YES(?,O(n^1)) 1105.26/298.36 YES(?,O(n^1)) 1105.26/298.36 1105.26/298.36 We are left with following problem, upon which TcT provides the 1105.26/298.36 certificate YES(?,O(n^1)). 1105.26/298.36 1105.26/298.36 Strict Trs: 1105.26/298.36 { 0(0(1(0(0(3(5(3(x1)))))))) -> 0(0(0(2(3(2(2(3(x1)))))))) 1105.26/298.36 , 0(1(2(x1))) -> 0(3(3(x1))) 1105.26/298.36 , 0(3(0(2(1(3(4(2(1(5(2(4(3(0(1(0(2(x1))))))))))))))))) -> 1105.26/298.36 2(0(4(5(5(2(0(0(1(0(3(2(5(4(1(3(3(x1))))))))))))))))) 1105.26/298.36 , 0(3(2(2(5(4(0(2(4(0(1(3(3(1(0(3(4(3(1(5(x1)))))))))))))))))))) -> 1105.26/298.36 0(3(1(0(5(4(3(2(0(3(3(4(1(0(4(3(3(3(1(1(x1)))))))))))))))))))) 1105.26/298.36 , 0(4(2(5(3(2(x1)))))) -> 0(1(2(4(0(x1))))) 1105.26/298.36 , 1(0(4(3(2(1(4(1(5(1(1(2(x1)))))))))))) -> 1105.26/298.36 4(2(0(3(3(5(3(1(4(5(3(3(5(x1))))))))))))) 1105.26/298.36 , 1(0(5(2(2(3(2(0(5(5(3(4(4(3(1(0(0(2(1(2(x1)))))))))))))))))))) -> 1105.26/298.36 1(3(1(4(5(3(3(3(3(0(2(5(1(4(5(4(3(1(5(1(x1)))))))))))))))))))) 1105.26/298.36 , 1(1(0(0(5(2(5(2(2(x1))))))))) -> 1(3(1(1(5(3(3(5(1(x1))))))))) 1105.26/298.36 , 1(1(5(5(0(3(1(4(0(0(3(5(5(4(x1)))))))))))))) -> 1105.26/298.36 0(1(3(1(3(0(3(4(5(0(4(1(5(4(x1)))))))))))))) 1105.26/298.36 , 1(2(0(4(4(0(3(0(5(2(4(0(3(3(1(1(4(x1))))))))))))))))) -> 1105.26/298.36 4(5(4(0(4(3(5(0(2(5(0(5(3(0(3(1(4(x1))))))))))))))))) 1105.26/298.36 , 3(0(2(2(2(0(0(4(3(2(2(5(5(0(3(2(1(2(2(2(0(x1))))))))))))))))))))) 1105.26/298.36 -> 5(2(2(5(1(3(5(0(3(2(1(1(1(0(4(5(3(4(0(5(x1)))))))))))))))))))) 1105.26/298.36 , 3(1(3(0(1(4(5(2(5(0(2(2(4(3(x1)))))))))))))) -> 1105.26/298.36 3(0(5(2(2(0(4(5(2(1(5(5(5(x1))))))))))))) 1105.26/298.36 , 4(0(1(5(4(1(3(5(5(0(0(5(4(5(4(0(5(4(x1)))))))))))))))))) -> 1105.26/298.36 2(1(2(5(0(0(4(1(0(1(5(5(4(5(2(4(1(4(x1)))))))))))))))))) 1105.26/298.36 , 4(1(5(5(5(3(3(1(3(3(3(4(5(x1))))))))))))) -> 1105.26/298.36 4(1(4(3(4(5(1(1(1(1(2(5(x1)))))))))))) 1105.26/298.36 , 4(3(2(4(0(0(2(2(3(5(0(x1))))))))))) -> 1105.26/298.36 1(0(5(2(2(5(2(1(5(5(x1)))))))))) 1105.26/298.36 , 4(3(3(3(5(5(1(2(5(0(4(1(4(4(2(3(0(4(2(x1))))))))))))))))))) -> 1105.26/298.36 4(3(4(5(5(0(2(5(5(0(2(2(5(2(0(0(3(3(x1)))))))))))))))))) 1105.26/298.36 , 4(4(1(2(0(1(2(3(1(0(1(0(0(3(3(4(4(1(1(1(2(x1))))))))))))))))))))) 1105.26/298.36 -> 1105.26/298.36 4(1(0(1(0(3(1(4(1(5(3(3(3(0(1(2(3(1(2(5(1(x1))))))))))))))))))))) 1105.26/298.36 , 4(4(1(4(2(1(1(x1))))))) -> 5(0(1(1(1(5(x1)))))) 1105.26/298.36 , 