YES(?,O(n^1)) 1106.26/297.07 YES(?,O(n^1)) 1106.26/297.07 1106.26/297.07 We are left with following problem, upon which TcT provides the 1106.26/297.07 certificate YES(?,O(n^1)). 1106.26/297.07 1106.26/297.07 Strict Trs: 1106.26/297.07 { 0(0(1(2(x1)))) -> 0(2(3(x1))) 1106.26/297.07 , 0(0(3(0(5(3(2(5(2(4(1(1(5(5(1(4(5(2(3(0(1(x1))))))))))))))))))))) 1106.26/297.07 -> 1106.26/297.07 0(2(4(2(3(0(2(3(5(2(3(1(1(5(5(2(1(0(2(1(1(x1))))))))))))))))))))) 1106.26/297.07 , 0(1(0(1(2(0(4(1(3(0(3(2(1(x1))))))))))))) -> 1106.26/297.07 0(3(2(3(5(2(3(0(3(2(4(x1))))))))))) 1106.26/297.07 , 0(3(2(5(0(0(4(1(2(2(0(3(3(3(5(1(3(2(4(2(x1)))))))))))))))))))) -> 1106.26/297.07 0(1(4(3(4(4(5(0(3(5(5(3(0(1(5(5(3(2(1(2(x1)))))))))))))))))))) 1106.26/297.07 , 0(5(5(3(1(2(3(1(3(2(1(x1))))))))))) -> 1106.26/297.07 0(0(5(3(2(5(5(5(2(0(x1)))))))))) 1106.26/297.07 , 1(0(2(5(2(0(0(0(5(5(1(x1))))))))))) -> 1106.26/297.07 4(5(4(0(3(5(2(0(1(1(x1)))))))))) 1106.26/297.07 , 1(2(0(0(2(3(4(2(5(x1))))))))) -> 4(1(0(0(1(2(0(2(5(x1))))))))) 1106.26/297.07 , 1(3(3(2(3(0(3(2(4(3(x1)))))))))) -> 1106.26/297.07 1(3(2(1(1(5(4(1(2(2(3(x1))))))))))) 1106.26/297.07 , 1(5(1(0(5(3(5(0(1(1(2(x1))))))))))) -> 1106.26/297.07 1(4(0(3(4(0(5(3(3(x1))))))))) 1106.26/297.07 , 2(2(4(1(2(3(4(0(1(5(0(3(1(0(5(3(2(5(x1)))))))))))))))))) -> 1106.26/297.07 3(5(3(2(5(4(2(0(3(1(3(5(5(3(2(2(5(x1))))))))))))))))) 1106.26/297.07 , 2(3(4(4(0(2(5(2(1(1(1(3(4(3(3(0(5(4(1(0(1(x1))))))))))))))))))))) 1106.26/297.07 -> 1106.26/297.07 3(0(0(0(0(1(0(3(2(3(2(0(3(1(4(5(4(5(4(3(1(x1))))))))))))))))))))) 1106.26/297.07 , 2(3(5(5(2(x1))))) -> 2(3(5(3(x1)))) 1106.26/297.07 , 2(4(3(4(4(3(4(2(0(0(3(1(2(0(2(4(0(0(x1)))))))))))))))))) -> 1106.26/297.07 5(0(0(4(3(3(2(5(4(3(4(4(4(0(5(2(0(x1))))))))))))))))) 1106.26/297.07 , 3(0(0(5(4(4(0(x1))))))) -> 3(0(4(3(3(5(x1)))))) 1106.26/297.07 , 3(3(4(2(5(2(5(0(5(2(4(0(4(x1))))))))))))) -> 1106.26/297.07 3(3(4(3(5(1(1(0(4(0(2(4(4(x1))))))))))))) 1106.26/297.07 , 3(4(1(4(x1)))) -> 3(1(3(2(x1)))) 1106.26/297.07 , 4(1(3(5(3(3(5(3(5(1(2(3(4(5(5(0(x1)))))))))))))))) -> 1106.26/297.07 1(1(3(3(2(4(3(4(0(2(4(1(5(2(1(0(5(x1))))))))))))))))) 1106.26/297.07 , 4(1(4(1(5(5(0(3(3(4(2(2(x1)))))))))))) -> 1106.26/297.07 4(4(0(2(0(3(4(3(3(4(2(x1))))))))))) 1106.26/297.07 , 4(3(4(1(3(1(4(0(0(5(3(2(1(2(2(3(5(2(3(x1))))))))))))))))))) -> 1106.26/297.07 1(5(4(1(2(1(2(5(2(0(1(1(3(2(2(2(2(1(3(0(3(x1))))))))))))))))))))) 