YES(?,O(n^1)) 1108.76/297.07 YES(?,O(n^1)) 1108.76/297.07 1108.76/297.07 We are left with following problem, upon which TcT provides the 1108.76/297.07 certificate YES(?,O(n^1)). 1108.76/297.07 1108.76/297.07 Strict Trs: 1108.76/297.07 { 0(0(5(3(2(0(5(1(3(3(5(2(0(2(5(3(4(4(5(x1))))))))))))))))))) -> 1108.76/297.07 0(0(5(3(5(5(0(1(3(5(0(1(3(1(3(4(2(4(x1)))))))))))))))))) 1108.76/297.07 , 0(1(2(1(2(2(x1)))))) -> 0(3(4(3(5(2(x1)))))) 1108.76/297.07 , 0(4(2(4(5(0(4(4(4(0(2(1(1(5(3(1(5(1(1(5(0(x1))))))))))))))))))))) 1108.76/297.07 -> 1108.76/297.07 2(1(0(0(3(4(0(3(4(5(3(1(4(2(1(5(3(3(5(5(0(x1))))))))))))))))))))) 1108.76/297.07 , 1(1(2(2(3(0(3(1(2(3(3(5(4(2(0(1(3(0(0(2(3(x1))))))))))))))))))))) 1108.76/297.07 -> 1108.76/297.07 3(3(3(1(0(4(5(2(1(2(4(5(5(5(0(3(5(3(4(4(0(x1))))))))))))))))))))) 1108.76/297.07 , 1(4(5(1(5(0(1(1(1(0(3(2(3(3(1(x1))))))))))))))) -> 1108.76/297.07 1(1(3(2(3(4(3(5(4(4(3(5(3(1(x1)))))))))))))) 1108.76/297.07 , 2(1(3(0(3(3(5(x1))))))) -> 2(5(2(2(5(5(2(x1))))))) 1108.76/297.07 , 2(1(4(2(2(0(3(0(1(0(5(x1))))))))))) -> 1108.76/297.07 2(2(5(4(2(4(1(4(3(1(x1)))))))))) 1108.76/297.07 , 2(5(1(2(2(3(2(3(2(1(4(2(0(5(5(1(0(3(3(x1))))))))))))))))))) -> 1108.76/297.07 2(3(0(4(5(0(4(3(1(3(2(0(4(1(2(4(1(3(x1)))))))))))))))))) 1108.76/297.07 , 3(2(1(3(3(1(5(1(2(0(2(0(4(1(4(2(5(5(1(5(x1)))))))))))))))))))) -> 1108.76/297.07 5(1(0(1(3(1(1(4(2(0(0(2(3(2(5(3(5(1(2(x1))))))))))))))))))) 1108.76/297.07 , 3(2(1(4(2(1(1(0(4(0(1(2(2(3(1(3(5(1(4(5(x1)))))))))))))))))))) -> 1108.76/297.07 3(2(5(5(0(5(4(2(2(5(2(1(0(1(5(0(3(3(5(2(x1)))))))))))))))))))) 1108.76/297.07 , 3(3(0(0(0(5(2(x1))))))) -> 5(3(3(1(2(5(2(x1))))))) 1108.76/297.07 , 3(3(0(1(3(4(2(1(1(2(1(x1))))))))))) -> 1108.76/297.07 5(2(4(4(3(5(3(5(5(1(1(x1))))))))))) 1108.76/297.07 , 3(3(3(0(1(1(0(x1))))))) -> 5(3(3(0(2(1(0(x1))))))) 1108.76/297.07 , 3(3(3(4(0(5(4(4(3(2(1(4(2(0(0(2(x1)))))))))))))))) -> 1108.76/297.07 3(5(1(2(5(3(5(4(5(3(1(1(4(2(2(3(x1)))))))))))))))) 1108.76/297.07 , 3(3(5(3(2(1(2(3(3(1(0(0(2(3(3(x1))))))))))))))) -> 1108.76/297.07 3(5(2(1(1(3(3(0(2(2(1(2(0(3(3(x1))))))))))))))) 1108.76/297.07 , 3(5(4(1(4(3(0(5(5(0(2(5(1(4(3(1(5(3(x1)))))))))))))))))) -> 1108.76/297.07 3(4(0(5(0(0(1(0(4(0(4(3(4(5(0(2(3(1(x1)))))))))))))))))) 1108.76/297.07 , 4(0(1(0(3(0(x1)))))) -> 2(5(0(5(5(0(x1)))))) 