4(4(4(4(4(1(3(4(1(5(1(4(0(1(4(0(4(5(x1)))))))))))))))))) -> 1105.26/298.36 4(2(2(3(1(2(3(5(4(3(3(4(2(1(2(0(3(4(5(x1))))))))))))))))))) 1105.26/298.36 , 4(5(0(3(2(5(3(x1))))))) -> 4(1(1(0(2(3(x1)))))) 1105.26/298.36 , 5(1(1(3(1(5(4(2(x1)))))))) -> 5(5(3(4(4(2(0(2(x1)))))))) 1105.26/298.36 , 5(1(2(5(5(2(4(1(1(5(2(x1))))))))))) -> 1105.26/298.36 5(1(5(2(0(3(5(0(1(4(1(x1))))))))))) 1105.26/298.36 , 5(2(0(5(0(1(1(1(2(4(4(2(x1)))))))))))) -> 1105.26/298.36 5(2(0(2(0(3(3(0(0(4(2(4(x1)))))))))))) 1105.26/298.36 , 5(3(1(5(4(5(4(5(1(1(1(2(2(1(5(2(x1)))))))))))))))) -> 1105.26/298.36 5(0(0(5(2(3(2(4(4(1(1(1(5(5(5(x1))))))))))))))) 1105.26/298.36 , 5(4(4(2(2(2(3(0(1(5(3(5(1(0(2(3(1(5(4(1(x1)))))))))))))))))))) -> 1105.26/298.36 5(1(0(5(1(1(3(0(5(0(3(5(5(2(4(0(1(5(5(x1))))))))))))))))))) } 1105.26/298.36 Obligation: 1105.26/298.36 derivational complexity 1105.26/298.36 Answer: 1105.26/298.36 YES(?,O(n^1)) 1105.26/298.36 1105.26/298.36 The problem is match-bounded by 2. The enriched problem is 1105.26/298.36 compatible with the following automaton. 1105.26/298.36 { 0_0(1) -> 1 1105.26/298.36 , 0_1(1) -> 42 1105.26/298.36 , 0_1(2) -> 1 1105.26/298.36 , 0_1(2) -> 38 1105.26/298.36 , 0_1(2) -> 39 1105.26/298.36 , 0_1(2) -> 42 1105.26/298.36 , 0_1(2) -> 190 1105.26/298.36 , 0_1(2) -> 204 1105.26/298.36 , 0_1(3) -> 2 1105.26/298.36 , 0_1(4) -> 3 1105.26/298.36 , 0_1(7) -> 207 1105.26/298.36 , 0_1(8) -> 204 1105.26/298.36 , 0_1(9) -> 42 1105.26/298.36 , 0_1(10) -> 9 1105.26/298.36 , 0_1(15) -> 14 1105.26/298.36 , 0_1(16) -> 15 1105.26/298.36 , 0_1(18) -> 17 1105.26/298.36 , 0_1(24) -> 23 1105.26/298.36 , 0_1(29) -> 28 1105.26/298.36 , 0_1(34) -> 33 1105.26/298.36 , 0_1(37) -> 98 1105.26/298.36 , 0_1(43) -> 42 1105.26/298.36 , 0_1(45) -> 44 1105.26/298.36 , 0_1(54) -> 118 1105.26/298.36 , 0_1(64) -> 63 1105.26/298.36 , 0_1(79) -> 78 1105.26/298.36 , 0_1(83) -> 82 1105.26/298.36 , 0_1(89) -> 88 1105.26/298.36 , 0_1(93) -> 92 1105.26/298.36 , 0_1(96) -> 95 1105.26/298.36 , 0_1(99) -> 98 1105.26/298.36 , 0_1(108) -> 107 1105.26/298.36 , 0_1(114) -> 113 1105.26/298.36 , 0_1(120) -> 119 1105.26/298.36 , 0_1(124) -> 123 1105.26/298.36 , 0_1(133) -> 132 1105.26/298.36 , 0_1(134) -> 133 1105.26/298.36 , 0_1(137) -> 136 1105.26/298.36 , 0_1(153) -> 55 1105.26/298.36 , 0_1(158) -> 249 1105.26/298.36 , 0_1(163) -> 162 1105.26/298.36 , 0_1(167) -> 166 1105.26/298.36 , 0_1(173) -> 144 