1106.26/297.07 , 4(4(5(5(3(4(0(0(1(5(4(4(3(5(4(5(1(5(0(1(x1)))))))))))))))))))) -> 1106.26/297.07 0(1(4(2(2(2(3(1(2(0(2(2(2(2(4(5(2(3(1(x1))))))))))))))))))) 1106.26/297.07 , 4(5(4(5(5(1(3(0(4(4(5(3(4(0(x1)))))))))))))) -> 1106.26/297.07 4(2(5(4(4(1(1(2(0(1(3(0(3(5(x1)))))))))))))) 1106.26/297.07 , 5(0(1(1(2(4(4(4(3(2(1(2(3(2(x1)))))))))))))) -> 1106.26/297.07 4(4(3(2(1(2(3(0(2(4(2(4(2(x1))))))))))))) 1106.26/297.07 , 5(1(5(1(1(0(1(5(2(4(1(3(5(0(5(3(0(4(4(x1))))))))))))))))))) -> 1106.26/297.07 5(2(3(2(5(1(4(3(4(4(5(2(0(1(2(1(3(4(x1)))))))))))))))))) 1106.26/297.07 , 5(2(5(3(5(4(4(5(2(1(4(1(0(5(4(1(x1)))))))))))))))) -> 1106.26/297.07 5(2(5(4(4(4(2(0(2(3(4(2(0(3(5(x1))))))))))))))) 1106.26/297.07 , 5(5(2(2(1(0(0(0(0(x1))))))))) -> 5(3(4(2(5(5(3(x1))))))) } 1106.26/297.07 Obligation: 1106.26/297.07 derivational complexity 1106.26/297.07 Answer: 1106.26/297.07 YES(?,O(n^1)) 1106.26/297.07 1106.26/297.07 The problem is match-bounded by 2. The enriched problem is 1106.26/297.07 compatible with the following automaton. 1106.26/297.07 { 0_0(1) -> 1 1106.26/297.07 , 0_1(1) -> 56 1106.26/297.07 , 0_1(2) -> 1 1106.26/297.07 , 0_1(2) -> 30 1106.26/297.07 , 0_1(2) -> 56 1106.26/297.07 , 0_1(2) -> 143 1106.26/297.07 , 0_1(2) -> 158 1106.26/297.07 , 0_1(2) -> 184 1106.26/297.07 , 0_1(3) -> 184 1106.26/297.07 , 0_1(7) -> 6 1106.26/297.07 , 0_1(19) -> 18 1106.26/297.07 , 0_1(20) -> 63 1106.26/297.07 , 0_1(28) -> 27 1106.26/297.07 , 0_1(29) -> 141 1106.26/297.07 , 0_1(37) -> 36 1106.26/297.07 , 0_1(42) -> 41 1106.26/297.07 , 0_1(49) -> 2 1106.26/297.07 , 0_1(54) -> 131 1106.26/297.07 , 0_1(57) -> 68 1106.26/297.07 , 0_1(60) -> 59 1106.26/297.07 , 0_1(64) -> 1 1106.26/297.07 , 0_1(65) -> 64 1106.26/297.07 , 0_1(66) -> 65 1106.26/297.07 , 0_1(69) -> 68 1106.26/297.07 , 0_1(70) -> 158 1106.26/297.07 , 0_1(71) -> 1 1106.26/297.07 , 0_1(72) -> 18 1106.26/297.07 , 0_1(74) -> 1 1106.26/297.07 , 0_1(80) -> 79 1106.26/297.07 , 0_1(83) -> 82 1106.26/297.07 , 0_1(92) -> 91 1106.26/297.07 , 0_1(99) -> 85 1106.26/297.07 , 0_1(100) -> 99 1106.26/297.07 , 0_1(101) -> 100 1106.26/297.07 , 0_1(102) -> 101 1106.26/297.07 , 0_1(104) -> 103 1106.26/297.07 , 0_1(109) -> 108 1106.26/297.07 , 0_1(117) -> 184 1106.26/297.07 , 0_1(120) -> 119 1106.26/297.07 , 0_1(121) -> 120 1106.26/297.07 , 0_1(133) -> 207 1106.26/297.07 , 0_1(140) -> 139 1106.26/297.07 , 0_1(142) -> 141 1106.26/297.07 , 0_1(152) -> 