1108.76/297.07 , 4(0(2(3(1(4(1(x1))))))) -> 1(4(3(2(5(4(x1)))))) 1108.76/297.07 , 4(1(5(0(0(5(2(1(3(x1))))))))) -> 4(5(0(3(5(2(2(2(3(x1))))))))) 1108.76/297.07 , 4(5(3(3(2(5(5(1(3(5(1(5(0(0(2(5(5(1(x1)))))))))))))))))) -> 1108.76/297.07 4(5(5(2(2(3(0(3(3(0(4(1(3(1(1(1(x1)))))))))))))))) 1108.76/297.07 , 5(0(2(5(5(1(3(2(5(2(0(4(4(0(4(1(x1)))))))))))))))) -> 1108.76/297.07 5(1(1(0(0(2(2(2(1(3(4(3(2(5(4(x1))))))))))))))) 1108.76/297.07 , 5(2(3(5(5(0(0(0(3(4(0(2(5(x1))))))))))))) -> 1108.76/297.07 5(5(5(2(4(3(5(1(1(2(5(0(x1)))))))))))) 1108.76/297.07 , 5(2(5(1(5(0(3(0(4(2(x1)))))))))) -> 1108.76/297.07 3(3(2(5(1(3(3(5(0(2(x1)))))))))) 1108.76/297.07 , 5(3(2(3(5(0(4(0(2(3(4(5(x1)))))))))))) -> 1108.76/297.07 3(5(2(1(1(5(2(1(0(5(4(x1))))))))))) 1108.76/297.07 , 5(5(3(4(3(2(4(0(5(2(1(2(2(x1))))))))))))) -> 1108.76/297.07 5(5(4(4(0(1(0(1(3(1(4(2(x1)))))))))))) } 1108.76/297.07 Obligation: 1108.76/297.07 derivational complexity 1108.76/297.07 Answer: 1108.76/297.07 YES(?,O(n^1)) 1108.76/297.07 1108.76/297.07 The problem is match-bounded by 1. The enriched problem is 1108.76/297.07 compatible with the following automaton. 1108.76/297.07 { 0_0(1) -> 1 1108.76/297.07 , 0_1(1) -> 42 1108.76/297.07 , 0_1(2) -> 1 1108.76/297.07 , 0_1(2) -> 42 1108.76/297.07 , 0_1(3) -> 2 1108.76/297.07 , 0_1(8) -> 7 1108.76/297.07 , 0_1(12) -> 11 1108.76/297.07 , 0_1(22) -> 222 1108.76/297.07 , 0_1(25) -> 24 1108.76/297.07 , 0_1(26) -> 25 1108.76/297.07 , 0_1(29) -> 28 1108.76/297.07 , 0_1(40) -> 75 1108.76/297.07 , 0_1(43) -> 42 1108.76/297.07 , 0_1(47) -> 46 1108.76/297.07 , 0_1(57) -> 56 1108.76/297.07 , 0_1(75) -> 1 1108.76/297.07 , 0_1(84) -> 42 1108.76/297.07 , 0_1(85) -> 84 1108.76/297.07 , 0_1(88) -> 87 1108.76/297.07 , 0_1(94) -> 93 1108.76/297.07 , 0_1(100) -> 1 1108.76/297.07 , 0_1(102) -> 101 1108.76/297.07 , 0_1(109) -> 108 1108.76/297.07 , 0_1(110) -> 109 1108.76/297.07 , 0_1(120) -> 119 1108.76/297.07 , 0_1(128) -> 127 1108.76/297.07 , 0_1(131) -> 130 1108.76/297.07 , 0_1(143) -> 133 1108.76/297.07 , 0_1(163) -> 162 1108.76/297.07 , 0_1(168) -> 167 1108.76/297.07 , 0_1(170) -> 169 1108.76/297.07 , 0_1(172) -> 171 1108.76/297.07 , 0_1(173) -> 172 1108.76/297.07 , 0_1(175) -> 174 1108.76/297.07 , 0_1(177) -> 176 1108.76/297.07 , 0_1(182) -> 181 1108.76/297.07 , 0_1(185) -> 225 1108.76/297.07 , 0_1(188) -> 187 1108.76/297.07 , 0_1(195) -> 194 1108.76/297.07 , 0_1(198) -> 197 1108.76/297.07 , 0_1(203) -> 202 1108.76/297.07 , 0_1(204) -> 203 1108.76/297.07 , 0_1(228) -> 227 1108.76/297.07 , 0_1(230) -> 229 1108.76/297.07 , 1_0(1) -> 1 1108.76/297.07 , 1_1(1) -> 74 1108.76/297.07 , 1_1(9) -> 8 1108.76/297.07 , 1_1(13) -> 12 1108.76/297.07 , 1_1(15) -> 14 1108.76/297.07 , 1_1(22) -> 116 1108.76/297.07 , 1_1(23) -> 142 1108.76/297.07 , 1_1(24) -> 23 1108.76/297.07 , 1_1(34) -> 33 1108.76/297.07 , 1_1(37) -> 36 1108.76/297.07 , 1_1(42) -> 144 1108.76/297.07 , 1_1(43) -> 74 1108.76/297.07 , 1_1(46) -> 45 1108.76/297.07 , 1_1(51) -> 50 1108.76/297.07 , 1_1(62) -> 1 1108.76/297.07 , 1_1(62) -> 18 1108.76/297.07 , 1_1(62) -> 61 1108.76/297.07 , 1_1(62) -> 74 1108.76/297.07 , 1_1(63) -> 62 1108.76/297.07 , 1_1(74) -> 142 1108.76/297.07 , 1_1(83) -> 82 1108.76/297.07 , 1_1(91) -> 90 1108.76/297.07 , 1_1(96) -> 95 1108.76/297.07 , 1_1(99) -> 98 1108.76/297.07 , 1_1(100) -> 23 1108.76/297.07 , 1_1(101) -> 100 1108.76/297.07 , 1_1(103) -> 102 1108.76/297.07 , 1_1(105) -> 104 1108.76/297.07 , 1_1(106) -> 105 1108.76/297.07 , 1_1(127) -> 126 1108.76/297.07 , 1_1(129) -> 128 1108.76/297.07 , 1_1(132) -> 74 1108.76/297.07 , 1_1(134) -> 133 1108.76/297.07 , 1_1(142) -> 201 1108.76/297.07 , 1_1(146) -> 145 1108.76/297.07 , 1_1(154) -> 153 1108.76/297.07 , 1_1(155) -> 154 1108.76/297.07 , 1_1(159) -> 158 1108.76/297.07 , 1_1(160) -> 159 1108.76/297.07 , 1_1(166) -> 165 1108.76/297.07 , 1_1(174) -> 173 1108.76/297.07 , 1_1(200) -> 199 1108.76/297.07 , 1_1(202) -> 101 1108.76/297.07 , 1_1(208) -> 207 1108.76/297.07 , 1_1(209) -> 1 1108.76/297.07 , 1_1(215) -> 214 1108.76/297.07 , 1_1(216) -> 215 1108.76/297.07 , 1_1(219) -> 218 1108.76/297.07 , 1_1(225) -> 224 1108.76/297.07 , 1_1(229) -> 228 1108.76/297.07 , 1_1(231) -> 230 1108.76/297.07 , 1_1(233) -> 232 1108.76/297.07 , 2_0(1) -> 1 1108.76/297.07 , 2_1(1) -> 22 1108.76/297.07 , 2_1(18) -> 17 1108.76/297.07 , 2_1(21) -> 134 1108.76/297.07 , 2_1(22) -> 156 1108.76/297.07 , 2_1(23) -> 1 1108.76/297.07 , 2_1(23) -> 18 1108.76/297.07 , 2_1(23) -> 22 1108.76/297.07 , 2_1(23) -> 42 1108.76/297.07 , 2_1(23) -> 61 1108.76/297.07 , 2_1(23) -> 143 1108.76/297.07 , 2_1(23) -> 