5(1(5(2(3(3(2(x1)))))))))))))))))))) 1104.02/297.07 , 1(1(2(1(5(5(3(1(3(2(0(3(1(1(x1)))))))))))))) -> 1104.02/297.07 3(2(3(5(5(5(4(3(0(0(2(3(0(x1))))))))))))) 1104.02/297.07 , 1(4(5(1(1(5(0(1(5(0(2(3(0(4(5(5(4(5(0(5(3(x1))))))))))))))))))))) 1104.02/297.07 -> 4(3(3(0(1(5(4(2(1(4(5(3(5(5(3(4(5(5(2(0(x1)))))))))))))))))))) 1104.02/297.07 , 1(5(3(2(3(0(5(3(3(5(x1)))))))))) -> 1(5(5(1(0(1(3(4(5(x1))))))))) 1104.02/297.07 , 2(0(1(0(1(5(0(3(3(0(x1)))))))))) -> 3(3(5(0(3(3(0(4(0(x1))))))))) 1104.02/297.07 , 2(0(4(1(3(1(4(5(5(5(x1)))))))))) -> 1104.02/297.07 2(3(5(4(0(2(3(4(5(1(x1)))))))))) 1104.02/297.07 , 2(1(5(2(1(3(3(3(5(5(4(1(2(0(2(5(2(x1))))))))))))))))) -> 1104.02/297.07 3(0(3(2(2(3(2(3(1(2(1(1(3(5(2(1(1(1(x1)))))))))))))))))) 1104.02/297.07 , 2(2(5(3(1(4(4(3(3(x1))))))))) -> 3(0(0(0(3(3(1(2(5(x1))))))))) 1104.02/297.07 , 2(5(2(3(4(4(5(4(5(1(5(3(0(5(4(x1))))))))))))))) -> 1104.02/297.07 3(1(3(1(2(2(1(3(5(4(3(0(3(1(4(x1))))))))))))))) 1104.02/297.07 , 2(5(2(5(0(4(4(3(4(2(5(x1))))))))))) -> 1104.02/297.07 1(2(5(0(0(3(3(0(4(1(5(x1))))))))))) 1104.02/297.07 , 2(5(5(5(4(1(1(4(4(5(0(4(0(3(3(5(x1)))))))))))))))) -> 1104.02/297.07 5(4(2(5(1(2(2(5(1(3(5(0(1(5(0(0(5(x1))))))))))))))))) 1104.02/297.07 , 3(0(3(5(3(3(0(2(5(3(3(4(x1)))))))))))) -> 1104.02/297.07 2(3(3(1(5(4(3(5(3(0(4(x1))))))))))) 1104.02/297.07 , 3(3(2(0(5(2(3(2(2(1(0(3(5(4(2(2(1(3(5(4(x1)))))))))))))))))))) -> 1104.02/297.07 3(2(0(1(2(0(4(5(1(2(2(4(1(0(2(5(2(1(4(x1))))))))))))))))))) 1104.02/297.07 , 3(5(4(4(1(0(5(5(2(3(1(0(2(4(5(1(5(0(3(5(0(x1))))))))))))))))))))) 1104.02/297.07 -> 3(2(2(4(3(3(2(4(1(4(3(0(0(1(1(1(4(4(5(1(x1)))))))))))))))))))) 1104.02/297.07 , 4(0(0(1(2(3(1(0(2(1(5(3(2(1(3(1(0(x1))))))))))))))))) -> 1104.02/297.07 4(1(5(5(4(3(1(4(4(5(3(4(5(0(3(x1))))))))))))))) 1104.02/297.07 , 4(0(3(3(1(1(3(5(4(3(3(4(1(x1))))))))))))) -> 1104.02/297.07 4(0(5(0(5(3(4(2(4(2(2(0(x1)))))))))))) 1104.02/297.07 , 4(4(0(3(4(1(0(1(1(3(1(0(2(x1))))))))))))) -> 1104.02/297.07 4(0(4(1(5(1(3(1(2(2(1(2(x1)))))))))))) 1104.02/297.07 , 4(4(5(2(0(3(3(3(1(0(3(5(2(4(x1)))))))))))))) -> 1104.02/297.07 4(2(1(3(3(1(2(4(2(5(0(3(4(x1))))))))))))) 1104.02/297.07 , 5(0(3(4(3(1(5(x1))))))) -> 5(2(3(0(0(5(5(x1))))))) 1104.02/297.07 , 5(4(3(3(4(1(0(0(3(2(2(2(5(4(3(4(x1)))))))))))))))) -> 1104.02/297.07 5(4(2(3(2(0(3(4(5(4(4(2(1(1(3(4(x1)))))))))))))))) } 1104.02/297.07 Obligation: 1104.02/297.07 derivational complexity 1104.02/297.07 Answer: 1104.02/297.07 YES(?,O(n^1)) 1104.02/297.07 1104.02/297.07 The problem is match-bounded by 1. The enriched problem is 1104.02/297.07 compatible with the following automaton. 