YES(?,O(n^1)) 1126.72/298.33 YES(?,O(n^1)) 1126.72/298.33 1126.72/298.33 We are left with following problem, upon which TcT provides the 1126.72/298.33 certificate YES(?,O(n^1)). 1126.72/298.33 1126.72/298.33 Strict Trs: 1126.72/298.33 { 0(0(3(4(0(2(0(x1))))))) -> 4(3(4(3(0(2(0(x1))))))) 1126.72/298.33 , 0(1(2(1(x1)))) -> 0(3(1(x1))) 1126.72/298.33 , 0(1(5(3(3(4(1(0(1(4(3(4(0(5(5(2(3(5(5(x1))))))))))))))))))) -> 1126.72/298.33 3(1(2(3(4(5(2(4(0(4(5(2(2(3(1(0(2(2(3(x1))))))))))))))))))) 1126.72/298.33 , 0(2(5(3(5(0(4(x1))))))) -> 0(2(3(3(5(4(1(x1))))))) 1126.72/298.33 , 1(2(0(4(2(1(1(5(x1)))))))) -> 2(3(2(0(5(2(4(x1))))))) 1126.72/298.33 , 1(2(1(2(5(x1))))) -> 3(4(5(5(x1)))) 1126.72/298.33 , 1(2(3(1(2(1(x1)))))) -> 1(5(0(4(3(x1))))) 1126.72/298.33 , 1(4(3(2(0(3(0(5(5(0(4(2(x1)))))))))))) -> 1126.72/298.33 1(0(4(2(0(0(4(2(4(3(3(2(x1)))))))))))) 1126.72/298.33 , 1(5(0(0(5(4(4(3(4(3(2(2(2(2(3(4(4(1(3(0(2(x1))))))))))))))))))))) 1126.72/298.33 -> 1126.72/298.33 2(5(3(0(2(1(5(4(2(3(4(1(1(5(1(1(5(0(4(4(2(x1))))))))))))))))))))) 1126.72/298.33 , 1(5(3(5(0(1(3(2(2(0(4(0(4(4(5(0(x1)))))))))))))))) -> 1126.72/298.33 2(1(1(2(1(2(4(2(3(3(4(2(5(5(0(0(0(0(x1)))))))))))))))))) 1126.72/298.33 , 2(2(5(2(3(0(3(1(4(4(3(4(4(0(3(0(1(0(0(x1))))))))))))))))))) -> 1126.72/298.33 3(1(1(5(4(3(0(0(1(0(2(4(4(4(1(5(0(0(x1)))))))))))))))))) 1126.72/298.33 , 2(3(2(5(1(5(3(0(5(1(4(5(5(x1))))))))))))) -> 1126.72/298.33 1(4(2(1(3(0(1(5(4(1(5(4(x1)))))))))))) 1126.72/298.33 , 2(3(4(5(5(2(2(0(x1)))))))) -> 5(4(5(3(0(0(2(x1))))))) 1126.72/298.33 , 2(5(3(3(2(1(4(5(4(0(3(2(5(x1))))))))))))) -> 1126.72/298.33 5(0(3(1(0(5(5(3(5(0(1(x1))))))))))) 1126.72/298.33 , 3(0(2(0(2(4(2(1(1(0(1(x1))))))))))) -> 1126.72/298.33 3(0(4(5(3(1(5(5(4(1(x1)))))))))) 1126.72/298.33 , 3(3(2(0(1(0(3(5(5(5(2(5(x1)))))))))))) -> 1126.72/298.33 5(3(0(4(2(4(0(4(2(5(1(2(x1)))))))))))) 1126.72/298.33 , 3(3(5(2(4(3(x1)))))) -> 0(3(4(5(3(x1))))) 1126.72/298.33 , 3(4(2(0(x1)))) -> 3(1(4(x1))) 1126.72/298.33 , 4(0(1(1(5(3(4(1(5(x1))))))))) -> 0(1(4(4(2(4(5(3(x1)))))))) 1126.72/298.33 , 4(0(2(2(1(1(1(0(1(5(0(2(0(4(1(1(4(4(x1)))))))))))))))))) -> 1126.72/298.33 4(4(1(3(4(1(5(2(1(1(4(1(5(1(1(2(1(4(x1)))))))))))))))))) 1126.72/298.33 , 4(0(3(1(5(4(0(2(4(5(x1)))))))))) -> 1126.72/298.33 5(5(0(2(1(5(3(0(2(4(x1)))))))))) 1126.72/298.33 , 4(3(5(1(0(0(1(1(2(1(1(2(1(3(x1)))))))))))))) -> 1126.72/298.33 4(2(1(0(0(0(0(4(2(2(2(0(0(x1))))))))))))) 1126.72/298.33 , 5(0(5(0(1(3(1(3(2(4(1(4(4(0(4(5(0(1(x1)))))))))))))))))) -> 1126.72/298.33 5(3(3(4(2(0(2(2(0(1(0(5(2(2(0(0(3(0(1(x1))))))))))))))))))) 1126.72/298.33 , 