151 1106.26/297.07 , 0_1(160) -> 159 1106.26/297.07 , 0_1(162) -> 161 1106.26/297.07 , 0_1(175) -> 174 1106.26/297.07 , 0_1(191) -> 190 1106.26/297.07 , 0_1(205) -> 204 1106.26/297.07 , 0_1(213) -> 212 1106.26/297.07 , 0_1(216) -> 184 1106.26/297.07 , 0_1(227) -> 226 1106.26/297.07 , 0_1(236) -> 235 1106.26/297.07 , 0_1(243) -> 1 1106.26/297.07 , 0_2(243) -> 64 1106.26/297.07 , 1_0(1) -> 1 1106.26/297.07 , 1_1(1) -> 21 1106.26/297.07 , 1_1(2) -> 20 1106.26/297.07 , 1_1(13) -> 12 1106.26/297.07 , 1_1(14) -> 13 1106.26/297.07 , 1_1(18) -> 17 1106.26/297.07 , 1_1(21) -> 20 1106.26/297.07 , 1_1(31) -> 2 1106.26/297.07 , 1_1(43) -> 42 1106.26/297.07 , 1_1(48) -> 47 1106.26/297.07 , 1_1(57) -> 47 1106.26/297.07 , 1_1(64) -> 57 1106.26/297.07 , 1_1(67) -> 66 1106.26/297.07 , 1_1(71) -> 1 1106.26/297.07 , 1_1(71) -> 21 1106.26/297.07 , 1_1(71) -> 30 1106.26/297.07 , 1_1(74) -> 73 1106.26/297.07 , 1_1(75) -> 74 1106.26/297.07 , 1_1(78) -> 77 1106.26/297.07 , 1_1(94) -> 93 1106.26/297.07 , 1_1(103) -> 102 1106.26/297.07 , 1_1(111) -> 110 1106.26/297.07 , 1_1(138) -> 137 1106.26/297.07 , 1_1(139) -> 138 1106.26/297.07 , 1_1(141) -> 17 1106.26/297.07 , 1_1(144) -> 85 1106.26/297.07 , 1_1(145) -> 71 1106.26/297.07 , 1_1(155) -> 154 1106.26/297.07 , 1_1(158) -> 157 1106.26/297.07 , 1_1(169) -> 168 1106.26/297.07 , 1_1(171) -> 170 1106.26/297.07 , 1_1(176) -> 175 1106.26/297.07 , 1_1(177) -> 176 1106.26/297.07 , 1_1(183) -> 182 1106.26/297.07 , 1_1(189) -> 188 1106.26/297.07 , 1_1(202) -> 201 1106.26/297.07 , 1_1(203) -> 202 1106.26/297.07 , 1_1(206) -> 205 1106.26/297.07 , 1_1(210) -> 209 1106.26/297.07 , 1_1(220) -> 219 1106.26/297.07 , 1_1(228) -> 227 1106.26/297.07 , 1_1(230) -> 229 1106.26/297.07 , 1_2(299) -> 298 1106.26/297.07 , 2_0(1) -> 1 1106.26/297.07 , 2_1(1) -> 48 1106.26/297.07 , 2_1(2) -> 78 1106.26/297.07 , 2_1(3) -> 2 1106.26/297.07 , 2_1(5) -> 4 1106.26/297.07 , 2_1(8) -> 7 1106.26/297.07 , 2_1(11) -> 10 1106.26/297.07 , 2_1(17) -> 16 1106.26/297.07 , 2_1(20) -> 19 1106.26/297.07 , 2_1(23) -> 22 1106.26/297.07 , 2_1(26) -> 25 1106.26/297.07 , 2_1(30) -> 29 1106.26/297.07 , 2_1(47) -> 46 1106.26/297.07 , 2_1(52) -> 51 1106.26/297.07 , 2_1(56) -> 55 1106.26/297.07 , 2_1(57) -> 48 1106.26/297.07 , 2_1(63) -> 62 1106.26/297.07 , 2_1(64) -> 48 1106.26/297.07 , 2_1(68) -> 67 1106.26/297.07 , 2_1(69) -> 98 1106.26/297.07 , 2_1(70) -> 69 1106.26/297.07 , 