1105.26/298.36 , 0_1(175) -> 174 1105.26/298.36 , 0_1(184) -> 183 1105.26/298.36 , 0_1(189) -> 101 1105.26/298.36 , 0_1(205) -> 204 1105.26/298.36 , 0_1(213) -> 212 1105.26/298.36 , 0_1(217) -> 216 1105.26/298.36 , 0_1(220) -> 219 1105.26/298.36 , 0_1(221) -> 102 1105.26/298.36 , 0_1(223) -> 222 1105.26/298.36 , 0_1(226) -> 225 1105.26/298.36 , 0_1(227) -> 226 1105.26/298.36 , 0_1(229) -> 189 1105.26/298.36 , 0_1(237) -> 214 1105.26/298.36 , 0_1(242) -> 241 1105.26/298.36 , 0_1(244) -> 243 1105.26/298.36 , 0_2(250) -> 1 1105.26/298.36 , 0_2(250) -> 38 1105.26/298.36 , 0_2(250) -> 39 1105.26/298.36 , 0_2(250) -> 42 1105.26/298.36 , 0_2(250) -> 190 1105.26/298.36 , 0_2(250) -> 204 1105.26/298.36 , 0_2(252) -> 183 1105.26/298.36 , 1_0(1) -> 1 1105.26/298.36 , 1_1(1) -> 39 1105.26/298.36 , 1_1(2) -> 22 1105.26/298.36 , 1_1(7) -> 151 1105.26/298.36 , 1_1(9) -> 39 1105.26/298.36 , 1_1(17) -> 16 1105.26/298.36 , 1_1(23) -> 8 1105.26/298.36 , 1_1(33) -> 32 1105.26/298.36 , 1_1(39) -> 38 1105.26/298.36 , 1_1(40) -> 2 1105.26/298.36 , 1_1(50) -> 49 1105.26/298.36 , 1_1(54) -> 191 1105.26/298.36 , 1_1(55) -> 1 1105.26/298.36 , 1_1(55) -> 38 1105.26/298.36 , 1_1(55) -> 39 1105.26/298.36 , 1_1(55) -> 86 1105.26/298.36 , 1_1(57) -> 56 1105.26/298.36 , 1_1(67) -> 66 1105.26/298.36 , 1_1(72) -> 71 1105.26/298.36 , 1_1(73) -> 57 1105.26/298.36 , 1_1(77) -> 76 1105.26/298.36 , 1_1(85) -> 84 1105.26/298.36 , 1_1(86) -> 100 1105.26/298.36 , 1_1(101) -> 39 1105.26/298.36 , 1_1(102) -> 39 1105.26/298.36 , 1_1(103) -> 39 1105.26/298.36 , 1_1(105) -> 104 1105.26/298.36 , 1_1(111) -> 110 1105.26/298.36 , 1_1(112) -> 111 1105.26/298.36 , 1_1(113) -> 112 1105.26/298.36 , 1_1(127) -> 236 1105.26/298.36 , 1_1(128) -> 127 1105.26/298.36 , 1_1(129) -> 158 1105.26/298.36 , 1_1(130) -> 9 1105.26/298.36 , 1_1(131) -> 39 1105.26/298.36 , 1_1(136) -> 135 1105.26/298.36 , 1_1(138) -> 137 1105.26/298.36 , 1_1(143) -> 220 1105.26/298.36 , 1_1(144) -> 43 1105.26/298.36 , 1_1(149) -> 148 1105.26/298.36 , 1_1(150) -> 149 1105.26/298.36 , 1_1(151) -> 150 1105.26/298.36 , 1_1(152) -> 151 1105.26/298.36 , 1_1(174) -> 173 1105.26/298.36 , 1_1(177) -> 176 1105.26/298.36 , 1_1(179) -> 178 1105.26/298.36 , 1_1(185) -> 184 1105.26/298.36 , 1_1(188) -> 187 1105.26/298.36 , 1_1(190) -> 189 1105.26/298.36 , 1_1(191) -> 190 1105.26/298.36 , 1_1(194) -> 193 1105.26/298.36 , 1_1(203) -> 202 1105.26/298.36 , 1_1(207) -> 