5(2(3(0(5(4(1(0(4(1(4(3(3(3(5(5(2(x1))))))))))))))))) -> 1126.72/298.33 5(2(3(4(5(4(0(5(3(5(3(4(4(5(0(2(x1)))))))))))))))) 1126.72/298.33 , 5(2(3(1(3(4(x1)))))) -> 5(0(1(4(3(x1))))) } 1126.72/298.33 Obligation: 1126.72/298.33 derivational complexity 1126.72/298.33 Answer: 1126.72/298.33 YES(?,O(n^1)) 1126.72/298.33 1126.72/298.33 The problem is match-bounded by 2. The enriched problem is 1126.72/298.33 compatible with the following automaton. 1126.72/298.33 { 0_0(1) -> 1 1126.72/298.33 , 0_1(1) -> 7 1126.72/298.33 , 0_1(2) -> 180 1126.72/298.33 , 0_1(6) -> 5 1126.72/298.33 , 0_1(7) -> 85 1126.72/298.33 , 0_1(8) -> 1 1126.72/298.33 , 0_1(8) -> 7 1126.72/298.33 , 0_1(8) -> 27 1126.72/298.33 , 0_1(8) -> 37 1126.72/298.33 , 0_1(8) -> 50 1126.72/298.33 , 0_1(8) -> 112 1126.72/298.33 , 0_1(8) -> 120 1126.72/298.33 , 0_1(9) -> 120 1126.72/298.33 , 0_1(10) -> 7 1126.72/298.33 , 0_1(18) -> 17 1126.72/298.33 , 0_1(25) -> 24 1126.72/298.33 , 0_1(35) -> 34 1126.72/298.33 , 0_1(36) -> 158 1126.72/298.33 , 0_1(42) -> 41 1126.72/298.33 , 0_1(43) -> 40 1126.72/298.33 , 0_1(46) -> 45 1126.72/298.33 , 0_1(47) -> 46 1126.72/298.33 , 0_1(50) -> 180 1126.72/298.33 , 0_1(52) -> 112 1126.72/298.33 , 0_1(55) -> 54 1126.72/298.33 , 0_1(69) -> 68 1126.72/298.33 , 0_1(70) -> 46 1126.72/298.33 , 0_1(84) -> 83 1126.72/298.33 , 0_1(85) -> 84 1126.72/298.33 , 0_1(90) -> 89 1126.72/298.33 , 0_1(91) -> 90 1126.72/298.33 , 0_1(93) -> 92 1126.72/298.33 , 0_1(103) -> 102 1126.72/298.33 , 0_1(108) -> 85 1126.72/298.33 , 0_1(112) -> 111 1126.72/298.33 , 0_1(113) -> 108 1126.72/298.33 , 0_1(116) -> 115 1126.72/298.33 , 0_1(121) -> 10 1126.72/298.33 , 0_1(127) -> 126 1126.72/298.33 , 0_1(131) -> 130 1126.72/298.33 , 0_1(154) -> 153 1126.72/298.33 , 0_1(161) -> 160 1126.72/298.33 , 0_1(162) -> 161 1126.72/298.33 , 0_1(163) -> 162 1126.72/298.33 , 0_1(164) -> 163 1126.72/298.33 , 0_1(171) -> 170 1126.72/298.33 , 0_1(174) -> 173 1126.72/298.33 , 0_1(176) -> 175 1126.72/298.33 , 0_1(180) -> 179 1126.72/298.33 , 0_1(181) -> 180 1126.72/298.33 , 0_1(187) -> 186 1126.72/298.33 , 0_2(194) -> 120 1126.72/298.33 , 0_2(260) -> 259 1126.72/298.33 , 1_0(1) -> 1 1126.72/298.33 , 1_1(1) -> 9 1126.72/298.33 , 1_1(2) -> 9 1126.72/298.33 , 1_1(11) -> 10 1126.72/298.33 , 1_1(24) -> 23 1126.72/298.33 , 1_1(37) -> 10 1126.72/298.33 , 1_1(40) -> 1 1126.72/298.33 , 1_1(40) -> 9 1126.72/298.33 , 1_1(40) -> 10 1126.72/298.33 , 1_1(40) -> 26 1126.72/298.33 , 1_1(40) -> 52 1126.72/298.33 , 1_1(40) -> 113 1126.72/298.33 , 1_1(40) -> 134 1126.72/298.33 , 1_1(42) -> 113 1126.72/298.33 , 1_1(52) -> 134 1126.72/298.33 , 