YES(?,O(n^1)) 1130.43/297.07 YES(?,O(n^1)) 1130.43/297.07 1130.43/297.07 We are left with following problem, upon which TcT provides the 1130.43/297.07 certificate YES(?,O(n^1)). 1130.43/297.07 1130.43/297.07 Strict Trs: 1130.43/297.07 { 1(1(2(0(4(5(x1)))))) -> 3(0(5(4(2(1(0(2(3(3(x1)))))))))) 1130.43/297.07 , 1(1(3(4(5(0(0(x1))))))) -> 1(3(1(5(3(4(1(4(5(3(x1)))))))))) 1130.43/297.07 , 1(2(0(x1))) -> 4(0(3(3(5(4(5(1(4(3(x1)))))))))) 1130.43/297.07 , 1(0(0(4(5(x1))))) -> 1(4(3(1(3(1(4(5(2(3(x1)))))))))) 1130.43/297.07 , 1(0(5(2(2(0(0(x1))))))) -> 1(5(4(4(3(4(5(4(5(2(x1)))))))))) 1130.43/297.07 , 1(4(3(1(5(0(5(x1))))))) -> 5(0(3(3(2(4(1(3(3(2(x1)))))))))) 1130.43/297.07 , 1(5(0(2(0(5(5(x1))))))) -> 2(5(2(5(4(2(0(0(5(5(x1)))))))))) 1130.43/297.07 , 2(1(1(0(1(2(x1)))))) -> 3(4(4(1(3(2(2(2(5(5(x1)))))))))) 1130.43/297.07 , 2(1(0(1(0(x1))))) -> 3(5(4(5(4(3(3(1(1(2(x1)))))))))) 1130.43/297.07 , 2(2(0(1(1(1(x1)))))) -> 2(3(4(1(5(2(2(2(5(4(x1)))))))))) 1130.43/297.07 , 2(0(1(5(2(0(5(x1))))))) -> 4(3(3(5(5(3(1(3(5(5(x1)))))))))) 1130.43/297.07 , 2(0(3(0(2(x1))))) -> 3(3(1(2(2(4(5(0(4(3(x1)))))))))) 1130.43/297.07 , 2(4(1(0(4(2(x1)))))) -> 1(5(1(3(2(3(4(4(4(0(x1)))))))))) 1130.43/297.07 , 2(4(2(1(1(1(x1)))))) -> 1(3(5(4(3(4(3(1(4(4(x1)))))))))) 1130.43/297.07 , 2(4(0(5(4(1(4(x1))))))) -> 3(4(5(5(1(5(3(5(1(4(x1)))))))))) 1130.43/297.07 , 0(2(1(1(1(1(0(x1))))))) -> 0(1(5(5(3(5(2(5(5(5(x1)))))))))) 1130.43/297.07 , 0(2(4(1(1(1(5(x1))))))) -> 4(4(3(4(3(2(3(0(2(2(x1)))))))))) 1130.43/297.07 , 0(4(2(0(0(4(1(x1))))))) -> 4(2(5(4(1(0(4(3(3(1(x1)))))))))) 1130.43/297.07 , 0(4(3(0(5(4(1(x1))))))) -> 0(3(1(5(3(1(2(5(4(1(x1)))))))))) 1130.43/297.07 , 0(3(5(2(4(0(x1)))))) -> 4(4(0(2(3(2(2(5(3(2(x1)))))))))) 1130.43/297.07 , 4(1(1(1(0(1(2(x1))))))) -> 3(3(2(3(3(0(1(5(5(2(x1)))))))))) 1130.43/297.07 , 4(1(1(2(0(2(x1)))))) -> 4(0(3(4(4(4(2(3(2(3(x1)))))))))) 1130.43/297.07 , 4(1(0(4(2(0(0(x1))))))) -> 4(2(2(3(1(0(0(3(4(0(x1)))))))))) 1130.43/297.07 , 4(1(0(4(2(0(3(x1))))))) -> 0(4(3(0(0(1(5(4(3(2(x1)))))))))) 1130.43/297.07 , 3(0(1(1(1(1(x1)))))) -> 3(2(2(4(4(5(2(4(5(1(x1)))))))))) 1130.43/297.07 , 3(0(1(0(0(2(x1)))))) -> 2(4(2(5(3(5(0(3(3(2(x1)))))))))) 1130.43/297.07 , 3(4(1(4(0(4(5(x1))))))) -> 3(2(2(1(3(4(3(3(0(3(x1)))))))))) 1130.43/297.07 , 3(4(2(0(2(x1))))) -> 3(5(3(0(3(3(2(5(3(2(x1)))))))))) } 1130.43/297.07 Obligation: 1130.43/297.07 derivational complexity 1130.43/297.07 Answer: 1130.43/297.07 YES(?,O(n^1)) 1130.43/297.07 1130.43/297.07 The problem is match-bounded by 2. The enriched problem is 1130.43/297.07 compatible with the following automaton. 