YES(?,O(n^1)) 1107.74/297.17 YES(?,O(n^1)) 1107.74/297.17 1107.74/297.17 We are left with following problem, upon which TcT provides the 1107.74/297.17 certificate YES(?,O(n^1)). 1107.74/297.17 1107.74/297.17 Strict Trs: 1107.74/297.17 { 0(0(1(2(1(x1))))) -> 0(2(3(4(x1)))) 1107.74/297.17 , 0(0(4(2(0(3(4(5(2(0(0(0(0(0(x1)))))))))))))) -> 1107.74/297.17 2(4(1(2(4(4(3(2(5(2(3(5(5(0(x1)))))))))))))) 1107.74/297.17 , 0(1(5(2(3(2(x1)))))) -> 0(5(3(1(3(2(x1)))))) 1107.74/297.17 , 0(3(5(0(0(0(4(1(2(1(3(5(5(5(0(3(5(0(3(4(x1)))))))))))))))))))) -> 1107.74/297.17 0(3(5(3(3(2(4(5(5(4(0(2(3(0(2(5(2(4(3(4(x1)))))))))))))))))))) 1107.74/297.17 , 0(4(2(4(3(5(4(2(5(1(4(3(2(5(3(5(4(2(3(0(x1)))))))))))))))))))) -> 1107.74/297.17 5(2(3(3(4(1(5(3(2(2(3(5(1(1(1(2(1(2(2(1(x1)))))))))))))))))))) 1107.74/297.17 , 0(4(5(4(0(3(1(4(4(0(3(4(2(5(4(1(0(0(5(1(2(x1))))))))))))))))))))) 1107.74/297.17 -> 1107.74/297.17 3(5(4(4(4(5(5(0(2(4(4(1(5(2(1(2(5(2(5(2(2(x1))))))))))))))))))))) 1107.74/297.17 , 1(3(0(4(1(4(x1)))))) -> 1(2(0(1(2(x1))))) 1107.74/297.17 , 1(3(2(5(2(3(1(x1))))))) -> 1(0(5(1(3(4(x1)))))) 1107.74/297.17 , 1(4(5(3(2(x1))))) -> 1(5(0(5(x1)))) 1107.74/297.17 , 2(2(2(3(5(5(2(1(4(1(2(2(1(5(2(1(1(0(2(2(x1)))))))))))))))))))) -> 1107.74/297.17 2(3(2(3(2(5(4(2(0(3(2(0(2(4(5(2(4(4(x1)))))))))))))))))) 1107.74/297.17 , 2(4(0(1(1(5(0(2(0(5(2(3(5(4(0(2(x1)))))))))))))))) -> 1107.74/297.17 5(0(2(0(2(0(2(5(4(0(0(5(5(2(0(x1))))))))))))))) 1107.74/297.17 , 2(4(2(0(3(4(0(3(3(1(x1)))))))))) -> 3(5(2(0(5(3(3(2(2(x1))))))))) 1107.74/297.17 , 2(4(2(3(0(3(4(5(2(x1))))))))) -> 2(4(0(0(0(0(0(5(2(x1))))))))) 1107.74/297.17 , 3(0(2(3(0(x1))))) -> 5(0(2(1(1(x1))))) 1107.74/297.17 , 3(0(4(5(3(5(0(3(5(2(3(1(5(4(2(1(x1)))))))))))))))) -> 1107.74/297.17 2(5(3(3(2(3(0(2(5(4(0(2(4(5(2(1(x1)))))))))))))))) 1107.74/297.17 , 3(1(5(3(2(4(2(2(4(3(4(2(3(4(5(1(4(4(5(x1))))))))))))))))))) -> 1107.74/297.17 3(4(3(2(2(4(1(2(1(3(3(0(0(3(3(4(2(4(x1)))))))))))))))))) 1107.74/297.17 , 3(2(1(2(5(4(3(1(x1)))))))) -> 2(5(0(4(4(3(5(x1))))))) 1107.74/297.17 , 3(2(3(2(2(0(4(5(0(3(5(3(4(4(5(x1))))))))))))))) -> 1107.74/297.17 5(2(3(5(2(1(4(4(1(5(5(3(0(1(4(2(x1)))))))))))))))) 1107.74/297.17 , 3(3(2(0(2(2(5(3(2(3(3(1(3(5(5(1(3(0(2(1(x1)))))))))))))))))))) -> 1107.74/297.17 3(0(5(1(1(3(2(1(2(5(5(4(3(4(3(0(5(5(3(4(x1)))))))))))))))))))) 1107.74/297.17 , 3(4(2(4(0(2(1(0(2(x1))))))))) -> 3(1(0(5(0(5(0(1(x1)))))))) 1107.74/297.17 , 3(5(3(2(4(3(3(1(0(0(5(4(0(2(1(1(x1)))))))))))))))) -> 1107.74/297.17 