YES(?,O(n^1)) 1113.19/297.07 YES(?,O(n^1)) 1113.19/297.07 1113.19/297.07 We are left with following problem, upon which TcT provides the 1113.19/297.07 certificate YES(?,O(n^1)). 1113.19/297.07 1113.19/297.07 Strict Trs: 1113.19/297.07 { 0(1(2(3(x1)))) -> 4(4(2(3(x1)))) 1113.19/297.07 , 0(1(2(4(3(1(1(4(1(5(0(2(5(3(2(4(3(x1))))))))))))))))) -> 1113.19/297.07 4(2(2(1(3(1(3(0(4(5(1(2(2(5(5(4(1(x1))))))))))))))))) 1113.19/297.07 , 2(3(1(5(0(5(x1)))))) -> 2(1(3(5(0(5(x1)))))) 1113.19/297.07 , 2(4(3(0(4(2(0(0(2(5(1(0(2(0(0(4(4(x1))))))))))))))))) -> 1113.19/297.07 5(4(1(2(1(2(1(0(2(0(4(3(1(0(0(2(x1)))))))))))))))) 1113.19/297.07 , 3(0(2(5(1(5(0(1(5(0(x1)))))))))) -> 1(2(2(0(0(4(3(4(4(x1))))))))) 1113.19/297.07 , 3(0(4(3(3(5(0(4(4(0(4(2(x1)))))))))))) -> 1113.19/297.07 3(4(5(5(3(2(0(5(1(4(2(x1))))))))))) 1113.19/297.07 , 3(0(4(5(4(1(4(3(5(5(3(5(4(0(1(4(3(5(0(3(2(x1))))))))))))))))))))) 1113.19/297.07 -> 1113.19/297.07 1(2(4(1(1(2(5(4(2(4(0(4(2(5(1(4(2(1(3(1(2(x1))))))))))))))))))))) 1113.19/297.07 , 3(1(2(2(2(1(3(1(3(x1))))))))) -> 1(4(3(1(5(0(2(2(x1)))))))) 1113.19/297.07 , 3(1(5(2(5(5(3(3(4(4(5(2(3(2(4(x1))))))))))))))) -> 1113.19/297.07 3(0(5(4(4(4(2(0(0(1(4(3(2(4(x1)))))))))))))) 1113.19/297.07 , 3(3(3(1(0(2(1(1(5(2(4(0(0(4(5(2(2(0(2(x1))))))))))))))))))) -> 1113.19/297.07 3(2(2(3(1(5(5(5(3(0(3(1(4(3(2(3(1(x1))))))))))))))))) 1113.19/297.07 , 3(3(4(3(1(3(0(5(x1)))))))) -> 3(5(2(4(5(0(5(2(x1)))))))) 1113.19/297.07 , 3(4(2(0(5(2(3(5(3(x1))))))))) -> 3(5(4(4(2(2(0(5(1(x1))))))))) 1113.19/297.07 , 3(5(5(4(4(4(2(0(0(3(x1)))))))))) -> 1(1(2(3(2(3(4(1(x1)))))))) 1113.19/297.07 , 4(0(4(0(5(1(0(3(2(5(3(1(3(0(2(5(3(5(0(0(x1)))))))))))))))))))) -> 1113.19/297.07 1(5(3(5(2(0(5(4(4(5(0(1(4(4(3(1(3(2(5(1(x1)))))))))))))))))))) 1113.19/297.07 , 4(5(5(4(3(4(4(2(4(2(4(3(3(3(3(x1))))))))))))))) -> 1113.19/297.07 4(5(0(0(4(4(5(4(4(3(4(0(0(0(x1)))))))))))))) 1113.19/297.07 , 5(1(4(5(1(1(5(x1))))))) -> 1(4(0(2(3(2(5(x1))))))) 1113.19/297.07 , 5(2(0(4(5(0(2(1(1(1(2(0(x1)))))))))))) -> 1113.19/297.07 3(0(0(2(2(4(5(1(3(1(0(x1))))))))))) 1113.19/297.07 , 5(2(1(3(0(2(2(4(5(2(2(0(0(1(x1)))))))))))))) -> 1113.19/297.07 3(4(5(1(4(3(3(5(0(3(0(1(x1)))))))))))) 1113.19/297.07 , 5(3(2(2(5(2(1(3(0(2(4(3(2(5(3(3(0(5(4(x1))))))))))))))))))) -> 1113.19/297.07 1(3(0(3(3(4(5(5(0(5(5(4(0(2(1(1(0(0(2(x1))))))))))))))))))) 1113.19/297.07 , 5(3(3(5(4(x1))))) -> 5(1(0(2(x1)))) 1113.19/297.07 , 5(3(3(5(5(4(x1)))))) -> 4(2(4(3(2(x1))))) 1113.19/297.07 , 5(4(2(1(3(2(5(4(2(2(0(0(5(5(1(0(5(1(3(0(x1)))))))))))))))))))) -> 1113.19/297.07 4(4(2(4(0(1(3(2(5(1(3(4(4(0(0(1(1(1(2(0(x1)))))))))))))))))))) 