216 1108.76/297.07 , 2_1(36) -> 35 1108.76/297.07 , 2_1(41) -> 216 1108.76/297.07 , 2_1(42) -> 166 1108.76/297.07 , 2_1(50) -> 49 1108.76/297.07 , 2_1(52) -> 51 1108.76/297.07 , 2_1(65) -> 64 1108.76/297.07 , 2_1(73) -> 182 1108.76/297.07 , 2_1(74) -> 143 1108.76/297.07 , 2_1(76) -> 75 1108.76/297.07 , 2_1(77) -> 76 1108.76/297.07 , 2_1(78) -> 23 1108.76/297.07 , 2_1(81) -> 80 1108.76/297.07 , 2_1(93) -> 92 1108.76/297.07 , 2_1(97) -> 96 1108.76/297.07 , 2_1(99) -> 157 1108.76/297.07 , 2_1(100) -> 22 1108.76/297.07 , 2_1(101) -> 143 1108.76/297.07 , 2_1(108) -> 107 1108.76/297.07 , 2_1(111) -> 110 1108.76/297.07 , 2_1(113) -> 112 1108.76/297.07 , 2_1(117) -> 43 1108.76/297.07 , 2_1(123) -> 122 1108.76/297.07 , 2_1(124) -> 123 1108.76/297.07 , 2_1(126) -> 125 1108.76/297.07 , 2_1(135) -> 100 1108.76/297.07 , 2_1(144) -> 143 1108.76/297.07 , 2_1(145) -> 22 1108.76/297.07 , 2_1(147) -> 146 1108.76/297.07 , 2_1(156) -> 190 1108.76/297.07 , 2_1(157) -> 156 1108.76/297.07 , 2_1(158) -> 145 1108.76/297.07 , 2_1(164) -> 163 1108.76/297.07 , 2_1(165) -> 164 1108.76/297.07 , 2_1(167) -> 166 1108.76/297.07 , 2_1(185) -> 184 1108.76/297.07 , 2_1(187) -> 22 1108.76/297.07 , 2_1(192) -> 191 1108.76/297.07 , 2_1(193) -> 192 1108.76/297.07 , 2_1(205) -> 204 1108.76/297.07 , 2_1(206) -> 205 1108.76/297.07 , 2_1(207) -> 206 1108.76/297.07 , 2_1(210) -> 22 1108.76/297.07 , 2_1(211) -> 210 1108.76/297.07 , 2_1(217) -> 44 1108.76/297.07 , 2_1(224) -> 223 1108.76/297.07 , 3_0(1) -> 1 1108.76/297.07 , 3_1(1) -> 99 1108.76/297.07 , 3_1(5) -> 4 1108.76/297.07 , 3_1(10) -> 9 1108.76/297.07 , 3_1(14) -> 13 1108.76/297.07 , 3_1(16) -> 15 1108.76/297.07 , 3_1(19) -> 2 1108.76/297.07 , 3_1(20) -> 131 1108.76/297.07 , 3_1(21) -> 20 1108.76/297.07 , 3_1(23) -> 99 1108.76/297.07 , 3_1(27) -> 26 1108.76/297.07 , 3_1(30) -> 29 1108.76/297.07 , 3_1(33) -> 32 1108.76/297.07 , 3_1(39) -> 38 1108.76/297.07 , 3_1(40) -> 39 1108.76/297.07 , 3_1(43) -> 1 1108.76/297.07 , 3_1(43) -> 21 1108.76/297.07 , 3_1(43) -> 41 1108.76/297.07 , 3_1(43) -> 72 1108.76/297.07 , 3_1(43) -> 74 1108.76/297.07 , 3_1(43) -> 99 1108.76/297.07 , 3_1(43) -> 142 1108.76/297.07 , 3_1(43) -> 168 1108.76/297.07 , 3_1(44) -> 43 1108.76/297.07 , 3_1(45) -> 44 1108.76/297.07 , 3_1(58) -> 57 1108.76/297.07 , 