3(5(3(3(3(2(5(4(1(5(5(1(3(5(1(x1))))))))))))))) 1107.74/297.17 , 3(5(4(4(1(1(x1)))))) -> 0(2(3(0(4(x1))))) 1107.74/297.17 , 4(4(1(5(4(1(1(2(1(5(1(1(4(4(2(2(4(2(4(5(3(x1))))))))))))))))))))) 1107.74/297.17 -> 0(3(2(3(2(0(3(2(1(1(4(5(2(2(0(1(1(2(3(x1))))))))))))))))))) 1107.74/297.17 , 4(5(3(3(0(5(2(0(3(5(0(3(3(2(3(1(3(3(4(x1))))))))))))))))))) -> 1107.74/297.17 4(0(4(1(5(1(4(2(4(2(5(4(1(2(5(2(1(2(5(2(2(x1))))))))))))))))))))) 1107.74/297.17 , 4(5(5(4(5(5(x1)))))) -> 4(3(1(5(1(5(x1)))))) } 1107.74/297.17 Obligation: 1107.74/297.17 derivational complexity 1107.74/297.17 Answer: 1107.74/297.17 YES(?,O(n^1)) 1107.74/297.17 1107.74/297.17 The problem is match-bounded by 2. The enriched problem is 1107.74/297.17 compatible with the following automaton. 1107.74/297.17 { 0_0(1) -> 1 1107.74/297.17 , 0_1(1) -> 17 1107.74/297.17 , 0_1(2) -> 1 1107.74/297.17 , 0_1(2) -> 4 1107.74/297.17 , 0_1(2) -> 17 1107.74/297.17 , 0_1(2) -> 20 1107.74/297.17 , 0_1(2) -> 96 1107.74/297.17 , 0_1(2) -> 115 1107.74/297.17 , 0_1(2) -> 146 1107.74/297.17 , 0_1(2) -> 178 1107.74/297.17 , 0_1(3) -> 17 1107.74/297.17 , 0_1(4) -> 4 1107.74/297.17 , 0_1(5) -> 17 1107.74/297.17 , 0_1(16) -> 81 1107.74/297.17 , 0_1(17) -> 115 1107.74/297.17 , 0_1(19) -> 178 1107.74/297.17 , 0_1(31) -> 30 1107.74/297.17 , 0_1(34) -> 33 1107.74/297.17 , 0_1(56) -> 178 1107.74/297.17 , 0_1(64) -> 63 1107.74/297.17 , 0_1(74) -> 116 1107.74/297.17 , 0_1(78) -> 77 1107.74/297.17 , 0_1(79) -> 76 1107.74/297.17 , 0_1(80) -> 178 1107.74/297.17 , 0_1(81) -> 115 1107.74/297.17 , 0_1(89) -> 88 1107.74/297.17 , 0_1(92) -> 91 1107.74/297.17 , 0_1(97) -> 38 1107.74/297.17 , 0_1(99) -> 98 1107.74/297.17 , 0_1(101) -> 100 1107.74/297.17 , 0_1(105) -> 104 1107.74/297.17 , 0_1(106) -> 105 1107.74/297.17 , 0_1(110) -> 109 1107.74/297.17 , 0_1(113) -> 6 1107.74/297.17 , 0_1(114) -> 113 1107.74/297.17 , 0_1(115) -> 114 1107.74/297.17 , 0_1(116) -> 115 1107.74/297.17 , 0_1(122) -> 121 1107.74/297.17 , 0_1(126) -> 125 1107.74/297.17 , 0_1(129) -> 17 1107.74/297.17 , 0_1(139) -> 138 1107.74/297.17 , 0_1(140) -> 139 1107.74/297.17 , 0_1(144) -> 117 1107.74/297.17 , 0_1(156) -> 155 1107.74/297.17 , 0_1(158) -> 57 1107.74/297.17 , 0_1(172) -> 171 1107.74/297.17 , 0_1(175) -> 174 1107.74/297.17 , 0_1(177) -> 176 1107.74/297.17 , 0_1(193) -> 192 1107.74/297.17 , 0_1(202) -> 201 1107.74/297.17 , 0_1(206) -> 205 1107.74/297.17 , 0_2(243) -> 242 1107.74/297.17 , 1_0(1) -> 1 1107.74/297.17 , 1_1(1) -> 56 