YES(?,O(n^1)) 1105.72/297.07 YES(?,O(n^1)) 1105.72/297.07 1105.72/297.07 We are left with following problem, upon which TcT provides the 1105.72/297.07 certificate YES(?,O(n^1)). 1105.72/297.07 1105.72/297.07 Strict Trs: 1105.72/297.07 { 0(1(2(3(1(x1))))) -> 0(0(1(1(x1)))) 1105.72/297.07 , 0(2(2(3(3(2(5(0(4(x1))))))))) -> 0(2(2(1(3(4(1(4(x1)))))))) 1105.72/297.07 , 0(5(1(0(1(1(2(2(1(1(2(2(2(2(x1)))))))))))))) -> 1105.72/297.07 0(3(0(5(3(1(3(0(3(4(2(3(3(1(4(x1))))))))))))))) 1105.72/297.07 , 0(5(2(1(1(4(2(5(2(0(1(3(3(3(x1)))))))))))))) -> 1105.72/297.07 0(4(0(4(4(4(5(0(2(4(0(3(2(2(x1)))))))))))))) 1105.72/297.07 , 0(5(2(3(4(0(5(3(2(4(2(2(4(0(3(4(x1)))))))))))))))) -> 1105.72/297.07 0(0(0(5(1(3(2(2(3(0(1(3(2(1(x1)))))))))))))) 1105.72/297.07 , 1(1(4(0(4(2(1(2(4(5(3(x1))))))))))) -> 1105.72/297.07 1(1(0(1(5(2(2(0(2(4(x1)))))))))) 1105.72/297.07 , 2(2(0(1(4(3(5(4(2(2(5(1(0(5(0(5(4(5(2(x1))))))))))))))))))) -> 1105.72/297.07 3(3(4(2(0(4(5(2(5(2(0(0(4(4(3(5(1(4(5(2(x1)))))))))))))))))))) 1105.72/297.07 , 2(2(5(5(2(2(1(x1))))))) -> 3(2(3(3(1(0(x1)))))) 1105.72/297.07 , 2(3(0(3(2(3(1(1(4(2(5(3(4(2(5(2(5(0(2(3(1(x1))))))))))))))))))))) 1105.72/297.07 -> 3(2(4(3(2(1(3(3(1(0(1(1(3(3(0(3(0(5(1(x1))))))))))))))))))) 1105.72/297.07 , 2(3(0(4(0(0(5(2(4(x1))))))))) -> 3(2(2(2(3(0(4(0(4(x1))))))))) 1105.72/297.07 , 2(3(5(3(3(4(1(5(1(2(x1)))))))))) -> 1105.72/297.07 2(0(3(5(2(5(1(3(4(2(x1)))))))))) 1105.72/297.07 , 2(4(3(3(3(5(0(1(3(x1))))))))) -> 0(1(0(0(5(0(5(x1))))))) 1105.72/297.07 , 2(5(3(4(1(3(2(5(3(1(1(2(2(1(0(2(4(3(3(x1))))))))))))))))))) -> 1105.72/297.07 0(3(5(2(3(1(1(0(3(4(3(4(0(0(5(2(2(3(x1)))))))))))))))))) 1105.72/297.07 , 3(0(1(2(4(0(0(3(3(4(x1)))))))))) -> 1105.72/297.07 3(1(5(0(4(2(0(2(5(4(x1)))))))))) 1105.72/297.07 , 3(0(2(3(2(0(3(3(2(1(2(2(0(1(3(x1))))))))))))))) -> 1105.72/297.07 2(1(5(3(2(1(2(2(0(4(0(1(3(1(x1)))))))))))))) 1105.72/297.07 , 3(1(2(1(3(1(2(2(4(1(1(3(2(4(4(3(2(0(3(4(5(x1))))))))))))))))))))) 1105.72/297.07 -> 2(5(5(1(1(2(1(0(1(3(1(0(5(2(4(1(1(5(x1)))))))))))))))))) 1105.72/297.07 , 3(1(2(4(0(0(3(3(1(4(5(x1))))))))))) -> 1105.72/297.07 2(3(1(1(4(0(4(2(2(2(5(x1))))))))))) 1105.72/297.07 , 4(3(0(4(1(0(4(1(5(0(3(x1))))))))))) -> 1105.72/297.07 