1130.43/297.07 { 1_0(1) -> 1 1130.43/297.07 , 1_1(1) -> 132 1130.43/297.07 , 1_1(7) -> 6 1130.43/297.07 , 1_1(11) -> 1 1130.43/297.07 , 1_1(11) -> 41 1130.43/297.07 , 1_1(11) -> 132 1130.43/297.07 , 1_1(13) -> 12 1130.43/297.07 , 1_1(17) -> 16 1130.43/297.07 , 1_1(26) -> 25 1130.43/297.07 , 1_1(29) -> 28 1130.43/297.07 , 1_1(31) -> 30 1130.43/297.07 , 1_1(41) -> 71 1130.43/297.07 , 1_1(48) -> 47 1130.43/297.07 , 1_1(61) -> 60 1130.43/297.07 , 1_1(71) -> 70 1130.43/297.07 , 1_1(74) -> 73 1130.43/297.07 , 1_1(77) -> 136 1130.43/297.07 , 1_1(79) -> 110 1130.43/297.07 , 1_1(85) -> 84 1130.43/297.07 , 1_1(87) -> 86 1130.43/297.07 , 1_1(92) -> 34 1130.43/297.07 , 1_1(104) -> 103 1130.43/297.07 , 1_1(107) -> 106 1130.43/297.07 , 1_1(112) -> 111 1130.43/297.07 , 1_1(128) -> 127 1130.43/297.07 , 1_1(134) -> 133 1130.43/297.07 , 1_1(137) -> 136 1130.43/297.07 , 1_1(149) -> 148 1130.43/297.07 , 1_1(156) -> 155 1130.43/297.07 , 1_1(163) -> 162 1130.43/297.07 , 1_1(177) -> 166 1130.43/297.07 , 1_2(192) -> 191 1130.43/297.07 , 2_0(1) -> 1 1130.43/297.07 , 2_1(1) -> 41 1130.43/297.07 , 2_1(2) -> 41 1130.43/297.07 , 2_1(6) -> 5 1130.43/297.07 , 2_1(9) -> 8 1130.43/297.07 , 2_1(10) -> 33 1130.43/297.07 , 2_1(20) -> 41 1130.43/297.07 , 2_1(34) -> 41 1130.43/297.07 , 2_1(39) -> 169 1130.43/297.07 , 2_1(41) -> 124 1130.43/297.07 , 2_1(42) -> 41 1130.43/297.07 , 2_1(46) -> 45 1130.43/297.07 , 2_1(50) -> 1 1130.43/297.07 , 2_1(50) -> 10 1130.43/297.07 , 2_1(50) -> 41 1130.43/297.07 , 2_1(50) -> 124 1130.43/297.07 , 2_1(50) -> 132 1130.43/297.07 , 2_1(52) -> 51 1130.43/297.07 , 2_1(55) -> 54 1130.43/297.07 , 2_1(57) -> 64 1130.43/297.07 , 2_1(63) -> 62 1130.43/297.07 , 2_1(64) -> 63 1130.43/297.07 , 2_1(76) -> 75 1130.43/297.07 , 2_1(77) -> 76 1130.43/297.07 , 2_1(78) -> 77 1130.43/297.07 , 2_1(88) -> 87 1130.43/297.07 , 2_1(89) -> 88 1130.43/297.07 , 2_1(94) -> 93 1130.43/297.07 , 2_1(111) -> 41 1130.43/297.07 , 2_1(117) -> 116 1130.43/297.07 , 2_1(122) -> 121 