1107.74/297.17 , 1_1(2) -> 56 1107.74/297.17 , 1_1(3) -> 80 1107.74/297.17 , 1_1(4) -> 56 1107.74/297.17 , 1_1(5) -> 56 1107.74/297.17 , 1_1(7) -> 6 1107.74/297.17 , 1_1(16) -> 223 1107.74/297.17 , 1_1(20) -> 19 1107.74/297.17 , 1_1(21) -> 78 1107.74/297.17 , 1_1(43) -> 42 1107.74/297.17 , 1_1(50) -> 49 1107.74/297.17 , 1_1(51) -> 50 1107.74/297.17 , 1_1(52) -> 51 1107.74/297.17 , 1_1(54) -> 53 1107.74/297.17 , 1_1(56) -> 98 1107.74/297.17 , 1_1(68) -> 67 1107.74/297.17 , 1_1(71) -> 70 1107.74/297.17 , 1_1(73) -> 220 1107.74/297.17 , 1_1(76) -> 1 1107.74/297.17 , 1_1(76) -> 19 1107.74/297.17 , 1_1(76) -> 56 1107.74/297.17 , 1_1(76) -> 80 1107.74/297.17 , 1_1(76) -> 245 1107.74/297.17 , 1_1(129) -> 19 1107.74/297.17 , 1_1(134) -> 133 1107.74/297.17 , 1_1(136) -> 135 1107.74/297.17 , 1_1(149) -> 148 1107.74/297.17 , 1_1(152) -> 151 1107.74/297.17 , 1_1(157) -> 156 1107.74/297.17 , 1_1(158) -> 56 1107.74/297.17 , 1_1(160) -> 159 1107.74/297.17 , 1_1(161) -> 160 1107.74/297.17 , 1_1(164) -> 163 1107.74/297.17 , 1_1(174) -> 57 1107.74/297.17 , 1_1(185) -> 184 1107.74/297.17 , 1_1(188) -> 187 1107.74/297.17 , 1_1(189) -> 221 1107.74/297.17 , 1_1(196) -> 195 1107.74/297.17 , 1_1(197) -> 196 1107.74/297.17 , 1_1(203) -> 202 1107.74/297.17 , 1_1(204) -> 203 1107.74/297.17 , 1_1(208) -> 207 1107.74/297.17 , 1_1(210) -> 209 1107.74/297.17 , 1_1(217) -> 216 1107.74/297.17 , 1_1(222) -> 221 1107.74/297.17 , 1_2(2) -> 245 1107.74/297.17 , 1_2(4) -> 245 1107.74/297.17 , 1_2(158) -> 245 1107.74/297.17 , 1_2(245) -> 244 1107.74/297.17 , 2_0(1) -> 1 1107.74/297.17 , 2_1(1) -> 21 1107.74/297.17 , 2_1(3) -> 2 1107.74/297.17 , 2_1(4) -> 143 1107.74/297.17 , 2_1(5) -> 1 1107.74/297.17 , 2_1(5) -> 3 1107.74/297.17 , 2_1(5) -> 4 1107.74/297.17 , 2_1(5) -> 17 1107.74/297.17 , 2_1(5) -> 20 1107.74/297.17 , 2_1(5) -> 21 1107.74/297.17 , 2_1(5) -> 75 1107.74/297.17 , 2_1(5) -> 115 1107.74/297.17 , 2_1(5) -> 143 1107.74/297.17 , 2_1(8) -> 7 1107.74/297.17 , 2_1(12) -> 11 1107.74/297.17 , 2_1(14) -> 13 1107.74/297.17 , 2_1(16) -> 73 1107.74/297.17 , 2_1(17) -> 108 1107.74/297.17 , 2_1(20) -> 204 1107.74/297.17 , 2_1(21) -> 75 1107.74/297.17 , 2_1(26) -> 25 1107.74/297.17 , 2_1(32) -> 31 1107.74/297.17 , 2_1(35) -> 34 1107.74/297.17 , 2_1(37) -> 36 1107.74/297.17 , 2_1(38) -> 21 1107.74/297.17 , 2_1(39) -> 38 1107.74/297.17 , 2_1(46) -> 45 1107.74/297.17 , 2_1(47) -> 46 1107.74/297.17 , 2_1(53) -> 52 1107.74/297.17 , 2_1(55) -> 54 1107.74/297.17 , 2_1(56) -> 