3_1(60) -> 59 1108.76/297.07 , 3_1(62) -> 208 1108.76/297.07 , 3_1(64) -> 63 1108.76/297.07 , 3_1(66) -> 65 1108.76/297.07 , 3_1(68) -> 67 1108.76/297.07 , 3_1(72) -> 71 1108.76/297.07 , 3_1(74) -> 73 1108.76/297.07 , 3_1(76) -> 99 1108.76/297.07 , 3_1(84) -> 23 1108.76/297.07 , 3_1(90) -> 89 1108.76/297.07 , 3_1(92) -> 91 1108.76/297.07 , 3_1(99) -> 168 1108.76/297.07 , 3_1(104) -> 103 1108.76/297.07 , 3_1(112) -> 111 1108.76/297.07 , 3_1(115) -> 114 1108.76/297.07 , 3_1(132) -> 100 1108.76/297.07 , 3_1(133) -> 132 1108.76/297.07 , 3_1(135) -> 99 1108.76/297.07 , 3_1(138) -> 137 1108.76/297.07 , 3_1(140) -> 139 1108.76/297.07 , 3_1(142) -> 200 1108.76/297.07 , 3_1(149) -> 148 1108.76/297.07 , 3_1(153) -> 152 1108.76/297.07 , 3_1(161) -> 160 1108.76/297.07 , 3_1(162) -> 161 1108.76/297.07 , 3_1(179) -> 178 1108.76/297.07 , 3_1(184) -> 183 1108.76/297.07 , 3_1(189) -> 188 1108.76/297.07 , 3_1(194) -> 193 1108.76/297.07 , 3_1(196) -> 195 1108.76/297.07 , 3_1(197) -> 196 1108.76/297.07 , 3_1(201) -> 200 1108.76/297.07 , 3_1(213) -> 212 1108.76/297.07 , 3_1(220) -> 219 1108.76/297.07 , 3_1(221) -> 220 1108.76/297.07 , 3_1(232) -> 231 1108.76/297.07 , 4_0(1) -> 1 1108.76/297.07 , 4_1(1) -> 18 1108.76/297.07 , 4_1(17) -> 16 1108.76/297.07 , 4_1(20) -> 19 1108.76/297.07 , 4_1(22) -> 233 1108.76/297.07 , 4_1(23) -> 233 1108.76/297.07 , 4_1(28) -> 27 1108.76/297.07 , 4_1(31) -> 30 1108.76/297.07 , 4_1(35) -> 34 1108.76/297.07 , 4_1(42) -> 61 1108.76/297.07 , 4_1(48) -> 47 1108.76/297.07 , 4_1(53) -> 52 1108.76/297.07 , 4_1(61) -> 60 1108.76/297.07 , 4_1(62) -> 18 1108.76/297.07 , 4_1(67) -> 66 1108.76/297.07 , 4_1(70) -> 69 1108.76/297.07 , 4_1(71) -> 70 1108.76/297.07 , 4_1(73) -> 83 1108.76/297.07 , 4_1(74) -> 97 1108.76/297.07 , 4_1(80) -> 79 1108.76/297.07 , 4_1(82) -> 81 1108.76/297.07 , 4_1(86) -> 85 1108.76/297.07 , 4_1(89) -> 88 1108.76/297.07 , 4_1(95) -> 94 1108.76/297.07 , 4_1(98) -> 97 1108.76/297.07 , 4_1(99) -> 83 1108.76/297.07 , 4_1(100) -> 18 1108.76/297.07 , 4_1(107) -> 106 1108.76/297.07 , 4_1(122) -> 121 1108.76/297.07 , 4_1(136) -> 135 1108.76/297.07 , 4_1(137) -> 136 1108.76/297.07 , 4_1(151) -> 150 1108.76/297.07 , 4_1(156) -> 155 1108.76/297.07 , 4_1(169) -> 43 1108.76/297.07 , 4_1(176) -> 175 1108.76/297.07 , 4_1(178) -> 177 