1104.02/297.07 { 0_0(1) -> 1 1104.02/297.07 , 0_1(1) -> 58 1104.02/297.07 , 0_1(2) -> 1 1104.02/297.07 , 0_1(2) -> 58 1104.02/297.07 , 0_1(4) -> 3 1104.02/297.07 , 0_1(7) -> 193 1104.02/297.07 , 0_1(8) -> 58 1104.02/297.07 , 0_1(12) -> 21 1104.02/297.07 , 0_1(13) -> 84 1104.02/297.07 , 0_1(21) -> 20 1104.02/297.07 , 0_1(23) -> 148 1104.02/297.07 , 0_1(27) -> 26 1104.02/297.07 , 0_1(28) -> 27 1104.02/297.07 , 0_1(30) -> 58 1104.02/297.07 , 0_1(33) -> 32 1104.02/297.07 , 0_1(36) -> 35 1104.02/297.07 , 0_1(37) -> 36 1104.02/297.07 , 0_1(47) -> 58 1104.02/297.07 , 0_1(55) -> 54 1104.02/297.07 , 0_1(56) -> 55 1104.02/297.07 , 0_1(61) -> 60 1104.02/297.07 , 0_1(78) -> 77 1104.02/297.07 , 0_1(80) -> 148 1104.02/297.07 , 0_1(82) -> 81 1104.02/297.07 , 0_1(85) -> 84 1104.02/297.07 , 0_1(89) -> 88 1104.02/297.07 , 0_1(94) -> 47 1104.02/297.07 , 0_1(109) -> 94 1104.02/297.07 , 0_1(110) -> 109 1104.02/297.07 , 0_1(124) -> 123 1104.02/297.07 , 0_1(128) -> 127 1104.02/297.07 , 0_1(129) -> 128 1104.02/297.07 , 0_1(132) -> 131 1104.02/297.07 , 0_1(145) -> 144 1104.02/297.07 , 0_1(148) -> 147 1104.02/297.07 , 0_1(154) -> 48 1104.02/297.07 , 0_1(157) -> 156 1104.02/297.07 , 0_1(165) -> 164 1104.02/297.07 , 0_1(177) -> 176 1104.02/297.07 , 0_1(178) -> 177 1104.02/297.07 , 0_1(182) -> 14 1104.02/297.07 , 0_1(194) -> 22 1104.02/297.07 , 0_1(196) -> 195 1104.02/297.07 , 0_1(219) -> 218 1104.02/297.07 , 0_1(222) -> 221 1104.02/297.07 , 0_1(223) -> 222 1104.02/297.07 , 0_1(226) -> 225 1104.02/297.07 , 1_0(1) -> 1 1104.02/297.07 , 1_1(1) -> 93 1104.02/297.07 , 1_1(2) -> 93 1104.02/297.07 , 1_1(5) -> 4 1104.02/297.07 , 1_1(8) -> 1 1104.02/297.07 , 1_1(8) -> 24 1104.02/297.07 , 1_1(8) -> 58 1104.02/297.07 , 1_1(8) -> 93 1104.02/297.07 , 1_1(8) -> 113 1104.02/297.07 , 1_1(8) -> 133 1104.02/297.07 , 1_1(11) -> 10 1104.02/297.07 , 1_1(12) -> 11 1104.02/297.07 , 1_1(13) -> 125 1104.02/297.07 , 1_1(14) -> 93 1104.02/297.07 , 1_1(23) -> 133 1104.02/297.07 , 1_1(24) -> 209 1104.02/297.07 , 1_1(25) -> 15 1104.02/297.07 , 1_1(26) -> 25 1104.02/297.07 , 1_1(30) -> 8 1104.02/297.07 , 1_1(34) -> 33 1104.02/297.07 , 1_1(39) -> 38 1104.02/297.07 , 1_1(43) -> 42 1104.02/297.07 , 1_1(62) -> 61 1104.02/297.07 , 1_1(66) -> 65 1104.02/297.07 , 1_1(77) -> 76 1104.02/297.07 , 1_1(79) -> 78 1104.02/297.07 , 1_1(93) -> 108 1104.02/297.07 , 1_1(101) -> 100 1104.02/297.07 , 1_1(103) -> 102 1104.02/297.07 , 1_1(104) -> 103 1104.02/297.07 , 1_1(108) -> 107 1104.02/297.07 , 1_1(113) -> 112 1104.02/297.07 , 1_1(114) -> 47 1104.02/297.07 , 1_1(116) -> 115 1104.02/297.07 , 1_1(119) -> 118 1104.02/297.07 , 1_1(134) -> 93 1104.02/297.07 , 1_1(138) -> 137 1104.02/297.07 , 1_1(142) -> 141 1104.02/297.07 , 1_1(146) -> 145 1104.02/297.07 , 1_1(150) -> 149 1104.02/297.07 , 1_1(155) -> 154 1104.02/297.07 , 1_1(160) -> 159 1104.02/297.07 , 1_1(164) -> 163 1104.02/297.07 , 1_1(174) -> 173 1104.02/297.07 , 1_1(179) -> 178 1104.02/297.07 , 1_1(180) -> 179 1104.02/297.07 , 1_1(181) -> 180 1104.02/297.07 , 1_1(182) -> 22 1104.02/297.07 , 1_1(187) -> 186 1104.02/297.07 , 1_1(203) -> 202 1104.02/297.07 , 1_1(205) -> 204 1104.02/297.07 , 1_1(207) -> 206 1104.02/297.07 , 1_1(211) -> 210 1104.02/297.07 , 1_1(214) -> 213 1104.02/297.07 , 1_1(219) -> 233 1104.02/297.07 , 1_1(220) -> 93 1104.02/297.07 , 1_1(233) -> 232 1104.02/297.07 , 2_0(1) -> 1 1104.02/297.07 , 2_1(1) -> 24 1104.02/297.07 , 2_1(14) -> 1 1104.02/297.07 , 2_1(14) -> 7 1104.02/297.07 , 2_1(14) -> 24 1104.02/297.07 , 2_1(14) -> 57 1104.02/297.07 , 2_1(14) -> 58 1104.02/297.07 , 2_1(14) -> 75 1104.02/297.07 , 2_1(14) -> 84 1104.02/297.07 , 2_1(16) -> 15 1104.02/297.07 , 2_1(23) -> 113 1104.02/297.07 , 2_1(40) -> 39 1104.02/297.07 , 2_1(41) -> 40 1104.02/297.07 , 2_1(45) -> 44 1104.02/297.07 , 2_1(48) -> 47 1104.02/297.07 , 2_1(57) -> 56 1104.02/297.07 , 2_1(58) -> 75 1104.02/297.07 , 2_1(65) -> 64 1104.02/297.07 , 2_1(75) -> 201 1104.02/297.07 , 2_1(90) -> 89 1104.02/297.07 , 2_1(93) -> 167 1104.02/297.07 , 2_1(96) -> 95 1104.02/297.07 , 2_1(97) -> 96 1104.02/297.07 , 2_1(99) -> 98 1104.02/297.07 , 2_1(102) -> 101 1104.02/297.07 , 2_1(107) -> 106 1104.02/297.07 , 2_1(117) -> 116 1104.02/297.07 , 2_1(118) -> 117 1104.02/297.07 , 2_1(125) -> 167 1104.02/297.07 , 2_1(126) -> 8 1104.02/297.07 , 2_1(136) -> 135 1104.02/297.07 , 2_1(139) -> 138 1104.02/297.07 , 2_1(140) -> 139 1104.02/297.07 , 2_1(156) -> 155 1104.02/297.07 , 2_1(161) -> 160 1104.02/297.07 , 2_1(162) -> 161 1104.02/297.07 , 2_1(166) -> 165 1104.02/297.07 , 2_1(168) -> 48 1104.02/297.07 , 2_1(172) -> 171 1104.02/297.07 , 2_1(200) -> 199 1104.02/297.07 , 2_1(208) -> 207 1104.02/297.07 , 2_1(209) -> 208 1104.02/297.07 , 2_1(210) -> 22 1104.02/297.07 , 2_1(215) -> 214 1104.02/297.07 , 2_1(217) -> 216 1104.02/297.07 , 2_1(220) -> 134 1104.02/297.07 , 2_1(225) -> 224 1104.02/297.07 , 2_1(232) -> 231 1104.02/297.07 , 3_0(1) -> 1 1104.02/297.07 , 3_1(1) -> 7 1104.02/297.07 , 3_1(2) -> 7 1104.02/297.07 , 3_1(3) -> 2 1104.02/297.07 , 3_1(7) -> 45 1104.02/297.07 , 3_1(10) -> 9 1104.02/297.07 , 3_1(13) -> 219 1104.02/297.07 , 3_1(14) -> 219 1104.02/297.07 , 3_1(22) -> 79 1104.02/297.07 , 3_1(24) -> 