2_1(73) -> 72 1106.26/297.07 , 2_1(79) -> 48 1106.26/297.07 , 2_1(88) -> 87 1106.26/297.07 , 2_1(91) -> 90 1106.26/297.07 , 2_1(106) -> 105 1106.26/297.07 , 2_1(108) -> 107 1106.26/297.07 , 2_1(116) -> 197 1106.26/297.07 , 2_1(117) -> 1 1106.26/297.07 , 2_1(117) -> 2 1106.26/297.07 , 2_1(117) -> 48 1106.26/297.07 , 2_1(125) -> 124 1106.26/297.07 , 2_1(143) -> 142 1106.26/297.07 , 2_1(148) -> 147 1106.26/297.07 , 2_1(153) -> 152 1106.26/297.07 , 2_1(157) -> 156 1106.26/297.07 , 2_1(161) -> 160 1106.26/297.07 , 2_1(166) -> 215 1106.26/297.07 , 2_1(170) -> 169 1106.26/297.07 , 2_1(172) -> 171 1106.26/297.07 , 2_1(174) -> 173 1106.26/297.07 , 2_1(179) -> 178 1106.26/297.07 , 2_1(180) -> 179 1106.26/297.07 , 2_1(181) -> 180 1106.26/297.07 , 2_1(182) -> 181 1106.26/297.07 , 2_1(185) -> 32 1106.26/297.07 , 2_1(186) -> 185 1106.26/297.07 , 2_1(187) -> 186 1106.26/297.07 , 2_1(190) -> 189 1106.26/297.07 , 2_1(192) -> 191 1106.26/297.07 , 2_1(193) -> 192 1106.26/297.07 , 2_1(194) -> 193 1106.26/297.07 , 2_1(195) -> 194 1106.26/297.07 , 2_1(198) -> 57 1106.26/297.07 , 2_1(204) -> 203 1106.26/297.07 , 2_1(207) -> 239 1106.26/297.07 , 2_1(209) -> 208 1106.26/297.07 , 2_1(211) -> 210 1106.26/297.07 , 2_1(214) -> 213 1106.26/297.07 , 2_1(216) -> 119 1106.26/297.07 , 2_1(218) -> 217 1106.26/297.07 , 2_1(226) -> 225 1106.26/297.07 , 2_1(229) -> 228 1106.26/297.07 , 2_1(235) -> 234 1106.26/297.07 , 2_1(237) -> 236 1106.26/297.07 , 2_1(242) -> 241 1106.26/297.07 , 2_2(79) -> 300 1106.26/297.07 , 2_2(244) -> 243 1106.26/297.07 , 3_0(1) -> 1 1106.26/297.07 , 3_1(1) -> 3 1106.26/297.07 , 3_1(2) -> 116 1106.26/297.07 , 3_1(3) -> 84 1106.26/297.07 , 3_1(6) -> 5 1106.26/297.07 , 3_1(9) -> 8 1106.26/297.07 , 3_1(12) -> 11 1106.26/297.07 , 3_1(21) -> 116 1106.26/297.07 , 3_1(22) -> 2 1106.26/297.07 , 3_1(24) -> 23 1106.26/297.07 , 3_1(27) -> 26 1106.26/297.07 , 3_1(29) -> 28 1106.26/297.07 , 3_1(30) -> 230 1106.26/297.07 , 3_1(33) -> 32 1106.26/297.07 , 3_1(38) -> 37 1106.26/297.07 , 3_1(41) -> 40 1106.26/297.07 , 3_1(46) -> 45 1106.26/297.07 , 3_1(48) -> 144 1106.26/297.07 , 3_1(49) -> 3 1106.26/297.07 , 3_1(51) -> 50 1106.26/297.07 , 3_1(57) -> 230 1106.26/297.07 , 3_1(61) -> 60 1106.26/297.07 , 3_1(64) -> 3 1106.26/297.07 , 3_1(65) -> 3 1106.26/297.07 , 3_1(66) -> 3 1106.26/297.07 , 3_1(70) -> 133 1106.26/297.07 , 3_1(71) -> 116 1106.26/297.07 , 3_1(72) -> 71 1106.26/297.07 , 