144 1105.26/298.36 , 1_1(214) -> 101 1105.26/298.36 , 1_1(236) -> 235 1105.26/298.36 , 1_1(239) -> 238 1105.26/298.36 , 1_1(240) -> 239 1105.26/298.36 , 2_0(1) -> 1 1105.26/298.36 , 2_1(1) -> 213 1105.26/298.36 , 2_1(5) -> 4 1105.26/298.36 , 2_1(7) -> 6 1105.26/298.36 , 2_1(8) -> 7 1105.26/298.36 , 2_1(9) -> 1 1105.26/298.36 , 2_1(9) -> 41 1105.26/298.36 , 2_1(9) -> 42 1105.26/298.36 , 2_1(9) -> 86 1105.26/298.36 , 2_1(9) -> 204 1105.26/298.36 , 2_1(14) -> 13 1105.26/298.36 , 2_1(20) -> 19 1105.26/298.36 , 2_1(28) -> 27 1105.26/298.36 , 2_1(41) -> 40 1105.26/298.36 , 2_1(42) -> 170 1105.26/298.36 , 2_1(43) -> 152 1105.26/298.36 , 2_1(44) -> 43 1105.26/298.36 , 2_1(54) -> 152 1105.26/298.36 , 2_1(65) -> 64 1105.26/298.36 , 2_1(72) -> 188 1105.26/298.36 , 2_1(86) -> 228 1105.26/298.36 , 2_1(94) -> 93 1105.26/298.36 , 2_1(102) -> 101 1105.26/298.36 , 2_1(103) -> 102 1105.26/298.36 , 2_1(110) -> 109 1105.26/298.36 , 2_1(122) -> 121 1105.26/298.36 , 2_1(123) -> 122 1105.26/298.36 , 2_1(127) -> 126 1105.26/298.36 , 2_1(131) -> 130 1105.26/298.36 , 2_1(143) -> 142 1105.26/298.36 , 2_1(155) -> 154 1105.26/298.36 , 2_1(156) -> 155 1105.26/298.36 , 2_1(158) -> 157 1105.26/298.36 , 2_1(164) -> 163 1105.26/298.36 , 2_1(168) -> 167 1105.26/298.36 , 2_1(169) -> 168 1105.26/298.36 , 2_1(186) -> 185 1105.26/298.36 , 2_1(192) -> 44 1105.26/298.36 , 2_1(195) -> 194 1105.26/298.36 , 2_1(202) -> 201 1105.26/298.36 , 2_1(204) -> 203 1105.26/298.36 , 2_1(212) -> 211 1105.26/298.36 , 2_1(216) -> 215 1105.26/298.36 , 2_1(222) -> 221 1105.26/298.36 , 2_1(231) -> 230 1105.26/298.36 , 2_1(233) -> 232 1105.26/298.36 , 2_1(248) -> 247 1105.26/298.36 , 3_0(1) -> 1 1105.26/298.36 , 3_1(1) -> 8 1105.26/298.36 , 3_1(6) -> 5 1105.26/298.36 , 3_1(8) -> 2 1105.26/298.36 , 3_1(9) -> 8 1105.26/298.36 , 3_1(19) -> 18 1105.26/298.36 , 3_1(27) -> 26 1105.26/298.36 , 3_1(30) -> 29 1105.26/298.36 , 3_1(31) -> 30 1105.26/298.36 , 3_1(36) -> 35 1105.26/298.36 , 3_1(37) -> 36 1105.26/298.36 , 3_1(38) -> 37 1105.26/298.36 , 3_1(44) -> 8 1105.26/298.36 , 3_1(46) -> 45 1105.26/298.36 , 3_1(47) -> 46 1105.26/298.36 , 3_1(49) -> 48 1105.26/298.36 , 3_1(53) -> 52 1105.26/298.36 , 3_1(54) -> 53 1105.26/298.36 , 3_1(56) -> 55 1105.26/298.36 , 3_1(60) -> 59 1105.26/298.36 , 3_1(61) -> 60 1105.26/298.36 , 3_1(62) -> 61 1105.26/298.36 , 3_1(63) -> 62 1105.26/298.36 , 3_1(71) -> 70 1105.26/298.36 , 3_1(72) -> 