YES(?,O(n^1)) 1122.63/297.08 YES(?,O(n^1)) 1122.63/297.08 1122.63/297.08 We are left with following problem, upon which TcT provides the 1122.63/297.08 certificate YES(?,O(n^1)). 1122.63/297.08 1122.63/297.08 Strict Trs: 1122.63/297.08 { 0(0(2(2(5(0(3(0(4(0(4(0(2(3(1(5(x1)))))))))))))))) -> 1122.63/297.08 0(4(2(5(2(5(3(0(4(3(2(0(2(4(5(x1))))))))))))))) 1122.63/297.08 , 0(1(1(2(x1)))) -> 0(0(1(x1))) 1122.63/297.08 , 0(5(3(2(3(1(5(4(4(x1))))))))) -> 0(0(4(4(1(0(3(4(x1)))))))) 1122.63/297.08 , 1(0(4(3(5(2(1(0(1(x1))))))))) -> 1(4(2(0(1(1(3(4(1(x1))))))))) 1122.63/297.08 , 1(0(5(5(5(3(4(1(x1)))))))) -> 4(3(0(3(4(3(0(5(0(x1))))))))) 1122.63/297.08 , 1(1(0(1(1(4(5(0(4(1(3(0(4(4(0(5(5(0(2(0(x1)))))))))))))))))))) -> 1122.63/297.08 4(0(5(3(5(3(2(2(5(3(5(1(2(4(2(4(5(0(5(5(x1)))))))))))))))))))) 1122.63/297.08 , 1(2(0(3(1(0(4(3(3(0(3(0(5(3(x1)))))))))))))) -> 1122.63/297.08 4(2(0(5(3(3(4(4(3(1(5(0(4(x1))))))))))))) 1122.63/297.08 , 1(2(3(3(4(5(x1)))))) -> 4(0(0(1(5(x1))))) 1122.63/297.08 , 1(2(4(4(4(5(5(0(2(2(x1)))))))))) -> 4(4(1(1(0(5(5(5(0(x1))))))))) 1122.63/297.08 , 1(5(0(0(1(4(5(3(5(4(1(0(1(2(1(2(0(x1))))))))))))))))) -> 1122.63/297.08 1(4(0(1(3(5(3(3(4(1(0(4(3(3(0(5(1(0(x1)))))))))))))))))) 1122.63/297.08 , 1(5(4(4(3(2(4(0(1(5(2(0(5(2(x1)))))))))))))) -> 1122.63/297.08 1(5(5(2(2(2(4(0(0(5(3(3(2(2(2(0(x1)))))))))))))))) 1122.63/297.08 , 2(0(3(1(1(0(2(5(3(3(2(3(x1)))))))))))) -> 1122.63/297.08 5(4(0(4(4(4(1(4(0(3(x1)))))))))) 1122.63/297.08 , 2(1(3(0(5(1(2(2(5(5(1(0(2(1(3(2(x1)))))))))))))))) -> 1122.63/297.08 5(5(2(3(2(4(5(0(2(0(3(3(4(1(1(x1))))))))))))))) 1122.63/297.08 , 2(1(3(1(5(5(5(1(1(1(x1)))))))))) -> 5(4(2(3(5(4(2(2(1(x1))))))))) 1122.63/297.08 , 2(4(4(1(5(2(3(3(2(0(4(5(3(5(0(2(x1)))))))))))))))) -> 1122.63/297.08 0(5(1(4(5(2(4(1(1(5(4(3(3(x1))))))))))))) 1122.63/297.08 , 3(1(2(1(3(1(1(4(3(5(2(0(3(3(2(3(1(3(0(1(x1)))))))))))))))))))) -> 1122.63/297.08 0(4(3(5(1(4(2(4(0(5(3(2(4(1(5(5(1(x1))))))))))))))))) 1122.63/297.08 , 3(2(3(4(3(5(5(3(4(0(5(4(3(5(2(x1))))))))))))))) -> 1122.63/297.08 3(5(5(0(1(4(3(4(1(1(5(1(0(x1))))))))))))) 1122.63/297.08 , 3(4(1(1(4(0(1(2(2(4(5(3(2(x1))))))))))))) -> 1122.63/297.08 5(3(1(3(4(5(4(0(3(0(1(x1))))))))))) 1122.63/297.08 , 3(4(3(0(4(0(3(2(x1)))))))) -> 5(1(5(4(2(x1))))) 1122.63/297.08 , 3(5(0(1(4(0(0(1(3(5(4(1(0(2(x1)))))))))))))) -> 1122.63/297.08 1(1(4(1(1(5(0(3(0(0(4(5(0(x1))))))))))))) 