1113.19/297.07 , 5(4(5(5(5(2(0(1(2(1(0(1(2(1(5(3(1(3(1(x1))))))))))))))))))) -> 1113.19/297.07 0(0(3(5(3(0(2(0(1(4(0(5(4(3(0(2(4(1(x1)))))))))))))))))) 1113.19/297.07 , 5(5(1(3(3(5(4(0(0(x1))))))))) -> 3(1(0(1(4(2(4(3(x1)))))))) 1113.19/297.07 , 5(5(4(3(3(4(5(4(5(0(0(4(5(x1))))))))))))) -> 1113.19/297.07 5(0(1(0(3(1(4(1(2(3(1(x1))))))))))) } 1113.19/297.07 Obligation: 1113.19/297.07 derivational complexity 1113.19/297.07 Answer: 1113.19/297.07 YES(?,O(n^1)) 1113.19/297.07 1113.19/297.07 The problem is match-bounded by 2. The enriched problem is 1113.19/297.07 compatible with the following automaton. 1113.19/297.07 { 0_0(1) -> 1 1113.19/297.07 , 0_1(1) -> 148 1113.19/297.07 , 0_1(11) -> 10 1113.19/297.07 , 0_1(19) -> 165 1113.19/297.07 , 0_1(24) -> 23 1113.19/297.07 , 0_1(32) -> 31 1113.19/297.07 , 0_1(34) -> 33 1113.19/297.07 , 0_1(38) -> 37 1113.19/297.07 , 0_1(39) -> 38 1113.19/297.07 , 0_1(43) -> 42 1113.19/297.07 , 0_1(44) -> 43 1113.19/297.07 , 0_1(48) -> 148 1113.19/297.07 , 0_1(54) -> 53 1113.19/297.07 , 0_1(65) -> 64 1113.19/297.07 , 0_1(78) -> 77 1113.19/297.07 , 0_1(86) -> 48 1113.19/297.07 , 0_1(92) -> 91 1113.19/297.07 , 0_1(93) -> 92 1113.19/297.07 , 0_1(96) -> 250 1113.19/297.07 , 0_1(105) -> 104 1113.19/297.07 , 0_1(114) -> 113 1113.19/297.07 , 0_1(125) -> 124 1113.19/297.07 , 0_1(130) -> 129 1113.19/297.07 , 0_1(138) -> 137 1113.19/297.07 , 0_1(139) -> 138 1113.19/297.07 , 0_1(147) -> 146 1113.19/297.07 , 0_1(148) -> 147 1113.19/297.07 , 0_1(149) -> 74 1113.19/297.07 , 0_1(152) -> 86 1113.19/297.07 , 0_1(164) -> 163 1113.19/297.07 , 0_1(167) -> 166 1113.19/297.07 , 0_1(173) -> 172 1113.19/297.07 , 0_1(177) -> 176 1113.19/297.07 , 0_1(180) -> 179 1113.19/297.07 , 0_1(194) -> 193 1113.19/297.07 , 0_1(195) -> 194 1113.19/297.07 , 0_1(237) -> 1 1113.19/297.07 , 0_1(237) -> 24 1113.19/297.07 , 0_1(238) -> 237 1113.19/297.07 , 0_1(242) -> 241 1113.19/297.07 , 0_1(244) -> 243 1113.19/297.07 , 0_1(247) -> 246 1113.19/297.07 , 0_1(251) -> 250 1113.19/297.07 , 0_1(253) -> 252 1113.19/297.07 , 0_1(257) -> 25 1113.19/297.07 , 0_1(259) -> 258 1113.19/297.07 , 0_2(84) -> 83 1113.19/297.07 , 1_0(1) -> 1 1113.19/297.07 , 1_1(1) -> 19 1113.19/297.07 , 1_1(7) -> 6 1113.19/297.07 , 1_1(9) -> 8 1113.19/297.07 , 1_1(14) -> 13 1113.19/297.07 , 1_1(20) -> 19 1113.19/297.07 , 1_1(21) -> 20 1113.19/297.07 , 1_1(25) -> 19 1113.19/297.07 , 1_1(27) -> 26 1113.19/297.07 , 1_1(29) -> 28 1113.19/297.07 , 1_1(31) -> 30 1113.19/297.07 , 1_1(36) -> 178 1113.19/297.07 , 1_1(37) -> 36 1113.19/297.07 , 1_1(38) -> 25 1113.19/297.07 , 1_1(39) -> 73 1113.19/297.07 , 1_1(40) -> 1 1113.19/297.07 , 1_1(40) -> 4 1113.19/297.07 , 1_1(40) -> 24 1113.19/297.07 , 1_1(40) -> 47 1113.19/297.07 , 1_1(40) -> 54 1113.19/297.07 , 1_1(40) -> 72 1113.19/297.07 , 1_1(40) -> 164 1113.19/297.07 , 1_1(47) -> 19 1113.19/297.07 , 1_1(48) -> 19 1113.19/297.07 , 1_1(56) -> 55 1113.19/297.07 , 1_1(58) -> 57 1113.19/297.07 , 1_1(59) -> 58 1113.19/297.07 , 1_1(69) -> 68 1113.19/297.07 , 1_1(72) -> 71 1113.19/297.07 , 1_1(73) -> 196 1113.19/297.07 , 1_1(76) -> 75 1113.19/297.07 , 1_1(94) -> 93 1113.19/297.07 , 1_1(100) -> 99 1113.19/297.07 , 1_1(107) -> 106 1113.19/297.07 , 1_1(109) -> 262 1113.19/297.07 , 1_1(117) -> 40 1113.19/297.07 , 1_1(131) -> 130 1113.19/297.07 , 1_1(135) -> 134 1113.19/297.07 , 1_1(137) -> 19 1113.19/297.07 , 1_1(148) -> 158 1113.19/297.07 , 1_1(157) -> 156 1113.19/297.07 , 1_1(159) -> 50 1113.19/297.07 , 1_1(181) -> 180 1113.19/297.07 , 1_1(190) -> 189 1113.19/297.07 , 1_1(196) -> 195 1113.19/297.07 , 1_1(197) -> 196 1113.19/297.07 , 1_1(198) -> 197 1113.19/297.07 , 1_1(237) -> 19 1113.19/297.07 , 1_1(238) -> 19 1113.19/297.07 , 1_1(239) -> 19 1113.19/297.07 , 1_1(245) -> 244 1113.19/297.07 , 1_1(252) -> 48 1113.19/297.07 , 1_1(254) -> 253 1113.19/297.07 , 1_1(258) -> 257 1113.19/297.07 , 1_1(261) -> 260 1113.19/297.07 , 1_2(79) -> 72 1113.19/297.07 , 1_2(82) -> 81 1113.19/297.07 , 2_0(1) -> 1 1113.19/297.07 , 2_1(1) -> 39 1113.19/297.07 , 2_1(2) -> 39 1113.19/297.07 , 2_1(3) -> 39 1113.19/297.07 , 2_1(4) -> 3 1113.19/297.07 , 2_1(5) -> 2 1113.19/297.07 , 2_1(6) -> 5 1113.19/297.07 , 2_1(15) -> 14 1113.19/297.07 , 2_1(16) -> 15 1113.19/297.07 , 2_1(18) -> 251 1113.19/297.07 , 2_1(20) -> 1 1113.19/297.07 , 2_1(20) -> 3 1113.19/297.07 , 2_1(20) -> 39 1113.19/297.07 , 2_1(20) -> 109 1113.19/297.07 , 2_1(24) -> 151 1113.19/297.07 , 2_1(25) -> 39 1113.19/297.07 , 2_1(26) -> 39 1113.19/297.07 , 2_1(28) -> 27 1113.19/297.07 , 2_1(30) -> 29 1113.19/297.07 , 2_1(33) -> 32 1113.19/297.07 , 2_1(39) -> 78 1113.19/297.07 , 2_1(40) -> 39 1113.19/297.07 , 2_1(41) -> 40 1113.19/297.07 , 2_1(42) -> 41 1113.19/297.07 , 2_1(47) -> 96 1113.19/297.07 , 2_1(48) -> 39 1113.19/297.07 , 2_1(52) -> 116 1113.19/297.07 , 2_1(53) -> 52 1113.19/297.07 , 2_1(54) -> 136 1113.19/297.07 , 2_1(60) -> 59 1113.19/297.07 , 2_1(63) -> 62 1113.19/297.07 , 2_1(67) -> 66 1113.19/297.07 , 2_1(71) -> 70 1113.19/297.07 , 2_1(72) -> 109 1113.19/297.07 , 2_1(87) -> 39 1113.19/297.07 , 2_1(88) -> 39 1113.19/297.07 , 2_1(91) -> 90 1113.19/297.07 , 2_1(94) -> 2 1113.19/297.07 , 2_1(95) -> 149 1113.19/297.07 , 2_1(97) -> 48 1113.19/297.07 , 2_1(98) -> 97 