46 1104.02/297.07 , 3_1(31) -> 30 1104.02/297.07 , 3_1(32) -> 31 1104.02/297.07 , 3_1(46) -> 45 1104.02/297.07 , 3_1(47) -> 1 1104.02/297.07 , 3_1(47) -> 7 1104.02/297.07 , 3_1(47) -> 24 1104.02/297.07 , 3_1(47) -> 45 1104.02/297.07 , 3_1(47) -> 75 1104.02/297.07 , 3_1(47) -> 93 1104.02/297.07 , 3_1(47) -> 108 1104.02/297.07 , 3_1(47) -> 113 1104.02/297.07 , 3_1(47) -> 167 1104.02/297.07 , 3_1(49) -> 48 1104.02/297.07 , 3_1(54) -> 53 1104.02/297.07 , 3_1(58) -> 57 1104.02/297.07 , 3_1(59) -> 22 1104.02/297.07 , 3_1(60) -> 59 1104.02/297.07 , 3_1(69) -> 68 1104.02/297.07 , 3_1(72) -> 71 1104.02/297.07 , 3_1(80) -> 47 1104.02/297.07 , 3_1(83) -> 82 1104.02/297.07 , 3_1(84) -> 83 1104.02/297.07 , 3_1(86) -> 14 1104.02/297.07 , 3_1(91) -> 90 1104.02/297.07 , 3_1(93) -> 124 1104.02/297.07 , 3_1(95) -> 94 1104.02/297.07 , 3_1(98) -> 97 1104.02/297.07 , 3_1(100) -> 99 1104.02/297.07 , 3_1(105) -> 104 1104.02/297.07 , 3_1(111) -> 110 1104.02/297.07 , 3_1(112) -> 111 1104.02/297.07 , 3_1(115) -> 114 1104.02/297.07 , 3_1(120) -> 119 1104.02/297.07 , 3_1(123) -> 122 1104.02/297.07 , 3_1(125) -> 124 1104.02/297.07 , 3_1(130) -> 129 1104.02/297.07 , 3_1(131) -> 130 1104.02/297.07 , 3_1(134) -> 7 1104.02/297.07 , 3_1(143) -> 142 1104.02/297.07 , 3_1(149) -> 86 1104.02/297.07 , 3_1(153) -> 152 1104.02/297.07 , 3_1(154) -> 7 1104.02/297.07 , 3_1(170) -> 169 1104.02/297.07 , 3_1(171) -> 170 1104.02/297.07 , 3_1(176) -> 175 1104.02/297.07 , 3_1(182) -> 7 1104.02/297.07 , 3_1(186) -> 185 1104.02/297.07 , 3_1(191) -> 190 1104.02/297.07 , 3_1(198) -> 197 1104.02/297.07 , 3_1(206) -> 205 1104.02/297.07 , 3_1(212) -> 211 1104.02/297.07 , 3_1(213) -> 212 1104.02/297.07 , 3_1(221) -> 220 1104.02/297.07 , 3_1(224) -> 136 1104.02/297.07 , 3_1(227) -> 226 1104.02/297.07 , 4_0(1) -> 1 1104.02/297.07 , 4_1(1) -> 13 1104.02/297.07 , 4_1(6) -> 29 1104.02/297.07 , 4_1(7) -> 6 1104.02/297.07 , 4_1(15) -> 14 1104.02/297.07 , 4_1(17) -> 16 1104.02/297.07 , 4_1(22) -> 1 1104.02/297.07 , 4_1(22) -> 13 1104.02/297.07 , 4_1(22) -> 58 1104.02/297.07 , 4_1(22) -> 85 1104.02/297.07 , 4_1(22) -> 93 1104.02/297.07 , 4_1(22) -> 125 1104.02/297.07 , 4_1(23) -> 22 1104.02/297.07 , 4_1(38) -> 37 1104.02/297.07 , 4_1(47) -> 13 1104.02/297.07 , 4_1(53) -> 52 1104.02/297.07 , 4_1(58) -> 85 1104.02/297.07 , 4_1(64) -> 63 1104.02/297.07 , 4_1(67) -> 66 1104.02/297.07 , 4_1(73) -> 72 1104.02/297.07 , 4_1(80) -> 22 1104.02/297.07 , 4_1(88) -> 87 1104.02/297.07 , 4_1(91) -> 181 1104.02/297.07 , 4_1(92) -> 91 1104.02/297.07 , 4_1(122) -> 121 1104.02/297.07 , 4_1(133) -> 132 1104.02/297.07 , 4_1(135) -> 134 1104.02/297.07 , 4_1(152) -> 151 1104.02/297.07 , 4_1(158) -> 157 1104.02/297.07 , 4_1(163) -> 162 1104.02/297.07 , 4_1(169) -> 168 1104.02/297.07 , 4_1(173) -> 172 1104.02/297.07 , 4_1(175) -> 174 1104.02/297.07 , 4_1(185) -> 184 1104.02/297.07 , 4_1(188) -> 187 1104.02/297.07 , 4_1(189) -> 188 1104.02/297.07 , 4_1(192) -> 191 1104.02/297.07 , 4_1(199) -> 198 1104.02/297.07 , 4_1(201) -> 200 1104.02/297.07 , 4_1(202) -> 194 1104.02/297.07 , 4_1(216) -> 215 1104.02/297.07 , 4_1(228) -> 227 1104.02/297.07 , 4_1(230) -> 229 1104.02/297.07 , 4_1(231) -> 230 1104.02/297.07 , 5_0(1) -> 1 1104.02/297.07 , 5_1(1) -> 23 1104.02/297.07 , 5_1(6) -> 5 1104.02/297.07 , 5_1(8) -> 223 1104.02/297.07 , 5_1(9) -> 8 1104.02/297.07 , 5_1(13) -> 12 1104.02/297.07 , 5_1(18) -> 17 1104.02/297.07 , 5_1(19) -> 18 1104.02/297.07 , 5_1(20) -> 19 1104.02/297.07 , 5_1(23) -> 223 1104.02/297.07 , 5_1(24) -> 23 1104.02/297.07 , 5_1(29) -> 28 1104.02/297.07 , 5_1(35) -> 34 1104.02/297.07 , 5_1(42) -> 41 1104.02/297.07 , 5_1(44) -> 43 1104.02/297.07 , 5_1(47) -> 23 1104.02/297.07 , 5_1(50) -> 49 1104.02/297.07 , 5_1(51) -> 50 1104.02/297.07 , 5_1(52) -> 51 1104.02/297.07 , 5_1(57) -> 153 1104.02/297.07 , 5_1(60) -> 23 1104.02/297.07 , 5_1(63) -> 62 1104.02/297.07 , 5_1(68) -> 67 1104.02/297.07 , 5_1(70) -> 69 1104.02/297.07 , 5_1(71) -> 70 1104.02/297.07 , 5_1(74) -> 73 1104.02/297.07 , 5_1(75) -> 74 1104.02/297.07 , 5_1(76) -> 9 1104.02/297.07 , 5_1(80) -> 23 1104.02/297.07 , 5_1(81) -> 80 1104.02/297.07 , 5_1(83) -> 153 1104.02/297.07 , 5_1(87) -> 86 1104.02/297.07 , 5_1(93) -> 92 1104.02/297.07 , 5_1(106) -> 105 1104.02/297.07 , 5_1(121) -> 120 1104.02/297.07 , 5_1(127) -> 126 1104.02/297.07 , 5_1(134) -> 1 1104.02/297.07 , 5_1(134) -> 5 1104.02/297.07 , 5_1(134) -> 12 1104.02/297.07 , 5_1(134) -> 23 1104.02/297.07 , 5_1(134) -> 24 1104.02/297.07 , 5_1(134) -> 113 1104.02/297.07 , 5_1(134) -> 192 1104.02/297.07 , 5_1(134) -> 217 1104.02/297.07 , 5_1(137) -> 136 1104.02/297.07 , 5_1(141) -> 140 1104.02/297.07 , 5_1(144) -> 143 1104.02/297.07 , 5_1(147) -> 146 1104.02/297.07 , 5_1(151) -> 150 1104.02/297.07 , 5_1(159) -> 158 1104.02/297.07 , 5_1(167) -> 166 1104.02/297.07 , 5_1(183) -> 182 1104.02/297.07 , 5_1(184) -> 183 1104.02/297.07 , 5_1(190) -> 189 1104.02/297.07 , 5_1(193) -> 192 1104.02/297.07 , 5_1(195) -> 194 1104.02/297.07 , 5_1(197) -> 196 1104.02/297.07 , 5_1(204) -> 203 1104.02/297.07 , 5_1(218) -> 217 1104.02/297.07 , 5_1(229) -> 228 } 1104.02/297.07 1104.02/297.07 Hurray, we answered YES(?,O(n^1)) 1104.82/297.68 EOF