0(4(2(3(0(0(1(5(5(1(x1)))))))))) 1105.72/297.07 , 4(4(2(5(3(3(1(1(3(1(1(0(5(3(1(4(x1)))))))))))))))) -> 1105.72/297.07 4(2(4(4(4(2(1(5(5(4(3(3(0(5(1(5(4(x1))))))))))))))))) 1105.72/297.07 , 4(5(2(1(1(3(4(x1))))))) -> 1(1(0(5(0(x1))))) 1105.72/297.07 , 4(5(2(3(5(x1))))) -> 4(4(0(5(x1)))) 1105.72/297.07 , 5(3(1(5(0(1(4(4(2(4(3(2(5(0(4(1(0(4(4(x1))))))))))))))))))) -> 1105.72/297.07 5(2(2(4(1(1(5(2(3(4(2(5(2(0(2(0(2(5(4(x1))))))))))))))))))) 1105.72/297.07 , 5(3(2(4(3(2(x1)))))) -> 5(3(0(5(4(x1))))) 1105.72/297.07 , 5(3(5(1(1(5(4(2(2(4(1(5(0(5(4(3(x1)))))))))))))))) -> 1105.72/297.07 0(0(4(2(2(1(3(2(1(0(5(1(1(1(x1)))))))))))))) 1105.72/297.07 , 5(4(3(1(3(4(5(3(0(1(3(4(0(2(2(4(3(3(0(5(3(x1))))))))))))))))))))) 1105.72/297.07 -> 5(5(1(1(5(2(4(0(0(1(0(1(2(0(5(1(3(5(x1)))))))))))))))))) } 1105.72/297.07 Obligation: 1105.72/297.07 derivational complexity 1105.72/297.07 Answer: 1105.72/297.07 YES(?,O(n^1)) 1105.72/297.07 1105.72/297.07 The problem is match-bounded by 2. The enriched problem is 1105.72/297.07 compatible with the following automaton. 1105.72/297.07 { 0_0(1) -> 1 1105.72/297.07 , 0_1(1) -> 73 1105.72/297.07 , 0_1(2) -> 1 1105.72/297.07 , 0_1(2) -> 2 1105.72/297.07 , 0_1(2) -> 10 1105.72/297.07 , 0_1(2) -> 33 1105.72/297.07 , 0_1(2) -> 51 1105.72/297.07 , 0_1(2) -> 73 1105.72/297.07 , 0_1(2) -> 87 1105.72/297.07 , 0_1(2) -> 105 1105.72/297.07 , 0_1(2) -> 106 1105.72/297.07 , 0_1(2) -> 162 1105.72/297.07 , 0_1(3) -> 2 1105.72/297.07 , 0_1(4) -> 2 1105.72/297.07 , 0_1(10) -> 93 1105.72/297.07 , 0_1(12) -> 11 1105.72/297.07 , 0_1(17) -> 16 1105.72/297.07 , 0_1(23) -> 22 1105.72/297.07 , 0_1(28) -> 27 1105.72/297.07 , 0_1(31) -> 30 1105.72/297.07 , 0_1(34) -> 3 1105.72/297.07 , 0_1(41) -> 40 1105.72/297.07 , 0_1(44) -> 73 1105.72/297.07 , 0_1(46) -> 45 1105.72/297.07 , 0_1(51) -> 50 1105.72/297.07 , 0_1(56) -> 55 1105.72/297.07 , 0_1(62) -> 61 1105.72/297.07 , 0_1(63) -> 62 1105.72/297.07 , 0_1(81) -> 80 1105.72/297.07 , 0_1(86) -> 85 1105.72/297.07 , 0_1(88) -> 87 1105.72/297.07 , 0_1(92) -> 91 1105.72/297.07 , 0_1(95) -> 94 1105.72/297.07 , 0_1(103) -> 102 1105.72/297.07 , 0_1(104) -> 103 1105.72/297.07 , 0_1(106) -> 105 1105.72/297.07 , 0_1(112) -> 111 1105.72/297.07 , 0_1(117) -> 116 1105.72/297.07 , 0_1(118) -> 117 1105.72/297.07 , 0_1(124) -> 123 1105.72/297.07 , 0_1(125) -> 194 1105.72/297.07 , 0_1(127) -> 126 1105.72/297.07 , 0_1(128) -> 195 1105.72/297.07 , 0_1(129) -> 73 1105.72/297.07 , 0_1(136) -> 135 1105.72/297.07 , 0_1(138) -> 137 1105.72/297.07 , 0_1(146) -> 145 1105.72/297.07 , 0_1(150) -> 149 1105.72/297.07 , 0_1(159) -> 158 1105.72/297.07 , 0_1(165) -> 164 1105.72/297.07 , 0_1(166) -> 165 1105.72/297.07 , 0_1(168) -> 73 1105.72/297.07 , 0_1(180) -> 179 1105.72/297.07 , 0_1(207) -> 206 1105.72/297.07 , 0_1(215) -> 214 1105.72/297.07 , 0_1(216) -> 215 1105.72/297.07 , 0_1(218) -> 217 1105.72/297.07 , 0_1(221) -> 220 1105.72/297.07 , 0_2(198) -> 197 1105.72/297.07 , 0_2(224) -> 2 1105.72/297.07 , 0_2(224) -> 137 1105.72/297.07 , 0_2(225) -> 224 1105.72/297.07 , 1_0(1) -> 1 1105.72/297.07 , 1_1(1) -> 4 1105.72/297.07 , 1_1(2) -> 9 1105.72/297.07 , 1_1(3) -> 208 1105.72/297.07 , 1_1(4) -> 3 1105.72/297.07 , 1_1(7) -> 6 1105.72/297.07 , 1_1(10) -> 9 1105.72/297.07 , 1_1(11) -> 4 1105.72/297.07 , 1_1(15) -> 14 1105.72/297.07 , 1_1(36) -> 35 1105.72/297.07 , 1_1(42) -> 41 1105.72/297.07 , 1_1(44) -> 1 1105.72/297.07 , 1_1(44) -> 3 1105.72/297.07 , 1_1(44) -> 4 1105.72/297.07 , 1_1(44) -> 10 1105.72/297.07 , 1_1(44) -> 68 1105.72/297.07 , 1_1(45) -> 44 1105.72/297.07 , 1_1(47) -> 46 1105.72/297.07 , 1_1(52) -> 4 1105.72/297.07 , 1_1(68) -> 67 1105.72/297.07 , 1_1(73) -> 72 1105.72/297.07 , 1_1(77) -> 76 1105.72/297.07 , 1_1(80) -> 79 1105.72/297.07 , 1_1(82) -> 81 1105.72/297.07 , 1_1(83) -> 82 1105.72/297.07 , 1_1(100) -> 99 1105.72/297.07 , 1_1(102) -> 2 1105.72/297.07 , 1_1(106) -> 154 1105.72/297.07 , 1_1(110) -> 109 1105.72/297.07 , 1_1(111) -> 110 1105.72/297.07 , 1_1(122) -> 52 1105.72/297.07 , 1_1(128) -> 181 1105.72/297.07 , 1_1(129) -> 94 1105.72/297.07 , 1_1(133) -> 132 1105.72/297.07 , 1_1(139) -> 138 1105.72/297.07 , 1_1(142) -> 141 1105.72/297.07 , 1_1(143) -> 142 1105.72/297.07 , 1_1(145) -> 144 1105.72/297.07 , 1_1(147) -> 146 1105.72/297.07 , 1_1(149) -> 148 1105.72/297.07 , 1_1(154) -> 153 1105.72/297.07 , 1_1(155) -> 3 1105.72/297.07 , 1_1(156) -> 155 1105.72/297.07 , 1_1(157) -> 156 1105.72/297.07 , 1_1(167) -> 166 1105.72/297.07 , 1_1(168) -> 4 1105.72/297.07 , 1_1(174) -> 173 1105.72/297.07 , 1_1(186) -> 185 1105.72/297.07 , 1_1(187) -> 186 1105.72/297.07 , 1_1(203) -> 202 1105.72/297.07 , 1_1(206) -> 205 1105.72/297.07 , 1_1(210) -> 209 1105.72/297.07 , 1_1(211) -> 210 1105.72/297.07 , 1_1(217) -> 216 1105.72/297.07 , 1_1(219) -> 218 1105.72/297.07 , 1_1(223) -> 222 1105.72/297.07 , 1_2(156) -> 226 1105.72/297.07 , 1_2(226) -> 225 1105.72/297.07 , 2_0(1) -> 1 1105.72/297.07 , 2_1(1) -> 33 1105.72/297.07 , 2_1(4) -> 43 1105.72/297.07 , 2_1(5) -> 2 1105.72/297.07 , 2_1(6) -> 5 1105.72/297.07 , 2_1(10) -> 51 1105.72/297.07 , 2_1(20) -> 19 1105.72/297.07 , 2_1(29) -> 28 1105.72/297.07 , 2_1(33) -> 32 1105.72/297.07 , 2_1(38) -> 37 1105.72/297.07 , 2_1(39) -> 38 1105.72/297.07 , 2_1(49) -> 48 1105.72/297.07 , 2_1(50) -> 49 1105.72/297.07 , 2_1(52) -> 33 1105.72/297.07 , 2_1(53) -> 33 1105.72/297.07 , 2_1(55) -> 54 1105.72/297.07 , 2_1(59) -> 58 1105.72/297.07 , 2_1(61) -> 60 1105.72/297.07 , 2_1(70) -> 52 1105.72/297.07 , 2_1(76) -> 75 1105.72/297.07 , 2_1(89) -> 70 1105.72/297.07 , 2_1(90) -> 89 1105.72/297.07 , 2_1(94) -> 1 1105.72/297.07 , 2_1(94) -> 33 1105.72/297.07 , 2_1(94) -> 120 1105.72/297.07 , 2_1(94) -> 121 1105.72/297.07 , 2_1(94) -> 139 1105.72/297.07 , 2_1(98) -> 97 1105.72/297.07 , 2_1(106) -> 162 1105.72/297.07 , 2_1(108) -> 107 1105.72/297.07 , 2_1(120) -> 119 1105.72/297.07 , 2_1(121) -> 120 1105.72/297.07 , 2_1(126) -> 125 1105.72/297.07 , 2_1(128) -> 127 1105.72/297.07 , 2_1(132) -> 131 1105.72/297.07 , 2_1(134) -> 133 1105.72/297.07 , 2_1(135) -> 134 1105.72/297.07 , 2_1(144) -> 143 1105.72/297.07 , 2_1(152) -> 151 1105.72/297.07 , 2_1(161) -> 160 1105.72/297.07 , 2_1(162) -> 161 1105.72/297.07 , 2_1(163) -> 22 1105.72/297.07 , 2_1(169) -> 168 1105.72/297.07 , 2_1(173) -> 172 1105.72/297.07 , 2_1(183) -> 182 1105.72/297.07 , 2_1(184) -> 183 1105.72/297.07 , 2_1(189) -> 188 1105.72/297.07 , 2_1(192) -> 191 1105.72/297.07 , 2_1(194) -> 193 1105.72/297.07 , 2_1(201) -> 200 1105.72/297.07 , 2_1(202) -> 201 1105.72/297.07 , 2_1(205) -> 204 1105.72/297.07 , 2_1(213) -> 212 1105.72/297.07 , 2_1(220) -> 219 1105.72/297.07 , 3_0(1) -> 1 