1_1(53) -> 9 1126.72/298.33 , 1_1(57) -> 56 1126.72/298.33 , 1_1(63) -> 62 1126.72/298.33 , 1_1(64) -> 63 1126.72/298.33 , 1_1(66) -> 65 1126.72/298.33 , 1_1(67) -> 66 1126.72/298.33 , 1_1(70) -> 10 1126.72/298.33 , 1_1(71) -> 32 1126.72/298.33 , 1_1(72) -> 71 1126.72/298.33 , 1_1(74) -> 73 1126.72/298.33 , 1_1(86) -> 11 1126.72/298.33 , 1_1(92) -> 91 1126.72/298.33 , 1_1(98) -> 97 1126.72/298.33 , 1_1(101) -> 100 1126.72/298.33 , 1_1(104) -> 103 1126.72/298.33 , 1_1(107) -> 106 1126.72/298.33 , 1_1(108) -> 9 1126.72/298.33 , 1_1(115) -> 114 1126.72/298.33 , 1_1(125) -> 124 1126.72/298.33 , 1_1(136) -> 8 1126.72/298.33 , 1_1(138) -> 151 1126.72/298.33 , 1_1(140) -> 139 1126.72/298.33 , 1_1(143) -> 142 1126.72/298.33 , 1_1(146) -> 145 1126.72/298.33 , 1_1(147) -> 146 1126.72/298.33 , 1_1(149) -> 148 1126.72/298.33 , 1_1(151) -> 150 1126.72/298.33 , 1_1(152) -> 151 1126.72/298.33 , 1_1(156) -> 155 1126.72/298.33 , 1_1(160) -> 159 1126.72/298.33 , 1_1(175) -> 174 1126.72/298.33 , 1_2(71) -> 195 1126.72/298.33 , 1_2(160) -> 195 1126.72/298.33 , 1_2(258) -> 134 1126.72/298.33 , 1_2(263) -> 262 1126.72/298.33 , 2_0(1) -> 1 1126.72/298.33 , 2_1(1) -> 52 1126.72/298.33 , 2_1(2) -> 26 1126.72/298.33 , 2_1(7) -> 6 1126.72/298.33 , 2_1(8) -> 52 1126.72/298.33 , 2_1(9) -> 138 1126.72/298.33 , 2_1(10) -> 152 1126.72/298.33 , 2_1(12) -> 11 1126.72/298.33 , 2_1(16) -> 15 1126.72/298.33 , 2_1(21) -> 20 1126.72/298.33 , 2_1(22) -> 21 1126.72/298.33 , 2_1(26) -> 25 1126.72/298.33 , 2_1(27) -> 26 1126.72/298.33 , 2_1(28) -> 8 1126.72/298.33 , 2_1(32) -> 1 1126.72/298.33 , 2_1(32) -> 9 1126.72/298.33 , 2_1(32) -> 97 1126.72/298.33 , 2_1(32) -> 134 1126.72/298.33 , 2_1(34) -> 33 1126.72/298.33 , 2_1(37) -> 36 1126.72/298.33 , 2_1(45) -> 44 1126.72/298.33 , 2_1(49) -> 48 1126.72/298.33 , 2_1(53) -> 52 1126.72/298.33 , 2_1(56) -> 55 1126.72/298.33 , 2_1(60) -> 59 1126.72/298.33 , 2_1(73) -> 72 1126.72/298.33 , 2_1(75) -> 74 1126.72/298.33 , 2_1(77) -> 76 1126.72/298.33 , 2_1(81) -> 80 1126.72/298.33 , 2_1(85) -> 167 1126.72/298.33 , 2_1(94) -> 93 1126.72/298.33 , 2_1(100) -> 99 1126.72/298.33 , 2_1(108) -> 52 1126.72/298.33 , 2_1(129) -> 128 1126.72/298.33 , 2_1(133) -> 132 1126.72/298.33 , 2_1(145) -> 144 1126.72/298.33 , 2_1(155) -> 154 1126.72/298.33 , 2_1(159) -> 2 1126.72/298.33 , 2_1(166) -> 165 1126.72/298.33 , 2_1(167) -> 166 1126.72/298.33 , 2_1(170) -> 169 1126.72/298.33 , 2_1(172) -> 171 1126.72/298.33 , 2_1(173) -> 172 1126.72/298.33 , 2_1(178) -> 177 1126.72/298.33 , 2_1(179) -> 178 1126.72/298.33 , 2_1(182) -> 108 1126.72/298.33 , 3_0(1) -> 1 