3_1(74) -> 116 1106.26/297.07 , 3_1(81) -> 80 1106.26/297.07 , 3_1(85) -> 1 1106.26/297.07 , 3_1(85) -> 2 1106.26/297.07 , 3_1(85) -> 3 1106.26/297.07 , 3_1(85) -> 48 1106.26/297.07 , 3_1(85) -> 84 1106.26/297.07 , 3_1(85) -> 164 1106.26/297.07 , 3_1(85) -> 230 1106.26/297.07 , 3_1(87) -> 86 1106.26/297.07 , 3_1(93) -> 92 1106.26/297.07 , 3_1(95) -> 94 1106.26/297.07 , 3_1(98) -> 97 1106.26/297.07 , 3_1(105) -> 104 1106.26/297.07 , 3_1(107) -> 106 1106.26/297.07 , 3_1(110) -> 109 1106.26/297.07 , 3_1(117) -> 3 1106.26/297.07 , 3_1(118) -> 117 1106.26/297.07 , 3_1(123) -> 122 1106.26/297.07 , 3_1(124) -> 123 1106.26/297.07 , 3_1(128) -> 127 1106.26/297.07 , 3_1(133) -> 132 1106.26/297.07 , 3_1(134) -> 85 1106.26/297.07 , 3_1(136) -> 135 1106.26/297.07 , 3_1(146) -> 145 1106.26/297.07 , 3_1(147) -> 146 1106.26/297.07 , 3_1(150) -> 149 1106.26/297.07 , 3_1(163) -> 162 1106.26/297.07 , 3_1(165) -> 164 1106.26/297.07 , 3_1(166) -> 165 1106.26/297.07 , 3_1(178) -> 177 1106.26/297.07 , 3_1(184) -> 183 1106.26/297.07 , 3_1(188) -> 187 1106.26/297.07 , 3_1(207) -> 206 1106.26/297.07 , 3_1(208) -> 159 1106.26/297.07 , 3_1(212) -> 211 1106.26/297.07 , 3_1(216) -> 3 1106.26/297.07 , 3_1(217) -> 216 1106.26/297.07 , 3_1(222) -> 221 1106.26/297.07 , 3_1(238) -> 237 1106.26/297.07 , 3_1(240) -> 119 1106.26/297.07 , 3_1(243) -> 3 1106.26/297.07 , 3_2(68) -> 244 1106.26/297.07 , 3_2(298) -> 230 1106.26/297.07 , 3_2(300) -> 299 1106.26/297.07 , 4_0(1) -> 1 1106.26/297.07 , 4_1(1) -> 30 1106.26/297.07 , 4_1(4) -> 3 1106.26/297.07 , 4_1(30) -> 143 1106.26/297.07 , 4_1(32) -> 31 1106.26/297.07 , 4_1(34) -> 33 1106.26/297.07 , 4_1(35) -> 34 1106.26/297.07 , 4_1(48) -> 166 1106.26/297.07 , 4_1(57) -> 1 1106.26/297.07 , 4_1(57) -> 21 1106.26/297.07 , 4_1(57) -> 30 1106.26/297.07 , 4_1(57) -> 47 1106.26/297.07 , 4_1(57) -> 70 1106.26/297.07 , 4_1(59) -> 58 1106.26/297.07 , 4_1(71) -> 30 1106.26/297.07 , 4_1(74) -> 30 1106.26/297.07 , 4_1(77) -> 76 1106.26/297.07 , 4_1(79) -> 71 1106.26/297.07 , 4_1(82) -> 81 1106.26/297.07 , 4_1(90) -> 89 1106.26/297.07 , 4_1(112) -> 111 1106.26/297.07 , 4_1(114) -> 113 1106.26/297.07 , 4_1(116) -> 115 1106.26/297.07 , 4_1(122) -> 121 1106.26/297.07 , 4_1(127) -> 126 1106.26/297.07 , 4_1(129) -> 128 1106.26/297.07 , 4_1(130) -> 129 1106.26/297.07 , 4_1(131) -> 130 1106.26/297.07 , 4_1(132) -> 99 1106.26/297.07 , 4_1(135) -> 134 1106.26/297.07 , 