1105.72/297.07 , 3_1(1) -> 121 1105.72/297.07 , 3_1(4) -> 139 1105.72/297.07 , 3_1(8) -> 7 1105.72/297.07 , 3_1(9) -> 21 1105.72/297.07 , 3_1(11) -> 2 1105.72/297.07 , 3_1(14) -> 13 1105.72/297.07 , 3_1(16) -> 15 1105.72/297.07 , 3_1(18) -> 17 1105.72/297.07 , 3_1(21) -> 20 1105.72/297.07 , 3_1(32) -> 31 1105.72/297.07 , 3_1(37) -> 36 1105.72/297.07 , 3_1(40) -> 39 1105.72/297.07 , 3_1(43) -> 42 1105.72/297.07 , 3_1(52) -> 1 1105.72/297.07 , 3_1(52) -> 32 1105.72/297.07 , 3_1(52) -> 33 1105.72/297.07 , 3_1(52) -> 120 1105.72/297.07 , 3_1(52) -> 121 1105.72/297.07 , 3_1(52) -> 161 1105.72/297.07 , 3_1(53) -> 52 1105.72/297.07 , 3_1(66) -> 65 1105.72/297.07 , 3_1(71) -> 70 1105.72/297.07 , 3_1(72) -> 71 1105.72/297.07 , 3_1(75) -> 74 1105.72/297.07 , 3_1(78) -> 77 1105.72/297.07 , 3_1(79) -> 78 1105.72/297.07 , 3_1(84) -> 83 1105.72/297.07 , 3_1(85) -> 84 1105.72/297.07 , 3_1(87) -> 86 1105.72/297.07 , 3_1(91) -> 90 1105.72/297.07 , 3_1(96) -> 95 1105.72/297.07 , 3_1(101) -> 100 1105.72/297.07 , 3_1(105) -> 86 1105.72/297.07 , 3_1(106) -> 223 1105.72/297.07 , 3_1(109) -> 108 1105.72/297.07 , 3_1(113) -> 112 1105.72/297.07 , 3_1(115) -> 114 1105.72/297.07 , 3_1(131) -> 130 1105.72/297.07 , 3_1(148) -> 147 1105.72/297.07 , 3_1(155) -> 94 1105.72/297.07 , 3_1(164) -> 163 1105.72/297.07 , 3_1(178) -> 177 1105.72/297.07 , 3_1(179) -> 178 1105.72/297.07 , 3_1(190) -> 189 1105.72/297.07 , 3_1(195) -> 182 1105.72/297.07 , 3_1(204) -> 203 1105.72/297.07 , 3_2(197) -> 196 1105.72/297.07 , 4_0(1) -> 1 1105.72/297.07 , 4_1(1) -> 10 1105.72/297.07 , 4_1(9) -> 8 1105.72/297.07 , 4_1(19) -> 18 1105.72/297.07 , 4_1(22) -> 2 1105.72/297.07 , 4_1(24) -> 23 1105.72/297.07 , 4_1(25) -> 24 1105.72/297.07 , 4_1(26) -> 25 1105.72/297.07 , 4_1(30) -> 29 1105.72/297.07 , 4_1(33) -> 101 1105.72/297.07 , 4_1(52) -> 10 1105.72/297.07 , 4_1(54) -> 53 1105.72/297.07 , 4_1(57) -> 56 1105.72/297.07 , 4_1(64) -> 63 1105.72/297.07 , 4_1(65) -> 64 1105.72/297.07 , 4_1(69) -> 68 1105.72/297.07 , 4_1(70) -> 10 1105.72/297.07 , 4_1(74) -> 70 1105.72/297.07 , 4_1(76) -> 10 1105.72/297.07 , 4_1(93) -> 92 1105.72/297.07 , 4_1(94) -> 10 1105.72/297.07 , 4_1(105) -> 168 1105.72/297.07 , 4_1(114) -> 113 1105.72/297.07 , 4_1(116) -> 115 1105.72/297.07 , 4_1(125) -> 124 1105.72/297.07 , 4_1(137) -> 136 1105.72/297.07 , 4_1(153) -> 152 1105.72/297.07 , 4_1(158) -> 157 1105.72/297.07 , 4_1(160) -> 159 1105.72/297.07 , 4_1(168) -> 1 1105.72/297.07 , 4_1(168) -> 10 1105.72/297.07 , 4_1(168) -> 68 1105.72/297.07 , 4_1(170) -> 169 1105.72/297.07 , 4_1(171) -> 170 1105.72/297.07 , 4_1(172) -> 171 1105.72/297.07 , 4_1(177) -> 176 1105.72/297.07 , 4_1(185) -> 184 1105.72/297.07 , 4_1(191) -> 190 1105.72/297.07 , 4_1(195) -> 10 1105.72/297.07 , 4_1(200) -> 3 1105.72/297.07 , 4_1(214) -> 213 1105.72/297.07 , 4_2(76) -> 199 1105.72/297.07 , 5_0(1) -> 1 1105.72/297.07 , 5_1(1) -> 106 1105.72/297.07 , 5_1(4) -> 88 1105.72/297.07 , 5_1(9) -> 66 1105.72/297.07 , 5_1(10) -> 128 1105.72/297.07 , 5_1(13) -> 12 1105.72/297.07 , 5_1(27) -> 26 1105.72/297.07 , 5_1(32) -> 118 1105.72/297.07 , 5_1(33) -> 69 1105.72/297.07 , 5_1(35) -> 34 1105.72/297.07 , 5_1(48) -> 47 1105.72/297.07 , 5_1(52) -> 106 1105.72/297.07 , 5_1(53) -> 128 1105.72/297.07 , 5_1(58) -> 57 1105.72/297.07 , 5_1(60) -> 59 1105.72/297.07 , 5_1(67) -> 66 1105.72/297.07 , 5_1(73) -> 46 1105.72/297.07 , 5_1(88) -> 167 1105.72/297.07 , 5_1(97) -> 96 1105.72/297.07 , 5_1(99) -> 98 1105.72/297.07 , 5_1(105) -> 104 1105.72/297.07 , 5_1(107) -> 11 1105.72/297.07 , 5_1(119) -> 118 1105.72/297.07 , 5_1(123) -> 122 1105.72/297.07 , 5_1(130) -> 129 1105.72/297.07 , 5_1(140) -> 94 1105.72/297.07 , 5_1(141) -> 140 1105.72/297.07 , 5_1(151) -> 150 1105.72/297.07 , 5_1(155) -> 2 1105.72/297.07 , 5_1(168) -> 128 1105.72/297.07 , 5_1(175) -> 174 1105.72/297.07 , 5_1(176) -> 175 1105.72/297.07 , 5_1(181) -> 180 1105.72/297.07 , 5_1(182) -> 1 1105.72/297.07 , 5_1(182) -> 106 1105.72/297.07 , 5_1(182) -> 128 1105.72/297.07 , 5_1(188) -> 187 1105.72/297.07 , 5_1(193) -> 192 1105.72/297.07 , 5_1(195) -> 106 1105.72/297.07 , 5_1(208) -> 207 1105.72/297.07 , 5_1(209) -> 182 1105.72/297.07 , 5_1(212) -> 211 1105.72/297.07 , 5_1(222) -> 221 1105.72/297.07 , 5_2(196) -> 69 1105.72/297.07 , 5_2(196) -> 106 1105.72/297.07 , 5_2(196) -> 118 1105.72/297.07 , 5_2(199) -> 198 } 1105.72/297.07 1105.72/297.07 Hurray, we answered YES(?,O(n^1)) 1106.37/297.57 EOF