75 1105.26/298.36 , 3_1(75) -> 74 1105.26/298.36 , 3_1(76) -> 40 1105.26/298.36 , 3_1(78) -> 77 1105.26/298.36 , 3_1(80) -> 79 1105.26/298.36 , 3_1(86) -> 8 1105.26/298.36 , 3_1(91) -> 90 1105.26/298.36 , 3_1(98) -> 97 1105.26/298.36 , 3_1(100) -> 99 1105.26/298.36 , 3_1(106) -> 105 1105.26/298.36 , 3_1(109) -> 108 1105.26/298.36 , 3_1(117) -> 116 1105.26/298.36 , 3_1(119) -> 1 1105.26/298.36 , 3_1(119) -> 8 1105.26/298.36 , 3_1(146) -> 145 1105.26/298.36 , 3_1(159) -> 43 1105.26/298.36 , 3_1(176) -> 175 1105.26/298.36 , 3_1(181) -> 180 1105.26/298.36 , 3_1(182) -> 181 1105.26/298.36 , 3_1(183) -> 182 1105.26/298.36 , 3_1(187) -> 186 1105.26/298.36 , 3_1(193) -> 192 1105.26/298.36 , 3_1(196) -> 195 1105.26/298.36 , 3_1(199) -> 198 1105.26/298.36 , 3_1(200) -> 199 1105.26/298.36 , 3_1(206) -> 205 1105.26/298.36 , 3_1(209) -> 208 1105.26/298.36 , 3_1(218) -> 217 1105.26/298.36 , 3_1(224) -> 223 1105.26/298.36 , 3_1(225) -> 224 1105.26/298.36 , 3_1(232) -> 231 1105.26/298.36 , 3_1(241) -> 240 1105.26/298.36 , 3_1(245) -> 244 1105.26/298.36 , 3_2(41) -> 251 1105.26/298.36 , 3_2(131) -> 251 1105.26/298.36 , 3_2(186) -> 253 1105.26/298.36 , 3_2(251) -> 250 1105.26/298.36 , 3_2(253) -> 252 1105.26/298.36 , 4_0(1) -> 1 1105.26/298.36 , 4_1(1) -> 86 1105.26/298.36 , 4_1(9) -> 86 1105.26/298.36 , 4_1(11) -> 10 1105.26/298.36 , 4_1(22) -> 21 1105.26/298.36 , 4_1(26) -> 25 1105.26/298.36 , 4_1(32) -> 31 1105.26/298.36 , 4_1(35) -> 34 1105.26/298.36 , 4_1(39) -> 143 1105.26/298.36 , 4_1(42) -> 41 1105.26/298.36 , 4_1(43) -> 1 1105.26/298.36 , 4_1(43) -> 39 1105.26/298.36 , 4_1(43) -> 86 1105.26/298.36 , 4_1(43) -> 143 1105.26/298.36 , 4_1(43) -> 206 1105.26/298.36 , 4_1(44) -> 86 1105.26/298.36 , 4_1(51) -> 50 1105.26/298.36 , 4_1(54) -> 206 1105.26/298.36 , 4_1(58) -> 57 1105.26/298.36 , 4_1(68) -> 67 1105.26/298.36 , 4_1(70) -> 69 1105.26/298.36 , 4_1(71) -> 83 1105.26/298.36 , 4_1(81) -> 80 1105.26/298.36 , 4_1(84) -> 83 1105.26/298.36 , 4_1(88) -> 87 1105.26/298.36 , 4_1(90) -> 89 1105.26/298.36 , 4_1(100) -> 143 1105.26/298.36 , 4_1(115) -> 114 1105.26/298.36 , 4_1(118) -> 117 1105.26/298.36 , 4_1(125) -> 124 1105.26/298.36 , 4_1(135) -> 134 1105.26/298.36 , 4_1(141) -> 140 1105.26/298.36 , 4_1(145) -> 144 1105.26/298.36 , 4_1(147) -> 146 1105.26/298.36 , 4_1(160) -> 159 1105.26/298.36 , 4_1(170) -> 210 1105.26/298.36 , 4_1(178) -> 177 1105.26/298.36 , 4_1(198) -> 