1108.76/297.07 , 4_1(180) -> 179 1108.76/297.07 , 4_1(183) -> 62 1108.76/297.07 , 4_1(186) -> 1 1108.76/297.07 , 4_1(186) -> 18 1108.76/297.07 , 4_1(186) -> 97 1108.76/297.07 , 4_1(187) -> 18 1108.76/297.07 , 4_1(199) -> 198 1108.76/297.07 , 4_1(209) -> 18 1108.76/297.07 , 4_1(212) -> 211 1108.76/297.07 , 4_1(226) -> 209 1108.76/297.07 , 4_1(227) -> 226 1108.76/297.07 , 5_0(1) -> 1 1108.76/297.07 , 5_1(1) -> 41 1108.76/297.07 , 5_1(4) -> 3 1108.76/297.07 , 5_1(6) -> 5 1108.76/297.07 , 5_1(7) -> 6 1108.76/297.07 , 5_1(11) -> 10 1108.76/297.07 , 5_1(18) -> 185 1108.76/297.07 , 5_1(21) -> 77 1108.76/297.07 , 5_1(22) -> 21 1108.76/297.07 , 5_1(23) -> 21 1108.76/297.07 , 5_1(32) -> 31 1108.76/297.07 , 5_1(38) -> 37 1108.76/297.07 , 5_1(41) -> 40 1108.76/297.07 , 5_1(42) -> 41 1108.76/297.07 , 5_1(49) -> 48 1108.76/297.07 , 5_1(54) -> 53 1108.76/297.07 , 5_1(55) -> 54 1108.76/297.07 , 5_1(56) -> 55 1108.76/297.07 , 5_1(59) -> 58 1108.76/297.07 , 5_1(69) -> 68 1108.76/297.07 , 5_1(73) -> 72 1108.76/297.07 , 5_1(74) -> 141 1108.76/297.07 , 5_1(75) -> 23 1108.76/297.07 , 5_1(79) -> 78 1108.76/297.07 , 5_1(87) -> 86 1108.76/297.07 , 5_1(99) -> 72 1108.76/297.07 , 5_1(100) -> 1 1108.76/297.07 , 5_1(100) -> 21 1108.76/297.07 , 5_1(100) -> 40 1108.76/297.07 , 5_1(100) -> 41 1108.76/297.07 , 5_1(100) -> 99 1108.76/297.07 , 5_1(100) -> 168 1108.76/297.07 , 5_1(100) -> 221 1108.76/297.07 , 5_1(114) -> 113 1108.76/297.07 , 5_1(116) -> 115 1108.76/297.07 , 5_1(118) -> 117 1108.76/297.07 , 5_1(119) -> 118 1108.76/297.07 , 5_1(121) -> 120 1108.76/297.07 , 5_1(125) -> 124 1108.76/297.07 , 5_1(130) -> 129 1108.76/297.07 , 5_1(139) -> 138 1108.76/297.07 , 5_1(141) -> 140 1108.76/297.07 , 5_1(142) -> 141 1108.76/297.07 , 5_1(145) -> 43 1108.76/297.07 , 5_1(148) -> 147 1108.76/297.07 , 5_1(150) -> 149 1108.76/297.07 , 5_1(152) -> 151 1108.76/297.07 , 5_1(171) -> 170 1108.76/297.07 , 5_1(181) -> 180 1108.76/297.07 , 5_1(187) -> 186 1108.76/297.07 , 5_1(190) -> 189 1108.76/297.07 , 5_1(191) -> 187 1108.76/297.07 , 5_1(209) -> 100 1108.76/297.07 , 5_1(210) -> 209 1108.76/297.07 , 5_1(214) -> 213 1108.76/297.07 , 5_1(218) -> 217 1108.76/297.07 , 5_1(222) -> 221 1108.76/297.07 , 5_1(223) -> 160 } 1108.76/297.07 1108.76/297.07 Hurray, we answered YES(?,O(n^1)) 1109.41/297.55 EOF