YES(?,O(n^1)) 1078.32/297.08 YES(?,O(n^1)) 1078.32/297.08 1078.32/297.08 We are left with following problem, upon which TcT provides the 1078.32/297.08 certificate YES(?,O(n^1)). 1078.32/297.08 1078.32/297.08 Strict Trs: 1078.32/297.08 { 0(0(1(2(1(x1))))) -> 1(0(1(1(0(x1))))) 1078.32/297.08 , 0(1(1(3(2(2(0(0(0(5(0(2(4(3(3(0(1(x1))))))))))))))))) -> 1078.32/297.08 5(4(1(1(0(5(2(0(2(3(3(3(0(5(0(1(x1)))))))))))))))) 1078.32/297.08 , 0(3(1(2(4(x1))))) -> 0(5(1(4(x1)))) 1078.32/297.08 , 0(4(5(4(5(0(2(3(1(2(4(5(3(5(0(4(3(3(2(x1))))))))))))))))))) -> 1078.32/297.08 1(0(2(4(5(5(2(2(4(2(1(1(4(0(1(2(3(0(2(5(x1)))))))))))))))))))) 1078.32/297.08 , 0(5(1(0(3(3(2(5(5(4(0(5(5(5(2(x1))))))))))))))) -> 1078.32/297.08 1(0(1(3(4(5(3(3(3(2(2(3(3(5(2(x1))))))))))))))) 1078.32/297.08 , 1(4(1(3(2(3(3(1(2(1(x1)))))))))) -> 1(5(3(2(4(5(1(3(4(x1))))))))) 1078.32/297.08 , 2(1(1(4(0(2(x1)))))) -> 1(1(5(3(5(x1))))) 1078.32/297.08 , 2(1(1(5(3(1(3(4(3(5(3(3(2(4(3(1(4(x1))))))))))))))))) -> 1078.32/297.08 1(0(1(0(0(2(1(3(2(2(0(3(0(5(2(4(x1)))))))))))))))) 1078.32/297.08 , 2(2(4(1(3(4(2(x1))))))) -> 2(3(2(4(3(5(x1)))))) 1078.32/297.08 , 2(4(1(0(2(3(2(3(5(3(1(2(3(1(1(4(x1)))))))))))))))) -> 1078.32/297.08 2(2(2(1(4(5(0(1(0(3(1(3(5(1(2(x1))))))))))))))) 1078.32/297.08 , 2(4(3(5(0(2(5(5(1(5(0(4(4(4(1(4(3(x1))))))))))))))))) -> 1078.32/297.08 2(0(5(2(2(0(5(4(1(3(2(4(1(4(1(1(0(x1))))))))))))))))) 1078.32/297.08 , 3(1(2(4(3(4(3(2(0(3(2(3(4(3(4(5(4(3(4(1(1(x1))))))))))))))))))))) 1078.32/297.08 -> 3(4(0(0(2(4(5(0(0(4(3(5(4(3(0(3(2(2(1(1(x1)))))))))))))))))))) 1078.32/297.08 , 4(0(4(2(3(4(5(1(1(5(1(x1))))))))))) -> 1078.32/297.08 5(4(3(2(2(3(2(1(2(4(0(x1))))))))))) 1078.32/297.08 , 4(0(5(4(2(4(0(x1))))))) -> 0(1(2(2(2(2(0(x1))))))) 1078.32/297.08 , 4(2(4(2(5(1(0(1(5(x1))))))))) -> 5(0(3(1(0(2(2(5(x1)))))))) 1078.32/297.08 , 4(3(0(1(1(x1))))) -> 5(4(5(2(x1)))) 1078.32/297.08 , 4(3(4(2(2(x1))))) -> 0(5(0(2(x1)))) 1078.32/297.08 , 4(3(4(4(0(3(0(3(2(3(2(1(x1)))))))))))) -> 1078.32/297.08 5(5(5(5(5(0(2(2(4(4(2(0(x1)))))))))))) 1078.32/297.08 , 4(5(1(0(2(0(5(4(5(4(4(2(5(5(2(3(5(4(2(3(x1)))))))))))))))))))) -> 1078.32/297.08 0(5(5(2(0(5(2(4(2(5(2(5(2(0(1(5(2(3(3(0(x1)))))))))))))))))))) 1078.32/297.08 , 4(5(2(2(5(4(4(3(4(5(4(x1))))))))))) -> 1078.32/297.08 5(2(3(2(5(0(0(0(5(4(x1)))))))))) 1078.32/297.08 , 4(5(3(2(1(1(5(2(2(3(4(3(2(3(1(x1))))))))))))))) -> 1078.32/297.08 