1113.19/297.07 , 2_1(111) -> 110 1113.19/297.07 , 2_1(115) -> 39 1113.19/297.07 , 2_1(118) -> 117 1113.19/297.07 , 2_1(120) -> 119 1113.19/297.07 , 2_1(124) -> 123 1113.19/297.07 , 2_1(148) -> 198 1113.19/297.07 , 2_1(150) -> 149 1113.19/297.07 , 2_1(153) -> 152 1113.19/297.07 , 2_1(154) -> 153 1113.19/297.07 , 2_1(166) -> 39 1113.19/297.07 , 2_1(178) -> 177 1113.19/297.07 , 2_1(183) -> 182 1113.19/297.07 , 2_1(243) -> 242 1113.19/297.07 , 2_1(256) -> 255 1113.19/297.07 , 2_2(10) -> 85 1113.19/297.07 , 2_2(85) -> 84 1113.19/297.07 , 3_0(1) -> 1 1113.19/297.07 , 3_1(1) -> 4 1113.19/297.07 , 3_1(8) -> 7 1113.19/297.07 , 3_1(10) -> 9 1113.19/297.07 , 3_1(18) -> 120 1113.19/297.07 , 3_1(19) -> 72 1113.19/297.07 , 3_1(22) -> 21 1113.19/297.07 , 3_1(36) -> 35 1113.19/297.07 , 3_1(39) -> 95 1113.19/297.07 , 3_1(46) -> 45 1113.19/297.07 , 3_1(48) -> 1 1113.19/297.07 , 3_1(48) -> 4 1113.19/297.07 , 3_1(48) -> 24 1113.19/297.07 , 3_1(48) -> 72 1113.19/297.07 , 3_1(48) -> 114 1113.19/297.07 , 3_1(48) -> 164 1113.19/297.07 , 3_1(52) -> 51 1113.19/297.07 , 3_1(73) -> 72 1113.19/297.07 , 3_1(75) -> 74 1113.19/297.07 , 3_1(96) -> 95 1113.19/297.07 , 3_1(99) -> 98 1113.19/297.07 , 3_1(104) -> 103 1113.19/297.07 , 3_1(106) -> 105 1113.19/297.07 , 3_1(109) -> 108 1113.19/297.07 , 3_1(119) -> 118 1113.19/297.07 , 3_1(122) -> 121 1113.19/297.07 , 3_1(134) -> 133 1113.19/297.07 , 3_1(136) -> 135 1113.19/297.07 , 3_1(145) -> 144 1113.19/297.07 , 3_1(148) -> 164 1113.19/297.07 , 3_1(151) -> 150 1113.19/297.07 , 3_1(158) -> 157 1113.19/297.07 , 3_1(161) -> 160 1113.19/297.07 , 3_1(162) -> 161 1113.19/297.07 , 3_1(165) -> 164 1113.19/297.07 , 3_1(166) -> 40 1113.19/297.07 , 3_1(168) -> 167 1113.19/297.07 , 3_1(169) -> 168 1113.19/297.07 , 3_1(182) -> 181 1113.19/297.07 , 3_1(191) -> 190 1113.19/297.07 , 3_1(237) -> 4 1113.19/297.07 , 3_1(238) -> 4 1113.19/297.07 , 3_1(239) -> 238 1113.19/297.07 , 3_1(241) -> 240 1113.19/297.07 , 3_1(250) -> 249 1113.19/297.07 , 3_1(260) -> 259 1113.19/297.07 , 3_2(81) -> 80 1113.19/297.07 , 4_0(1) -> 1 1113.19/297.07 , 4_1(1) -> 47 1113.19/297.07 , 4_1(2) -> 1 1113.19/297.07 , 4_1(2) -> 24 1113.19/297.07 , 4_1(2) -> 47 1113.19/297.07 , 4_1(2) -> 148 1113.19/297.07 , 4_1(2) -> 165 1113.19/297.07 , 4_1(3) -> 2 1113.19/297.07 , 4_1(4) -> 256 1113.19/297.07 , 4_1(12) -> 11 1113.19/297.07 , 4_1(19) -> 18 1113.19/297.07 , 4_1(26) -> 25 1113.19/297.07 , 4_1(35) -> 34 1113.19/297.07 , 4_1(39) -> 56 1113.19/297.07 , 4_1(45) -> 44 1113.19/297.07 , 4_1(47) -> 46 1113.19/297.07 , 4_1(48) -> 18 1113.19/297.07 , 4_1(49) -> 48 1113.19/297.07 , 4_1(57) -> 