197 1105.26/298.36 , 4_1(201) -> 200 1105.26/298.36 , 4_1(210) -> 209 1105.26/298.36 , 4_1(211) -> 210 1105.26/298.36 , 4_1(228) -> 227 1105.26/298.36 , 4_1(234) -> 233 1105.26/298.36 , 4_1(235) -> 234 1105.26/298.36 , 4_1(249) -> 248 1105.26/298.36 , 5_0(1) -> 1 1105.26/298.36 , 5_1(1) -> 54 1105.26/298.36 , 5_1(2) -> 54 1105.26/298.36 , 5_1(9) -> 54 1105.26/298.36 , 5_1(10) -> 54 1105.26/298.36 , 5_1(12) -> 11 1105.26/298.36 , 5_1(13) -> 12 1105.26/298.36 , 5_1(21) -> 20 1105.26/298.36 , 5_1(25) -> 24 1105.26/298.36 , 5_1(39) -> 72 1105.26/298.36 , 5_1(48) -> 47 1105.26/298.36 , 5_1(52) -> 51 1105.26/298.36 , 5_1(54) -> 129 1105.26/298.36 , 5_1(55) -> 54 1105.26/298.36 , 5_1(59) -> 58 1105.26/298.36 , 5_1(66) -> 65 1105.26/298.36 , 5_1(69) -> 68 1105.26/298.36 , 5_1(74) -> 73 1105.26/298.36 , 5_1(82) -> 81 1105.26/298.36 , 5_1(86) -> 85 1105.26/298.36 , 5_1(87) -> 43 1105.26/298.36 , 5_1(92) -> 91 1105.26/298.36 , 5_1(95) -> 94 1105.26/298.36 , 5_1(97) -> 96 1105.26/298.36 , 5_1(101) -> 1 1105.26/298.36 , 5_1(101) -> 8 1105.26/298.36 , 5_1(101) -> 54 1105.26/298.36 , 5_1(101) -> 72 1105.26/298.36 , 5_1(101) -> 85 1105.26/298.36 , 5_1(101) -> 86 1105.26/298.36 , 5_1(101) -> 169 1105.26/298.36 , 5_1(102) -> 54 1105.26/298.36 , 5_1(104) -> 103 1105.26/298.36 , 5_1(107) -> 106 1105.26/298.36 , 5_1(116) -> 115 1105.26/298.36 , 5_1(119) -> 54 1105.26/298.36 , 5_1(121) -> 120 1105.26/298.36 , 5_1(126) -> 125 1105.26/298.36 , 5_1(129) -> 128 1105.26/298.36 , 5_1(132) -> 131 1105.26/298.36 , 5_1(139) -> 138 1105.26/298.36 , 5_1(140) -> 139 1105.26/298.36 , 5_1(142) -> 141 1105.26/298.36 , 5_1(144) -> 54 1105.26/298.36 , 5_1(148) -> 147 1105.26/298.36 , 5_1(154) -> 153 1105.26/298.36 , 5_1(157) -> 156 1105.26/298.36 , 5_1(159) -> 54 1105.26/298.36 , 5_1(161) -> 160 1105.26/298.36 , 5_1(162) -> 161 1105.26/298.36 , 5_1(165) -> 164 1105.26/298.36 , 5_1(166) -> 165 1105.26/298.36 , 5_1(170) -> 169 1105.26/298.36 , 5_1(180) -> 179 1105.26/298.36 , 5_1(189) -> 54 1105.26/298.36 , 5_1(197) -> 196 1105.26/298.36 , 5_1(208) -> 101 1105.26/298.36 , 5_1(215) -> 214 1105.26/298.36 , 5_1(219) -> 218 1105.26/298.36 , 5_1(230) -> 229 1105.26/298.36 , 5_1(238) -> 237 1105.26/298.36 , 5_1(243) -> 242 1105.26/298.36 , 5_1(246) -> 245 1105.26/298.36 , 5_1(247) -> 246 1105.26/298.36 , 5_1(250) -> 54 } 1105.26/298.36 1105.26/298.36 Hurray, we answered YES(?,O(n^1)) 1106.04/298.98 EOF