0(1(3(5(0(1(3(4(0(3(5(4(3(1(x1)))))))))))))) 1078.32/297.08 , 5(0(1(0(1(1(5(1(1(5(5(2(1(1(0(x1))))))))))))))) -> 1078.32/297.08 5(1(5(1(1(1(3(0(3(3(3(3(1(0(x1)))))))))))))) 1078.32/297.08 , 5(2(4(5(0(3(0(2(3(x1))))))))) -> 5(3(2(1(0(1(3(4(0(x1))))))))) 1078.32/297.08 , 5(3(0(4(4(1(1(5(3(4(1(1(2(3(2(x1))))))))))))))) -> 1078.32/297.08 5(4(1(4(0(2(1(2(2(5(3(5(3(4(4(x1))))))))))))))) 1078.32/297.08 , 5(3(4(4(3(3(5(2(5(2(1(1(4(2(x1)))))))))))))) -> 1078.32/297.08 5(4(0(5(2(5(5(3(1(0(3(3(5(x1))))))))))))) } 1078.32/297.08 Obligation: 1078.32/297.08 derivational complexity 1078.32/297.08 Answer: 1078.32/297.08 YES(?,O(n^1)) 1078.32/297.08 1078.32/297.08 The problem is match-bounded by 1. The enriched problem is 1078.32/297.08 compatible with the following automaton. 1078.32/297.08 { 0_0(1) -> 1 1078.32/297.08 , 0_1(1) -> 5 1078.32/297.08 , 0_1(2) -> 5 1078.32/297.08 , 0_1(3) -> 2 1078.32/297.08 , 0_1(5) -> 159 1078.32/297.08 , 0_1(10) -> 9 1078.32/297.08 , 0_1(13) -> 12 1078.32/297.08 , 0_1(18) -> 17 1078.32/297.08 , 0_1(20) -> 19 1078.32/297.08 , 0_1(21) -> 1 1078.32/297.08 , 0_1(21) -> 5 1078.32/297.08 , 0_1(21) -> 23 1078.32/297.08 , 0_1(21) -> 122 1078.32/297.08 , 0_1(35) -> 34 1078.32/297.08 , 0_1(39) -> 38 1078.32/297.08 , 0_1(51) -> 22 1078.32/297.08 , 0_1(60) -> 4 1078.32/297.08 , 0_1(61) -> 60 1078.32/297.08 , 0_1(67) -> 66 1078.32/297.08 , 0_1(69) -> 68 1078.32/297.08 , 0_1(71) -> 22 1078.32/297.08 , 0_1(72) -> 5 1078.32/297.08 , 0_1(79) -> 78 1078.32/297.08 , 0_1(81) -> 80 1078.32/297.08 , 0_1(86) -> 71 1078.32/297.08 , 0_1(90) -> 89 1078.32/297.08 , 0_1(98) -> 5 1078.32/297.08 , 0_1(100) -> 99 1078.32/297.08 , 0_1(101) -> 100 1078.32/297.08 , 0_1(105) -> 104 1078.32/297.08 , 0_1(106) -> 105 1078.32/297.08 , 0_1(112) -> 111 1078.32/297.08 , 0_1(125) -> 129 1078.32/297.08 , 0_1(127) -> 6 1078.32/297.08 , 0_1(130) -> 129 1078.32/297.08 , 0_1(135) -> 134 1078.32/297.08 , 0_1(141) -> 140 1078.32/297.08 , 0_1(150) -> 149 1078.32/297.08 , 0_1(159) -> 158 1078.32/297.08 , 0_1(160) -> 159 1078.32/297.08 , 0_1(161) -> 160 1078.32/297.08 , 0_1(164) -> 163 1078.32/297.08 , 0_1(168) -> 167 1078.32/297.08 , 0_1(172) -> 5 1078.32/297.08 , 0_1(178) -> 177 1078.32/297.08 , 0_1(185) -> 184 1078.32/297.08 , 0_1(189) -> 188 1078.32/297.08 , 0_1(232) -> 7 1078.32/297.08 , 0_1(242) -> 241 1078.32/297.08 , 1_0(1) -> 1 1078.32/297.08 , 1_1(1) -> 20 1078.32/297.08 , 1_1(2) -> 1 1078.32/297.08 , 1_1(2) -> 5 1078.32/297.08 , 1_1(2) -> 20 1078.32/297.08 , 1_1(2) -> 22 1078.32/297.08 , 1_1(2) -> 51 1078.32/297.08 , 1_1(2) -> 114 1078.32/297.08 , 1_1(2) -> 159 1078.32/297.08 , 1_1(4) -> 3 1078.32/297.08 , 1_1(5) -> 4 1078.32/297.08 , 1_1(8) -> 7 1078.32/297.08 , 1_1(9) -> 8 1078.32/297.08 , 1_1(20) -> 115 1078.32/297.08 , 1_1(23) -> 22 1078.32/297.08 , 1_1(32) -> 31 1078.32/297.08 , 1_1(33) -> 32 1078.32/297.08 , 1_1(36) -> 35 1078.32/297.08 , 1_1(51) -> 85 1078.32/297.08 , 1_1(57) -> 56 1078.32/297.08 , 1_1(58) -> 2 1078.32/297.08 , 1_1(63) -> 62 1078.32/297.08 , 1_1(76) -> 75 1078.32/297.08 , 1_1(80) -> 79 1078.32/297.08 , 1_1(83) -> 82 1078.32/297.08 , 1_1(93) -> 92 1078.32/297.08 , 1_1(97) -> 96 1078.32/297.08 , 1_1(121) -> 120 1078.32/297.08 , 1_1(123) -> 21 1078.32/297.08 , 1_1(129) -> 128 1078.32/297.08 , 1_1(151) -> 150 1078.32/297.08 , 1_1(165) -> 164 1078.32/297.08 , 1_1(172) -> 6 1078.32/297.08 , 1_1(174) -> 173 1078.32/297.08 , 1_1(175) -> 174 1078.32/297.08 , 1_1(176) -> 175 1078.32/297.08 , 1_1(184) -> 183 1078.32/297.08 , 1_1(186) -> 185 1078.32/297.08 , 1_1(191) -> 190 1078.32/297.08 , 1_1(241) -> 240 1078.32/297.08 , 2_0(1) -> 1 1078.32/297.08 , 2_1(1) -> 51 1078.32/297.08 , 2_1(2) -> 39 1078.32/297.08 , 2_1(5) -> 126 1078.32/297.08 , 2_1(12) -> 11 1078.32/297.08 , 2_1(14) -> 13 1078.32/297.08 , 2_1(23) -> 70 1078.32/297.08 , 2_1(24) -> 3 1078.32/297.08 , 2_1(28) -> 27 1078.32/297.08 , 2_1(29) -> 28 1078.32/297.08 , 2_1(31) -> 30 1078.32/297.08 , 2_1(37) -> 36 1078.32/297.08 , 2_1(39) -> 130 1078.32/297.08 , 2_1(40) -> 39 1078.32/297.08 , 2_1(47) -> 46 1078.32/297.08 , 2_1(48) -> 47 1078.32/297.08 , 2_1(51) -> 113 1078.32/297.08 , 2_1(54) -> 53 1078.32/297.08 , 2_1(58) -> 39 1078.32/297.08 , 2_1(62) -> 61 1078.32/297.08 , 2_1(65) -> 64 1078.32/297.08 , 2_1(66) -> 65 1078.32/297.08 , 2_1(71) -> 1 1078.32/297.08 , 2_1(71) -> 51 1078.32/297.08 , 2_1(71) -> 70 1078.32/297.08 , 2_1(71) -> 72 1078.32/297.08 , 2_1(71) -> 113 1078.32/297.08 , 2_1(73) -> 72 1078.32/297.08 , 2_1(74) -> 71 1078.32/297.08 , 2_1(75) -> 74 1078.32/297.08 , 2_1(88) -> 87 1078.32/297.08 , 2_1(89) -> 88 1078.32/297.08 , 2_1(95) -> 94 1078.32/297.08 , 2_1(102) -> 101 1078.32/297.08 , 2_1(114) -> 113 1078.32/297.08 , 2_1(115) -> 114 1078.32/297.08 , 2_1(117) -> 116 1078.32/297.08 , 2_1(118) -> 117 1078.32/297.08 , 