55 1107.74/297.17 , 2_1(65) -> 64 1107.74/297.17 , 2_1(70) -> 69 1107.74/297.17 , 2_1(72) -> 71 1107.74/297.17 , 2_1(74) -> 73 1107.74/297.17 , 2_1(76) -> 5 1107.74/297.17 , 2_1(77) -> 76 1107.74/297.17 , 2_1(83) -> 82 1107.74/297.17 , 2_1(85) -> 84 1107.74/297.17 , 2_1(88) -> 87 1107.74/297.17 , 2_1(91) -> 90 1107.74/297.17 , 2_1(93) -> 92 1107.74/297.17 , 2_1(96) -> 95 1107.74/297.17 , 2_1(98) -> 97 1107.74/297.17 , 2_1(100) -> 99 1107.74/297.17 , 2_1(102) -> 101 1107.74/297.17 , 2_1(109) -> 58 1107.74/297.17 , 2_1(120) -> 119 1107.74/297.17 , 2_1(123) -> 122 1107.74/297.17 , 2_1(127) -> 126 1107.74/297.17 , 2_1(129) -> 1 1107.74/297.17 , 2_1(131) -> 130 1107.74/297.17 , 2_1(132) -> 131 1107.74/297.17 , 2_1(135) -> 134 1107.74/297.17 , 2_1(148) -> 147 1107.74/297.17 , 2_1(163) -> 162 1107.74/297.17 , 2_1(165) -> 164 1107.74/297.17 , 2_1(174) -> 5 1107.74/297.17 , 2_1(182) -> 181 1107.74/297.17 , 2_1(190) -> 22 1107.74/297.17 , 2_1(192) -> 191 1107.74/297.17 , 2_1(195) -> 194 1107.74/297.17 , 2_1(200) -> 199 1107.74/297.17 , 2_1(201) -> 200 1107.74/297.17 , 2_1(205) -> 21 1107.74/297.17 , 2_1(212) -> 211 1107.74/297.17 , 2_1(214) -> 213 1107.74/297.17 , 2_1(218) -> 217 1107.74/297.17 , 2_1(220) -> 219 1107.74/297.17 , 2_2(244) -> 243 1107.74/297.17 , 3_0(1) -> 1 1107.74/297.17 , 3_1(1) -> 20 1107.74/297.17 , 3_1(4) -> 3 1107.74/297.17 , 3_1(11) -> 10 1107.74/297.17 , 3_1(15) -> 14 1107.74/297.17 , 3_1(16) -> 146 1107.74/297.17 , 3_1(19) -> 18 1107.74/297.17 , 3_1(21) -> 20 1107.74/297.17 , 3_1(22) -> 2 1107.74/297.17 , 3_1(24) -> 23 1107.74/297.17 , 3_1(25) -> 24 1107.74/297.17 , 3_1(33) -> 32 1107.74/297.17 , 3_1(40) -> 39 1107.74/297.17 , 3_1(41) -> 40 1107.74/297.17 , 3_1(45) -> 44 1107.74/297.17 , 3_1(48) -> 47 1107.74/297.17 , 3_1(56) -> 18 1107.74/297.17 , 3_1(57) -> 1 1107.74/297.17 , 3_1(57) -> 3 1107.74/297.17 , 3_1(57) -> 4 1107.74/297.17 , 3_1(57) -> 17 1107.74/297.17 , 3_1(57) -> 18 1107.74/297.17 , 3_1(57) -> 20 1107.74/297.17 , 3_1(57) -> 21 1107.74/297.17 , 3_1(57) -> 141 1107.74/297.17 , 3_1(57) -> 143 1107.74/297.17 , 3_1(57) -> 146 1107.74/297.17 , 3_1(75) -> 112 1107.74/297.17 , 3_1(82) -> 5 1107.74/297.17 , 3_1(84) -> 83 1107.74/297.17 , 3_1(90) -> 89 1107.74/297.17 , 3_1(112) -> 111 1107.74/297.17 , 3_1(118) -> 117 1107.74/297.17 , 3_1(119) -> 118 1107.74/297.17 , 3_1(121) -> 120 1107.74/297.17 , 3_1(130) -> 129 1107.74/297.17 , 3_1(137) -> 136 1107.74/297.17 , 3_1(138) -> 137 1107.74/297.17 , 