1126.72/298.33 , 3_1(1) -> 27 1126.72/298.33 , 3_1(2) -> 2 1126.72/298.33 , 3_1(3) -> 2 1126.72/298.33 , 3_1(5) -> 4 1126.72/298.33 , 3_1(9) -> 8 1126.72/298.33 , 3_1(10) -> 1 1126.72/298.33 , 3_1(10) -> 4 1126.72/298.33 , 3_1(10) -> 7 1126.72/298.33 , 3_1(10) -> 9 1126.72/298.33 , 3_1(10) -> 27 1126.72/298.33 , 3_1(10) -> 52 1126.72/298.33 , 3_1(10) -> 120 1126.72/298.33 , 3_1(10) -> 134 1126.72/298.33 , 3_1(10) -> 151 1126.72/298.33 , 3_1(13) -> 12 1126.72/298.33 , 3_1(23) -> 22 1126.72/298.33 , 3_1(27) -> 50 1126.72/298.33 , 3_1(29) -> 28 1126.72/298.33 , 3_1(30) -> 29 1126.72/298.33 , 3_1(32) -> 8 1126.72/298.33 , 3_1(33) -> 32 1126.72/298.33 , 3_1(38) -> 2 1126.72/298.33 , 3_1(40) -> 2 1126.72/298.33 , 3_1(41) -> 2 1126.72/298.33 , 3_1(51) -> 50 1126.72/298.33 , 3_1(52) -> 51 1126.72/298.33 , 3_1(54) -> 53 1126.72/298.33 , 3_1(61) -> 60 1126.72/298.33 , 3_1(71) -> 2 1126.72/298.33 , 3_1(78) -> 77 1126.72/298.33 , 3_1(79) -> 78 1126.72/298.33 , 3_1(89) -> 88 1126.72/298.33 , 3_1(102) -> 101 1126.72/298.33 , 3_1(108) -> 2 1126.72/298.33 , 3_1(111) -> 110 1126.72/298.33 , 3_1(114) -> 113 1126.72/298.33 , 3_1(119) -> 118 1126.72/298.33 , 3_1(120) -> 181 1126.72/298.33 , 3_1(124) -> 123 1126.72/298.33 , 3_1(126) -> 108 1126.72/298.33 , 3_1(141) -> 140 1126.72/298.33 , 3_1(153) -> 2 1126.72/298.33 , 3_1(158) -> 157 1126.72/298.33 , 3_1(168) -> 126 1126.72/298.33 , 3_1(183) -> 182 1126.72/298.33 , 3_1(189) -> 188 1126.72/298.33 , 3_1(191) -> 190 1126.72/298.33 , 3_2(71) -> 261 1126.72/298.33 , 3_2(160) -> 261 1126.72/298.33 , 3_2(195) -> 194 1126.72/298.33 , 3_2(262) -> 126 1126.72/298.33 , 3_2(264) -> 151 1126.72/298.33 , 4_0(1) -> 1 1126.72/298.33 , 4_1(1) -> 37 1126.72/298.33 , 4_1(2) -> 1 1126.72/298.33 , 4_1(2) -> 7 1126.72/298.33 , 4_1(2) -> 37 1126.72/298.33 , 4_1(2) -> 42 1126.72/298.33 , 4_1(2) -> 85 1126.72/298.33 , 4_1(4) -> 3 1126.72/298.33 , 4_1(8) -> 70 1126.72/298.33 , 4_1(9) -> 31 1126.72/298.33 , 4_1(14) -> 13 1126.72/298.33 , 4_1(17) -> 16 1126.72/298.33 , 4_1(19) -> 18 1126.72/298.33 , 4_1(27) -> 42 1126.72/298.33 , 4_1(37) -> 69 1126.72/298.33 , 4_1(38) -> 10 1126.72/298.33 , 4_1(41) -> 37 1126.72/298.33 , 4_1(44) -> 43 1126.72/298.33 , 4_1(48) -> 47 1126.72/298.33 , 4_1(50) -> 49 1126.72/298.33 , 4_1(52) -> 70 1126.72/298.33 , 4_1(59) -> 58 1126.72/298.33 , 4_1(62) -> 61 1126.72/298.33 , 4_1(70) -> 69 1126.72/298.33 , 4_1(76) -> 75 1126.72/298.33 , 4_1(80) -> 79 1126.72/298.33 , 4_1(88) -> 87 1126.72/298.33 , 4_1(95) -> 94 1126.72/298.33 , 4_1(96) -> 95 1126.72/298.33 , 4_1(97) -> 96 1126.72/298.33 , 4_1(98) -> 192 1126.72/298.33 , 4_1(99) -> 40 1126.72/298.33 , 4_1(106) -> 105 1126.72/298.33 , 4_1(108) -> 37 1126.72/298.33 , 4_1(109) -> 108 1126.72/298.33 , 4_1(119) -> 192 1126.72/298.33 , 4_1(122) -> 121 1126.72/298.33 , 4_1(128) -> 127 1126.72/298.33 , 4_1(130) -> 129 1126.72/298.33 , 4_1(132) -> 131 1126.72/298.33 , 4_1(135) -> 9 1126.72/298.33 , 4_1(137) -> 136 1126.72/298.33 , 4_1(138) -> 137 1126.72/298.33 , 4_1(139) -> 2 1126.72/298.33 , 4_1(142) -> 141 1126.72/298.33 , 4_1(148) -> 147 1126.72/298.33 , 4_1(153) -> 37 1126.72/298.33 , 4_1(165) -> 164 1126.72/298.33 , 4_1(169) -> 168 1126.72/298.33 , 4_1(184) -> 183 1126.72/298.33 , 4_1(186) -> 185 1126.72/298.33 , 4_1(192) -> 191 1126.72/298.33 , 4_1(193) -> 192 1126.72/298.33 , 4_2(171) -> 263 1126.72/298.33 , 4_2(261) -> 260 1126.72/298.33 , 4_2(265) -> 264 1126.72/298.33 , 5_0(1) -> 1 1126.72/298.33 , 5_1(1) -> 39 1126.72/298.33 , 5_1(2) -> 135 1126.72/298.33 , 5_1(15) -> 14 1126.72/298.33 , 5_1(20) -> 19 1126.72/298.33 , 5_1(27) -> 135 1126.72/298.33 , 5_1(30) -> 125 1126.72/298.33 , 5_1(31) -> 30 1126.72/298.33 , 5_1(32) -> 38 1126.72/298.33 , 5_1(36) -> 35 1126.72/298.33 , 5_1(37) -> 107 1126.72/298.33 , 5_1(39) -> 38 1126.72/298.33 , 5_1(41) -> 40 1126.72/298.33 , 5_1(53) -> 32 1126.72/298.33 , 5_1(58) -> 57 1126.72/298.33 , 5_1(65) -> 64 1126.72/298.33 , 5_1(68) -> 67 1126.72/298.33 , 5_1(70) -> 30 1126.72/298.33 , 5_1(82) -> 81 1126.72/298.33 , 5_1(83) -> 82 1126.72/298.33 , 5_1(85) -> 98 1126.72/298.33 , 5_1(87) -> 86 1126.72/298.33 , 5_1(105) -> 104 1126.72/298.33 , 5_1(108) -> 1 1126.72/298.33 , 5_1(108) -> 6 1126.72/298.33 , 5_1(108) -> 26 1126.72/298.33 , 5_1(108) -> 27 1126.72/298.33 , 5_1(108) -> 37 1126.72/298.33 , 5_1(108) -> 39 1126.72/298.33 , 5_1(108) -> 42 1126.72/298.33 , 5_1(108) -> 49 1126.72/298.33 , 5_1(108) -> 50 1126.72/298.33 , 5_1(108) -> 52 1126.72/298.33 , 5_1(108) -> 69 1126.72/298.33 , 5_1(108) -> 138 1126.72/298.33 , 5_1(110) -> 109 1126.72/298.33 , 5_1(112) -> 193 1126.72/298.33 , 5_1(117) -> 116 1126.72/298.33 , 5_1(118) -> 117 1126.72/298.33 , 5_1(120) -> 119 1126.72/298.33 , 5_1(123) -> 122 1126.72/298.33 , 5_1(134) -> 133 1126.72/298.33 , 5_1(144) -> 143 1126.72/298.33 , 5_1(150) -> 149 1126.72/298.33 , 5_1(153) -> 108 1126.72/298.33 , 5_1(157) -> 156 1126.72/298.33 , 5_1(177) -> 176 1126.72/298.33 , 5_1(185) -> 184 1126.72/298.33 , 5_1(188) -> 187 1126.72/298.33 , 5_1(190) -> 189 1126.72/298.33 , 5_2(53) -> 266 1126.72/298.33 , 5_2(259) -> 258 1126.72/298.33 , 5_2(266) -> 265 } 1126.72/298.33 1126.72/298.33 Hurray, we answered YES(?,O(n^1)) 1127.41/298.99 EOF