2_1(120) -> 119 1078.32/297.08 , 2_1(122) -> 121 1078.32/297.08 , 2_1(124) -> 123 1078.32/297.08 , 2_1(125) -> 124 1078.32/297.08 , 2_1(126) -> 125 1078.32/297.08 , 2_1(136) -> 135 1078.32/297.08 , 2_1(137) -> 136 1078.32/297.08 , 2_1(140) -> 139 1078.32/297.08 , 2_1(143) -> 142 1078.32/297.08 , 2_1(145) -> 144 1078.32/297.08 , 2_1(147) -> 146 1078.32/297.08 , 2_1(149) -> 148 1078.32/297.08 , 2_1(153) -> 152 1078.32/297.08 , 2_1(155) -> 6 1078.32/297.08 , 2_1(157) -> 156 1078.32/297.08 , 2_1(183) -> 182 1078.32/297.08 , 2_1(190) -> 189 1078.32/297.08 , 2_1(192) -> 191 1078.32/297.08 , 2_1(193) -> 192 1078.32/297.08 , 2_1(235) -> 234 1078.32/297.08 , 3_0(1) -> 1 1078.32/297.08 , 3_1(4) -> 181 1078.32/297.08 , 3_1(5) -> 154 1078.32/297.08 , 3_1(15) -> 14 1078.32/297.08 , 3_1(16) -> 15 1078.32/297.08 , 3_1(17) -> 16 1078.32/297.08 , 3_1(20) -> 171 1078.32/297.08 , 3_1(23) -> 57 1078.32/297.08 , 3_1(38) -> 37 1078.32/297.08 , 3_1(40) -> 59 1078.32/297.08 , 3_1(41) -> 4 1078.32/297.08 , 3_1(44) -> 43 1078.32/297.08 , 3_1(45) -> 44 1078.32/297.08 , 3_1(46) -> 45 1078.32/297.08 , 3_1(49) -> 48 1078.32/297.08 , 3_1(50) -> 49 1078.32/297.08 , 3_1(53) -> 52 1078.32/297.08 , 3_1(59) -> 242 1078.32/297.08 , 3_1(64) -> 63 1078.32/297.08 , 3_1(68) -> 67 1078.32/297.08 , 3_1(72) -> 71 1078.32/297.08 , 3_1(82) -> 81 1078.32/297.08 , 3_1(84) -> 83 1078.32/297.08 , 3_1(94) -> 93 1078.32/297.08 , 3_1(98) -> 1 1078.32/297.08 , 3_1(98) -> 171 1078.32/297.08 , 3_1(108) -> 107 1078.32/297.08 , 3_1(111) -> 110 1078.32/297.08 , 3_1(113) -> 112 1078.32/297.08 , 3_1(116) -> 7 1078.32/297.08 , 3_1(119) -> 118 1078.32/297.08 , 3_1(122) -> 186 1078.32/297.08 , 3_1(128) -> 127 1078.32/297.08 , 3_1(153) -> 179 1078.32/297.08 , 3_1(154) -> 153 1078.32/297.08 , 3_1(156) -> 155 1078.32/297.08 , 3_1(162) -> 123 1078.32/297.08 , 3_1(166) -> 165 1078.32/297.08 , 3_1(169) -> 168 1078.32/297.08 , 3_1(177) -> 176 1078.32/297.08 , 3_1(179) -> 178 1078.32/297.08 , 3_1(180) -> 179 1078.32/297.08 , 3_1(181) -> 180 1078.32/297.08 , 3_1(182) -> 6 1078.32/297.08 , 3_1(201) -> 200 1078.32/297.08 , 3_1(203) -> 202 1078.32/297.08 , 3_1(240) -> 239 1078.32/297.08 , 4_0(1) -> 1 1078.32/297.08 , 4_1(1) -> 23 1078.32/297.08 , 4_1(2) -> 23 1078.32/297.08 , 4_1(3) -> 97 1078.32/297.08 , 4_1(5) -> 122 1078.32/297.08 , 4_1(7) -> 6 1078.32/297.08 , 4_1(23) -> 203 1078.32/297.08 , 4_1(25) -> 24 