1122.63/297.08 , 4(0(4(4(2(1(4(2(0(3(1(2(5(5(5(5(3(1(2(x1))))))))))))))))))) -> 1122.63/297.08 3(5(4(4(2(0(4(4(4(0(1(0(2(4(0(4(1(5(x1)))))))))))))))))) 1122.63/297.08 , 4(4(3(4(3(1(3(x1))))))) -> 0(1(3(1(4(4(x1)))))) 1122.63/297.08 , 5(0(1(3(4(2(1(3(1(4(2(0(0(2(3(2(5(2(2(4(x1)))))))))))))))))))) -> 1122.63/297.08 5(4(1(5(5(0(1(3(1(2(1(1(2(4(3(2(5(x1))))))))))))))))) 1122.63/297.08 , 5(2(5(2(5(1(1(x1))))))) -> 5(4(5(5(1(x1))))) 1122.63/297.08 , 5(3(2(1(1(2(1(5(3(x1))))))))) -> 5(1(4(3(3(5(0(4(x1)))))))) } 1122.63/297.08 Obligation: 1122.63/297.08 derivational complexity 1122.63/297.08 Answer: 1122.63/297.08 YES(?,O(n^1)) 1122.63/297.08 1122.63/297.08 The problem is match-bounded by 1. The enriched problem is 1122.63/297.08 compatible with the following automaton. 1122.63/297.08 { 0_0(1) -> 1 1122.63/297.08 , 0_1(1) -> 36 1122.63/297.08 , 0_1(2) -> 1 1122.63/297.08 , 0_1(2) -> 2 1122.63/297.08 , 0_1(2) -> 21 1122.63/297.08 , 0_1(2) -> 36 1122.63/297.08 , 0_1(2) -> 105 1122.63/297.08 , 0_1(2) -> 163 1122.63/297.08 , 0_1(2) -> 188 1122.63/297.08 , 0_1(9) -> 8 1122.63/297.08 , 0_1(13) -> 12 1122.63/297.08 , 0_1(16) -> 2 1122.63/297.08 , 0_1(20) -> 19 1122.63/297.08 , 0_1(21) -> 63 1122.63/297.08 , 0_1(22) -> 36 1122.63/297.08 , 0_1(25) -> 24 1122.63/297.08 , 0_1(31) -> 30 1122.63/297.08 , 0_1(35) -> 34 1122.63/297.08 , 0_1(37) -> 29 1122.63/297.08 , 0_1(53) -> 52 1122.63/297.08 , 0_1(55) -> 54 1122.63/297.08 , 0_1(64) -> 37 1122.63/297.08 , 0_1(68) -> 67 1122.63/297.08 , 0_1(70) -> 23 1122.63/297.08 , 0_1(78) -> 77 1122.63/297.08 , 0_1(82) -> 81 1122.63/297.08 , 0_1(90) -> 89 1122.63/297.08 , 0_1(91) -> 90 1122.63/297.08 , 0_1(99) -> 98 1122.63/297.08 , 0_1(105) -> 104 1122.63/297.08 , 0_1(112) -> 111 1122.63/297.08 , 0_1(114) -> 113 1122.63/297.08 , 0_1(139) -> 138 1122.63/297.08 , 0_1(148) -> 147 1122.63/297.08 , 0_1(160) -> 159 1122.63/297.08 , 0_1(169) -> 168 1122.63/297.08 , 0_1(171) -> 170 1122.63/297.08 , 0_1(172) -> 171 1122.63/297.08 , 0_1(176) -> 175 1122.63/297.08 , 0_1(180) -> 179 1122.63/297.08 , 0_1(182) -> 181 1122.63/297.08 , 0_1(185) -> 184 1122.63/297.08 , 0_1(192) -> 191 1122.63/297.08 , 1_0(1) -> 1 1122.63/297.08 , 1_1(1) -> 16 1122.63/297.08 , 1_1(15) -> 64 1122.63/297.08 , 1_1(16) -> 117 1122.63/297.08 , 1_1(19) -> 18 1122.63/297.08 , 1_1(22) -> 1 1122.63/297.08 , 1_1(22) -> 16 