1130.43/297.07 , 2_1(125) -> 19 1130.43/297.07 , 2_1(133) -> 41 1130.43/297.07 , 2_1(138) -> 137 1130.43/297.07 , 2_1(141) -> 140 1130.43/297.07 , 2_1(143) -> 142 1130.43/297.07 , 2_1(144) -> 143 1130.43/297.07 , 2_1(145) -> 86 1130.43/297.07 , 2_1(153) -> 152 1130.43/297.07 , 2_1(154) -> 125 1130.43/297.07 , 2_1(165) -> 2 1130.43/297.07 , 2_1(166) -> 165 1130.43/297.07 , 2_1(170) -> 169 1130.43/297.07 , 2_1(173) -> 172 1130.43/297.07 , 0_0(1) -> 1 1130.43/297.07 , 0_1(1) -> 98 1130.43/297.07 , 0_1(3) -> 2 1130.43/297.07 , 0_1(8) -> 7 1130.43/297.07 , 0_1(10) -> 181 1130.43/297.07 , 0_1(20) -> 19 1130.43/297.07 , 0_1(26) -> 91 1130.43/297.07 , 0_1(43) -> 42 1130.43/297.07 , 0_1(48) -> 176 1130.43/297.07 , 0_1(50) -> 98 1130.43/297.07 , 0_1(56) -> 55 1130.43/297.07 , 0_1(57) -> 56 1130.43/297.07 , 0_1(58) -> 56 1130.43/297.07 , 0_1(111) -> 1 1130.43/297.07 , 0_1(111) -> 79 1130.43/297.07 , 0_1(111) -> 91 1130.43/297.07 , 0_1(111) -> 98 1130.43/297.07 , 0_1(111) -> 139 1130.43/297.07 , 0_1(124) -> 123 1130.43/297.07 , 0_1(125) -> 98 1130.43/297.07 , 0_1(129) -> 128 1130.43/297.07 , 0_1(140) -> 118 1130.43/297.07 , 0_1(148) -> 147 1130.43/297.07 , 0_1(157) -> 156 1130.43/297.07 , 0_1(158) -> 157 1130.43/297.07 , 0_1(161) -> 160 1130.43/297.07 , 0_1(162) -> 161 1130.43/297.07 , 0_1(183) -> 182 1130.43/297.07 , 0_2(186) -> 185 1130.43/297.07 , 4_0(1) -> 1 1130.43/297.07 , 4_1(1) -> 79 1130.43/297.07 , 4_1(5) -> 4 1130.43/297.07 , 4_1(10) -> 26 1130.43/297.07 , 4_1(11) -> 79 1130.43/297.07 , 4_1(16) -> 15 1130.43/297.07 , 4_1(18) -> 17 1130.43/297.07 , 4_1(19) -> 1 1130.43/297.07 , 4_1(19) -> 41 1130.43/297.07 , 4_1(19) -> 71 1130.43/297.07 , 4_1(19) -> 79 1130.43/297.07 , 4_1(19) -> 98 1130.43/297.07 , 4_1(19) -> 132 1130.43/297.07 , 4_1(19) -> 139 1130.43/297.07 , 4_1(19) -> 181 1130.43/297.07 , 4_1(24) -> 23 1130.43/297.07 , 4_1(27) -> 11 1130.43/297.07 , 4_1(32) -> 31 1130.43/297.07 , 4_1(35) -> 34 1130.43/297.07 , 4_1(36) -> 35 1130.43/297.07 , 4_1(38) -> 37 1130.43/297.07 , 4_1(40) -> 39 1130.43/297.07 , 4_1(47) -> 46 1130.43/297.07 , 4_1(48) -> 129 1130.43/297.07 , 4_1(49) -> 164 1130.43/297.07 , 4_1(54) -> 53 1130.43/297.07 , 4_1(59) -> 2 1130.43/297.07 , 4_1(60) -> 59 1130.43/297.07 , 4_1(66) -> 65 1130.43/297.07 , 4_1(68) -> 67 1130.43/297.07 , 4_1(73) -> 72 1130.43/297.07 , 4_1(79) -> 104 1130.43/297.07 , 4_1(90) -> 89 1130.43/297.07 , 4_1(96) -> 95 1130.43/297.07 , 4_1(97) -> 96 1130.43/297.07 , 4_1(98) -> 97 1130.43/297.07 , 4_1(100) -> 99 1130.43/297.07 , 4_1(102) -> 101 1130.43/297.07 , 4_1(118) -> 19 1130.43/297.07 , 4_1(120) -> 119 1130.43/297.07 , 4_1(127) -> 126 1130.43/297.07 , 4_1(130) -> 129 1130.43/297.07 , 4_1(132) -> 139 1130.43/297.07 , 4_1(150) -> 21 1130.43/297.07 , 4_1(151) -> 150 1130.43/297.07 , 4_1(152) -> 151 1130.43/297.07 , 4_1(159) -> 111 1130.43/297.07 , 4_1(167) -> 166 1130.43/297.07 , 4_1(168) -> 167 1130.43/297.07 , 4_1(171) -> 170 1130.43/297.07 , 4_1(172) -> 50 1130.43/297.07 , 4_1(179) -> 178 1130.43/297.07 , 4_2(185) -> 71 1130.43/297.07 , 4_2(190) -> 189 1130.43/297.07 , 4_2(193) -> 192 1130.43/297.07 , 3_0(1) -> 1 1130.43/297.07 , 3_1(1) -> 10 1130.43/297.07 , 3_1(2) -> 1 1130.43/297.07 , 3_1(2) -> 10 1130.43/297.07 , 3_1(2) -> 41 1130.43/297.07 , 3_1(2) -> 70 1130.43/297.07 , 3_1(2) -> 79 1130.43/297.07 , 3_1(2) -> 132 1130.43/297.07 , 3_1(2) -> 139 1130.43/297.07 , 3_1(10) -> 9 1130.43/297.07 , 3_1(12) -> 11 1130.43/297.07 , 3_1(15) -> 14 1130.43/297.07 , 3_1(21) -> 20 1130.43/297.07 , 3_1(22) -> 21 1130.43/297.07 , 3_1(28) -> 27 1130.43/297.07 , 3_1(30) -> 29 1130.43/297.07 , 3_1(33) -> 153 1130.43/297.07 , 3_1(37) -> 36 1130.43/297.07 , 3_1(41) -> 49 1130.43/297.07 , 3_1(42) -> 10 1130.43/297.07 , 3_1(44) -> 43 1130.43/297.07 , 3_1(45) -> 44 1130.43/297.07 , 3_1(49) -> 48 1130.43/297.07 , 3_1(50) -> 10 1130.43/297.07 , 3_1(57) -> 85 1130.43/297.07 , 3_1(58) -> 85 1130.43/297.07 , 3_1(62) -> 61 1130.43/297.07 , 3_1(69) -> 68 1130.43/297.07 , 3_1(70) -> 69 1130.43/297.08 , 3_1(72) -> 50 1130.43/297.08 , 3_1(80) -> 19 1130.43/297.08 , 3_1(81) -> 80 1130.43/297.08 , 3_1(84) -> 83 1130.43/297.08 , 3_1(86) -> 2 1130.43/297.08 , 3_1(93) -> 92 1130.43/297.08 , 3_1(95) -> 94 1130.43/297.08 , 3_1(97) -> 158 1130.43/297.08 , 3_1(101) -> 100 1130.43/297.08 , 3_1(103) -> 102 1130.43/297.08 , 3_1(109) -> 108 1130.43/297.08 , 3_1(111) -> 10 1130.43/297.08 , 3_1(115) -> 114 1130.43/297.08 , 3_1(119) -> 118 1130.43/297.08 , 3_1(121) -> 120 1130.43/297.08 , 3_1(123) -> 122 1130.43/297.08 , 3_1(131) -> 130 1130.43/297.08 , 3_1(132) -> 131 1130.43/297.08 , 3_1(133) -> 111 1130.43/297.08 , 3_1(136) -> 135 1130.43/297.08 , 3_1(142) -> 141 1130.43/297.08 , 3_1(143) -> 184 1130.43/297.08 , 3_1(146) -> 145 1130.43/297.08 , 3_1(147) -> 146 1130.43/297.08 , 3_1(155) -> 154 1130.43/297.08 , 3_1(160) -> 159 1130.43/297.08 , 3_1(175) -> 174 1130.43/297.08 , 3_1(178) -> 177 1130.43/297.08 , 3_1(180) -> 179 1130.43/297.08 , 3_1(181) -> 180 1130.43/297.08 , 3_1(182) -> 65 1130.43/297.08 , 3_1(184) -> 183 1130.43/297.08 , 3_2(3) -> 193 1130.43/297.08 , 3_2(43) -> 193 1130.43/297.08 , 3_2(111) -> 193 1130.43/297.08 , 3_2(187) -> 186 1130.43/297.08 , 3_2(188) -> 187 1130.43/297.08 , 5_0(1) -> 1 1130.43/297.08 , 5_1(1) -> 58 1130.43/297.08 , 5_1(4) -> 3 1130.43/297.08 , 5_1(10) -> 18 1130.43/297.08 , 5_1(14) -> 13 1130.43/297.08 , 5_1(23) -> 22 1130.43/297.08 , 5_1(25) -> 24 1130.43/297.08 , 5_1(33) -> 32 1130.43/297.08 , 5_1(34) -> 11 1130.43/297.08 , 5_1(39) -> 38 1130.43/297.08 , 5_1(40) -> 149 1130.43/297.08 , 5_1(41) -> 40 1130.43/297.08 , 5_1(42) -> 1 1130.43/297.08 , 5_1(42) -> 25 1130.43/297.08 , 5_1(42) -> 110 1130.43/297.08 , 5_1(42) -> 132 1130.43/297.08 , 5_1(49) -> 144 1130.43/297.08 , 5_1(50) -> 58 1130.43/297.08 , 5_1(51) -> 50 1130.43/297.08 , 5_1(53) -> 52 1130.43/297.08 , 5_1(57) -> 117 1130.43/297.08 , 5_1(58) -> 57 1130.43/297.08 , 5_1(65) -> 2 1130.43/297.08 , 5_1(67) -> 66 1130.43/297.08 , 5_1(71) -> 109 1130.43/297.08 , 5_1(75) -> 74 1130.43/297.08 , 5_1(79) -> 78 1130.43/297.08 , 5_1(82) -> 81 1130.43/297.08 , 5_1(83) -> 82 1130.43/297.08 , 5_1(85) -> 107 1130.43/297.08 , 5_1(91) -> 90 1130.43/297.08 , 5_1(99) -> 12 1130.43/297.08 , 5_1(105) -> 59 1130.43/297.08 , 5_1(106) -> 105 1130.43/297.08 , 5_1(108) -> 107 1130.43/297.08 , 5_1(110) -> 109 1130.43/297.08 , 5_1(111) -> 58 1130.43/297.08 , 5_1(113) -> 112 1130.43/297.08 , 5_1(114) -> 113 1130.43/297.08 , 5_1(116) -> 115 1130.43/297.08 , 5_1(126) -> 125 1130.43/297.08 , 5_1(132) -> 171 1130.43/297.08 , 5_1(135) -> 134 1130.43/297.08 , 5_1(139) -> 138 1130.43/297.08 , 5_1(164) -> 163 1130.43/297.08 , 5_1(169) -> 168 1130.43/297.08 , 5_1(174) -> 173 1130.43/297.08 , 5_1(176) -> 175 1130.43/297.08 , 5_2(189) -> 188 1130.43/297.08 , 5_2(191) -> 190 } 1130.43/297.08 1130.43/297.08 Hurray, we answered YES(?,O(n^1)) 1131.53/297.97 EOF