1078.32/297.08 , 4_1(30) -> 29 1078.32/297.08 , 4_1(34) -> 33 1078.32/297.08 , 4_1(42) -> 41 1078.32/297.08 , 4_1(50) -> 6 1078.32/297.08 , 4_1(55) -> 54 1078.32/297.08 , 4_1(59) -> 73 1078.32/297.08 , 4_1(71) -> 23 1078.32/297.08 , 4_1(73) -> 23 1078.32/297.08 , 4_1(77) -> 76 1078.32/297.08 , 4_1(92) -> 91 1078.32/297.08 , 4_1(96) -> 95 1078.32/297.08 , 4_1(99) -> 98 1078.32/297.08 , 4_1(103) -> 102 1078.32/297.08 , 4_1(107) -> 106 1078.32/297.08 , 4_1(110) -> 109 1078.32/297.08 , 4_1(126) -> 138 1078.32/297.08 , 4_1(138) -> 137 1078.32/297.08 , 4_1(144) -> 143 1078.32/297.08 , 4_1(167) -> 166 1078.32/297.08 , 4_1(171) -> 170 1078.32/297.08 , 4_1(188) -> 8 1078.32/297.08 , 5_0(1) -> 1 1078.32/297.08 , 5_1(1) -> 40 1078.32/297.08 , 5_1(5) -> 18 1078.32/297.08 , 5_1(6) -> 1 1078.32/297.08 , 5_1(6) -> 5 1078.32/297.08 , 5_1(6) -> 6 1078.32/297.08 , 5_1(6) -> 18 1078.32/297.08 , 5_1(6) -> 19 1078.32/297.08 , 5_1(6) -> 23 1078.32/297.08 , 5_1(6) -> 40 1078.32/297.08 , 5_1(6) -> 50 1078.32/297.08 , 5_1(6) -> 69 1078.32/297.08 , 5_1(6) -> 122 1078.32/297.08 , 5_1(6) -> 201 1078.32/297.08 , 5_1(11) -> 10 1078.32/297.08 , 5_1(19) -> 18 1078.32/297.08 , 5_1(22) -> 21 1078.32/297.08 , 5_1(23) -> 161 1078.32/297.08 , 5_1(26) -> 25 1078.32/297.08 , 5_1(27) -> 26 1078.32/297.08 , 5_1(39) -> 7 1078.32/297.08 , 5_1(43) -> 42 1078.32/297.08 , 5_1(51) -> 50 1078.32/297.08 , 5_1(52) -> 2 1078.32/297.08 , 5_1(56) -> 55 1078.32/297.08 , 5_1(59) -> 58 1078.32/297.08 , 5_1(70) -> 69 1078.32/297.08 , 5_1(71) -> 40 1078.32/297.08 , 5_1(78) -> 77 1078.32/297.08 , 5_1(85) -> 84 1078.32/297.08 , 5_1(87) -> 86 1078.32/297.08 , 5_1(91) -> 90 1078.32/297.08 , 5_1(104) -> 103 1078.32/297.08 , 5_1(109) -> 108 1078.32/297.08 , 5_1(131) -> 6 1078.32/297.08 , 5_1(132) -> 131 1078.32/297.08 , 5_1(133) -> 132 1078.32/297.08 , 5_1(134) -> 133 1078.32/297.08 , 5_1(139) -> 22 1078.32/297.08 , 5_1(142) -> 141 1078.32/297.08 , 5_1(146) -> 145 1078.32/297.08 , 5_1(148) -> 147 1078.32/297.08 , 5_1(152) -> 151 1078.32/297.08 , 5_1(158) -> 157 1078.32/297.08 , 5_1(163) -> 162 1078.32/297.08 , 5_1(170) -> 169 1078.32/297.08 , 5_1(173) -> 172 1078.32/297.08 , 5_1(200) -> 193 1078.32/297.08 , 5_1(202) -> 201 1078.32/297.08 , 5_1(234) -> 232 1078.32/297.08 , 5_1(238) -> 235 1078.32/297.08 , 5_1(239) -> 238 } 1078.32/297.08 1078.32/297.08 Hurray, we answered YES(?,O(n^1)) 1079.03/297.53 EOF