1122.63/297.08 , 1_1(22) -> 64 1122.63/297.08 , 1_1(22) -> 83 1122.63/297.08 , 1_1(22) -> 105 1122.63/297.08 , 1_1(26) -> 25 1122.63/297.08 , 1_1(27) -> 26 1122.63/297.08 , 1_1(36) -> 83 1122.63/297.08 , 1_1(47) -> 46 1122.63/297.08 , 1_1(53) -> 143 1122.63/297.08 , 1_1(62) -> 61 1122.63/297.08 , 1_1(66) -> 65 1122.63/297.08 , 1_1(67) -> 66 1122.63/297.08 , 1_1(71) -> 70 1122.63/297.08 , 1_1(77) -> 76 1122.63/297.08 , 1_1(82) -> 153 1122.63/297.08 , 1_1(103) -> 102 1122.63/297.08 , 1_1(104) -> 18 1122.63/297.08 , 1_1(124) -> 123 1122.63/297.08 , 1_1(129) -> 128 1122.63/297.08 , 1_1(130) -> 129 1122.63/297.08 , 1_1(135) -> 134 1122.63/297.08 , 1_1(144) -> 143 1122.63/297.08 , 1_1(149) -> 148 1122.63/297.08 , 1_1(153) -> 152 1122.63/297.08 , 1_1(155) -> 154 1122.63/297.08 , 1_1(161) -> 97 1122.63/297.08 , 1_1(164) -> 22 1122.63/297.08 , 1_1(166) -> 165 1122.63/297.08 , 1_1(167) -> 166 1122.63/297.08 , 1_1(181) -> 180 1122.63/297.08 , 1_1(186) -> 2 1122.63/297.08 , 1_1(188) -> 187 1122.63/297.08 , 1_1(189) -> 98 1122.63/297.08 , 1_1(193) -> 192 1122.63/297.08 , 1_1(195) -> 194 1122.63/297.08 , 1_1(197) -> 196 1122.63/297.08 , 1_1(198) -> 197 1122.63/297.08 , 2_0(1) -> 1 1122.63/297.08 , 2_1(1) -> 163 1122.63/297.08 , 2_1(4) -> 3 1122.63/297.08 , 2_1(6) -> 5 1122.63/297.08 , 2_1(12) -> 11 1122.63/297.08 , 2_1(14) -> 13 1122.63/297.08 , 2_1(15) -> 201 1122.63/297.08 , 2_1(16) -> 122 1122.63/297.08 , 2_1(22) -> 122 1122.63/297.08 , 2_1(24) -> 23 1122.63/297.08 , 2_1(36) -> 96 1122.63/297.08 , 2_1(42) -> 41 1122.63/297.08 , 2_1(43) -> 42 1122.63/297.08 , 2_1(48) -> 47 1122.63/297.08 , 2_1(50) -> 49 1122.63/297.08 , 2_1(54) -> 29 1122.63/297.08 , 2_1(86) -> 85 1122.63/297.08 , 2_1(87) -> 86 1122.63/297.08 , 2_1(88) -> 87 1122.63/297.08 , 2_1(95) -> 94 1122.63/297.08 , 2_1(96) -> 95 1122.63/297.08 , 2_1(107) -> 106 1122.63/297.08 , 2_1(109) -> 108 1122.63/297.08 , 2_1(113) -> 112 1122.63/297.08 , 2_1(118) -> 98 1122.63/297.08 , 2_1(122) -> 121 1122.63/297.08 , 2_1(127) -> 126 1122.63/297.08 , 2_1(137) -> 136 1122.63/297.08 , 2_1(142) -> 141 1122.63/297.08 , 2_1(175) -> 174 1122.63/297.08 , 2_1(183) -> 182 1122.63/297.08 , 2_1(196) -> 195 1122.63/297.08 , 2_1(199) -> 198 1122.63/297.08 , 3_0(1) -> 1 1122.63/297.08 , 3_1(1) -> 105 1122.63/297.08 , 3_1(2) -> 160 1122.63/297.08 , 3_1(8) -> 7 1122.63/297.08 , 3_1(11) -> 10 1122.63/297.08 , 3_1(21) -> 20 1122.63/297.08 , 3_1(28) -> 27 1122.63/297.08 , 3_1(29) -> 20 1122.63/297.08 , 3_1(30) -> 29 1122.63/297.08 , 3_1(32) -> 31 1122.63/297.08 , 3_1(34) -> 33 1122.63/297.08 , 3_1(39) -> 38 1122.63/297.08 , 3_1(41) -> 40 1122.63/297.08 , 3_1(45) -> 44 1122.63/297.08 , 3_1(57) -> 56 1122.63/297.08 , 3_1(58) -> 57 1122.63/297.08 , 3_1(61) -> 60 1122.63/297.08 , 3_1(62) -> 204 1122.63/297.08 , 3_1(72) -> 71 1122.63/297.08 , 3_1(74) -> 73 1122.63/297.08 , 3_1(75) -> 74 1122.63/297.08 , 3_1(80) -> 79 1122.63/297.08 , 3_1(81) -> 80 1122.63/297.08 , 3_1(93) -> 92 1122.63/297.08 , 3_1(94) -> 93 1122.63/297.08 , 3_1(105) -> 132 1122.63/297.08 , 3_1(108) -> 107 1122.63/297.08 , 3_1(115) -> 114 1122.63/297.08 , 3_1(116) -> 115 1122.63/297.08 , 3_1(119) -> 118 1122.63/297.08 , 3_1(133) -> 3 1122.63/297.08 , 3_1(141) -> 140 1122.63/297.08 , 3_1(145) -> 1 1122.63/297.08 , 3_1(145) -> 21 1122.63/297.08 , 3_1(145) -> 105 1122.63/297.08 , 3_1(151) -> 150 1122.63/297.08 , 3_1(154) -> 97 1122.63/297.08 , 3_1(156) -> 155 1122.63/297.08 , 3_1(170) -> 169 1122.63/297.08 , 3_1(187) -> 186 1122.63/297.08 , 3_1(194) -> 193 1122.63/297.08 , 3_1(201) -> 200 1122.63/297.08 , 3_1(204) -> 203 1122.63/297.08 , 4_0(1) -> 1 1122.63/297.08 , 4_1(1) -> 21 1122.63/297.08 , 4_1(2) -> 28 1122.63/297.08 , 4_1(3) -> 2 1122.63/297.08 , 4_1(10) -> 9 1122.63/297.08 , 4_1(15) -> 14 1122.63/297.08 , 4_1(16) -> 28 1122.63/297.08 , 4_1(17) -> 16 1122.63/297.08 , 4_1(18) -> 17 1122.63/297.08 , 4_1(21) -> 188 1122.63/297.08 , 4_1(22) -> 14 1122.63/297.08 , 4_1(23) -> 22 1122.63/297.08 , 4_1(29) -> 1 1122.63/297.08 , 4_1(29) -> 16 1122.63/297.08 , 4_1(29) -> 83 1122.63/297.08 , 4_1(29) -> 117 1122.63/297.08 , 4_1(33) -> 32 1122.63/297.08 , 4_1(35) -> 172 1122.63/297.08 , 4_1(49) -> 48 1122.63/297.08 , 4_1(51) -> 50 1122.63/297.08 , 4_1(59) -> 58 1122.63/297.08 , 4_1(60) -> 59 1122.63/297.08 , 4_1(64) -> 185 1122.63/297.08 , 4_1(65) -> 29 1122.63/297.08 , 4_1(76) -> 75 1122.63/297.08 , 4_1(79) -> 78 1122.63/297.08 , 4_1(89) -> 88 1122.63/297.08 , 4_1(98) -> 97 1122.63/297.08 , 4_1(100) -> 99 1122.63/297.08 , 4_1(101) -> 100 1122.63/297.08 , 4_1(102) -> 101 1122.63/297.08 , 4_1(104) -> 103 1122.63/297.08 , 4_1(110) -> 109 1122.63/297.08 , 4_1(117) -> 116 1122.63/297.08 , 4_1(121) -> 120 1122.63/297.08 , 4_1(125) -> 124 1122.63/297.08 , 4_1(128) -> 