4_1(141) -> 140 1106.26/297.07 , 4_1(149) -> 148 1106.26/297.07 , 4_1(151) -> 150 1106.26/297.07 , 4_1(154) -> 153 1106.26/297.07 , 4_1(159) -> 57 1106.26/297.07 , 4_1(164) -> 163 1106.26/297.07 , 4_1(168) -> 167 1106.26/297.07 , 4_1(196) -> 195 1106.26/297.07 , 4_1(200) -> 199 1106.26/297.07 , 4_1(201) -> 200 1106.26/297.07 , 4_1(215) -> 214 1106.26/297.07 , 4_1(221) -> 220 1106.26/297.07 , 4_1(223) -> 222 1106.26/297.07 , 4_1(224) -> 223 1106.26/297.07 , 4_1(232) -> 231 1106.26/297.07 , 4_1(233) -> 232 1106.26/297.07 , 4_1(234) -> 233 1106.26/297.07 , 4_1(239) -> 238 1106.26/297.07 , 4_1(241) -> 240 1106.26/297.07 , 5_0(1) -> 1 1106.26/297.07 , 5_1(1) -> 70 1106.26/297.07 , 5_1(2) -> 70 1106.26/297.07 , 5_1(3) -> 118 1106.26/297.07 , 5_1(10) -> 9 1106.26/297.07 , 5_1(15) -> 14 1106.26/297.07 , 5_1(16) -> 15 1106.26/297.07 , 5_1(25) -> 24 1106.26/297.07 , 5_1(36) -> 35 1106.26/297.07 , 5_1(39) -> 38 1106.26/297.07 , 5_1(40) -> 39 1106.26/297.07 , 5_1(44) -> 43 1106.26/297.07 , 5_1(45) -> 44 1106.26/297.07 , 5_1(48) -> 54 1106.26/297.07 , 5_1(50) -> 49 1106.26/297.07 , 5_1(53) -> 52 1106.26/297.07 , 5_1(54) -> 53 1106.26/297.07 , 5_1(55) -> 54 1106.26/297.07 , 5_1(58) -> 57 1106.26/297.07 , 5_1(62) -> 61 1106.26/297.07 , 5_1(64) -> 70 1106.26/297.07 , 5_1(71) -> 70 1106.26/297.07 , 5_1(74) -> 70 1106.26/297.07 , 5_1(76) -> 75 1106.26/297.07 , 5_1(78) -> 54 1106.26/297.07 , 5_1(84) -> 83 1106.26/297.07 , 5_1(86) -> 85 1106.26/297.07 , 5_1(89) -> 88 1106.26/297.07 , 5_1(96) -> 95 1106.26/297.07 , 5_1(97) -> 96 1106.26/297.07 , 5_1(113) -> 112 1106.26/297.07 , 5_1(115) -> 114 1106.26/297.07 , 5_1(116) -> 118 1106.26/297.07 , 5_1(118) -> 242 1106.26/297.07 , 5_1(119) -> 1 1106.26/297.07 , 5_1(119) -> 29 1106.26/297.07 , 5_1(119) -> 48 1106.26/297.07 , 5_1(119) -> 53 1106.26/297.07 , 5_1(119) -> 54 1106.26/297.07 , 5_1(119) -> 70 1106.26/297.07 , 5_1(120) -> 70 1106.26/297.07 , 5_1(126) -> 125 1106.26/297.07 , 5_1(137) -> 136 1106.26/297.07 , 5_1(156) -> 155 1106.26/297.07 , 5_1(160) -> 70 1106.26/297.07 , 5_1(167) -> 71 1106.26/297.07 , 5_1(169) -> 70 1106.26/297.07 , 5_1(173) -> 172 1106.26/297.07 , 5_1(197) -> 196 1106.26/297.07 , 5_1(199) -> 198 1106.26/297.07 , 5_1(219) -> 218 1106.26/297.07 , 5_1(225) -> 224 1106.26/297.07 , 5_1(231) -> 216 1106.26/297.07 , 5_1(243) -> 70 } 1106.26/297.07 1106.26/297.07 Hurray, we answered YES(?,O(n^1)) 1106.93/297.55 EOF