41 1113.19/297.07 , 4_1(62) -> 61 1113.19/297.07 , 4_1(64) -> 63 1113.19/297.07 , 4_1(66) -> 65 1113.19/297.07 , 4_1(70) -> 69 1113.19/297.07 , 4_1(74) -> 40 1113.19/297.07 , 4_1(88) -> 87 1113.19/297.07 , 4_1(89) -> 88 1113.19/297.07 , 4_1(90) -> 89 1113.19/297.07 , 4_1(95) -> 94 1113.19/297.07 , 4_1(108) -> 107 1113.19/297.07 , 4_1(112) -> 111 1113.19/297.07 , 4_1(115) -> 110 1113.19/297.07 , 4_1(116) -> 115 1113.19/297.07 , 4_1(127) -> 126 1113.19/297.07 , 4_1(128) -> 127 1113.19/297.07 , 4_1(132) -> 131 1113.19/297.07 , 4_1(133) -> 132 1113.19/297.07 , 4_1(140) -> 139 1113.19/297.07 , 4_1(141) -> 140 1113.19/297.07 , 4_1(143) -> 142 1113.19/297.07 , 4_1(144) -> 143 1113.19/297.07 , 4_1(146) -> 145 1113.19/297.07 , 4_1(155) -> 154 1113.19/297.07 , 4_1(160) -> 159 1113.19/297.07 , 4_1(170) -> 169 1113.19/297.07 , 4_1(176) -> 175 1113.19/297.07 , 4_1(179) -> 4 1113.19/297.07 , 4_1(192) -> 191 1113.19/297.07 , 4_1(193) -> 192 1113.19/297.07 , 4_1(237) -> 47 1113.19/297.07 , 4_1(246) -> 245 1113.19/297.07 , 4_1(249) -> 248 1113.19/297.07 , 4_1(255) -> 254 1113.19/297.07 , 4_1(257) -> 47 1113.19/297.07 , 4_1(262) -> 261 1113.19/297.07 , 4_2(80) -> 79 1113.19/297.07 , 5_0(1) -> 1 1113.19/297.07 , 5_1(1) -> 24 1113.19/297.07 , 5_1(13) -> 12 1113.19/297.07 , 5_1(17) -> 16 1113.19/297.07 , 5_1(18) -> 17 1113.19/297.07 , 5_1(19) -> 54 1113.19/297.07 , 5_1(23) -> 22 1113.19/297.07 , 5_1(25) -> 1 1113.19/297.07 , 5_1(25) -> 24 1113.19/297.07 , 5_1(25) -> 39 1113.19/297.07 , 5_1(25) -> 96 1113.19/297.07 , 5_1(25) -> 255 1113.19/297.07 , 5_1(39) -> 114 1113.19/297.07 , 5_1(50) -> 49 1113.19/297.07 , 5_1(51) -> 50 1113.19/297.07 , 5_1(55) -> 54 1113.19/297.07 , 5_1(61) -> 60 1113.19/297.07 , 5_1(68) -> 67 1113.19/297.07 , 5_1(71) -> 155 1113.19/297.07 , 5_1(77) -> 76 1113.19/297.07 , 5_1(87) -> 86 1113.19/297.07 , 5_1(101) -> 100 1113.19/297.07 , 5_1(102) -> 101 1113.19/297.07 , 5_1(103) -> 102 1113.19/297.07 , 5_1(110) -> 48 1113.19/297.07 , 5_1(113) -> 112 1113.19/297.07 , 5_1(121) -> 40 1113.19/297.07 , 5_1(123) -> 122 1113.19/297.07 , 5_1(126) -> 125 1113.19/297.07 , 5_1(129) -> 128 1113.19/297.07 , 5_1(137) -> 2 1113.19/297.07 , 5_1(142) -> 141 1113.19/297.07 , 5_1(156) -> 155 1113.19/297.07 , 5_1(163) -> 162 1113.19/297.07 , 5_1(171) -> 170 1113.19/297.07 , 5_1(172) -> 171 1113.19/297.07 , 5_1(174) -> 173 1113.19/297.07 , 5_1(175) -> 174 1113.19/297.07 , 5_1(189) -> 183 1113.19/297.07 , 5_1(240) -> 239 1113.19/297.07 , 5_1(248) -> 247 1113.19/297.07 , 5_2(83) -> 82 } 1113.19/297.07 1113.19/297.07 Hurray, we answered YES(?,O(n^1)) 1113.86/297.57 EOF