127 1122.63/297.08 , 4_1(132) -> 131 1122.63/297.08 , 4_1(136) -> 135 1122.63/297.08 , 4_1(138) -> 137 1122.63/297.08 , 4_1(143) -> 142 1122.63/297.08 , 4_1(144) -> 97 1122.63/297.08 , 4_1(145) -> 21 1122.63/297.08 , 4_1(150) -> 149 1122.63/297.08 , 4_1(152) -> 151 1122.63/297.08 , 4_1(154) -> 21 1122.63/297.08 , 4_1(157) -> 156 1122.63/297.08 , 4_1(159) -> 158 1122.63/297.08 , 4_1(163) -> 162 1122.63/297.08 , 4_1(165) -> 164 1122.63/297.08 , 4_1(173) -> 146 1122.63/297.08 , 4_1(174) -> 173 1122.63/297.08 , 4_1(177) -> 176 1122.63/297.08 , 4_1(178) -> 177 1122.63/297.08 , 4_1(179) -> 178 1122.63/297.08 , 4_1(184) -> 183 1122.63/297.08 , 4_1(200) -> 199 1122.63/297.08 , 4_1(203) -> 161 1122.63/297.08 , 5_0(1) -> 1 1122.63/297.08 , 5_1(1) -> 15 1122.63/297.08 , 5_1(2) -> 15 1122.63/297.08 , 5_1(5) -> 4 1122.63/297.08 , 5_1(7) -> 6 1122.63/297.08 , 5_1(15) -> 53 1122.63/297.08 , 5_1(16) -> 82 1122.63/297.08 , 5_1(22) -> 82 1122.63/297.08 , 5_1(29) -> 15 1122.63/297.08 , 5_1(35) -> 69 1122.63/297.08 , 5_1(36) -> 35 1122.63/297.08 , 5_1(38) -> 37 1122.63/297.08 , 5_1(40) -> 39 1122.63/297.08 , 5_1(44) -> 43 1122.63/297.08 , 5_1(46) -> 45 1122.63/297.08 , 5_1(52) -> 51 1122.63/297.08 , 5_1(56) -> 55 1122.63/297.08 , 5_1(63) -> 62 1122.63/297.08 , 5_1(69) -> 68 1122.63/297.08 , 5_1(73) -> 72 1122.63/297.08 , 5_1(82) -> 144 1122.63/297.08 , 5_1(83) -> 82 1122.63/297.08 , 5_1(84) -> 22 1122.63/297.08 , 5_1(85) -> 84 1122.63/297.08 , 5_1(92) -> 91 1122.63/297.08 , 5_1(97) -> 1 1122.63/297.08 , 5_1(97) -> 15 1122.63/297.08 , 5_1(97) -> 20 1122.63/297.08 , 5_1(97) -> 27 1122.63/297.08 , 5_1(97) -> 35 1122.63/297.08 , 5_1(97) -> 96 1122.63/297.08 , 5_1(97) -> 105 1122.63/297.08 , 5_1(97) -> 115 1122.63/297.08 , 5_1(97) -> 122 1122.63/297.08 , 5_1(97) -> 163 1122.63/297.08 , 5_1(106) -> 97 1122.63/297.08 , 5_1(111) -> 110 1122.63/297.08 , 5_1(120) -> 119 1122.63/297.08 , 5_1(123) -> 2 1122.63/297.08 , 5_1(126) -> 125 1122.63/297.08 , 5_1(131) -> 130 1122.63/297.08 , 5_1(134) -> 133 1122.63/297.08 , 5_1(140) -> 139 1122.63/297.08 , 5_1(146) -> 145 1122.63/297.08 , 5_1(147) -> 146 1122.63/297.08 , 5_1(158) -> 157 1122.63/297.08 , 5_1(162) -> 161 1122.63/297.08 , 5_1(168) -> 167 1122.63/297.08 , 5_1(190) -> 189 1122.63/297.08 , 5_1(191) -> 190 } 1122.63/297.08 1122.63/297.08 Hurray, we answered YES(?,O(n^1)) 1123.34/297.57 EOF