3_1(141) -> 140 1107.74/297.17 , 3_1(142) -> 141 1107.74/297.17 , 3_1(155) -> 154 1107.74/297.17 , 3_1(162) -> 161 1107.74/297.17 , 3_1(169) -> 168 1107.74/297.17 , 3_1(171) -> 170 1107.74/297.17 , 3_1(179) -> 58 1107.74/297.17 , 3_1(180) -> 179 1107.74/297.17 , 3_1(181) -> 180 1107.74/297.17 , 3_1(189) -> 188 1107.74/297.17 , 3_1(191) -> 190 1107.74/297.17 , 3_1(194) -> 193 1107.74/297.17 , 3_1(221) -> 205 1107.74/297.17 , 4_0(1) -> 1 1107.74/297.17 , 4_1(1) -> 4 1107.74/297.17 , 4_1(3) -> 37 1107.74/297.17 , 4_1(4) -> 96 1107.74/297.17 , 4_1(5) -> 4 1107.74/297.17 , 4_1(6) -> 5 1107.74/297.17 , 4_1(9) -> 8 1107.74/297.17 , 4_1(10) -> 9 1107.74/297.17 , 4_1(21) -> 157 1107.74/297.17 , 4_1(27) -> 26 1107.74/297.17 , 4_1(30) -> 29 1107.74/297.17 , 4_1(38) -> 4 1107.74/297.17 , 4_1(42) -> 41 1107.74/297.17 , 4_1(57) -> 96 1107.74/297.17 , 4_1(59) -> 58 1107.74/297.17 , 4_1(60) -> 59 1107.74/297.17 , 4_1(61) -> 60 1107.74/297.17 , 4_1(66) -> 65 1107.74/297.17 , 4_1(67) -> 66 1107.74/297.17 , 4_1(76) -> 4 1107.74/297.17 , 4_1(87) -> 86 1107.74/297.17 , 4_1(94) -> 93 1107.74/297.17 , 4_1(104) -> 103 1107.74/297.17 , 4_1(125) -> 124 1107.74/297.17 , 4_1(128) -> 127 1107.74/297.17 , 4_1(129) -> 57 1107.74/297.17 , 4_1(133) -> 132 1107.74/297.17 , 4_1(143) -> 142 1107.74/297.17 , 4_1(145) -> 144 1107.74/297.17 , 4_1(146) -> 145 1107.74/297.17 , 4_1(150) -> 149 1107.74/297.17 , 4_1(151) -> 150 1107.74/297.17 , 4_1(168) -> 167 1107.74/297.17 , 4_1(170) -> 169 1107.74/297.17 , 4_1(174) -> 4 1107.74/297.17 , 4_1(184) -> 183 1107.74/297.17 , 4_1(198) -> 197 1107.74/297.17 , 4_1(205) -> 1 1107.74/297.17 , 4_1(205) -> 4 1107.74/297.17 , 4_1(207) -> 206 1107.74/297.17 , 4_1(211) -> 210 1107.74/297.17 , 4_1(213) -> 212 1107.74/297.17 , 4_1(216) -> 215 1107.74/297.17 , 5_0(1) -> 1 1107.74/297.17 , 5_1(1) -> 16 1107.74/297.17 , 5_1(3) -> 173 1107.74/297.17 , 5_1(5) -> 16 1107.74/297.17 , 5_1(13) -> 12 1107.74/297.17 , 5_1(16) -> 15 1107.74/297.17 , 5_1(17) -> 16 1107.74/297.17 , 5_1(18) -> 2 1107.74/297.17 , 5_1(21) -> 74 1107.74/297.17 , 5_1(23) -> 22 1107.74/297.17 , 5_1(28) -> 27 1107.74/297.17 , 5_1(29) -> 28 1107.74/297.17 , 5_1(36) -> 35 1107.74/297.17 , 5_1(38) -> 1 1107.74/297.17 , 5_1(38) -> 4 1107.74/297.17 , 5_1(38) -> 17 1107.74/297.17 , 5_1(38) -> 20 1107.74/297.17 , 5_1(38) -> 21 1107.74/297.17 , 5_1(38) -> 143 1107.74/297.17 , 5_1(44) -> 43 1107.74/297.17 , 5_1(49) -> 48 1107.74/297.17 , 5_1(55) -> 128 1107.74/297.17 , 5_1(56) -> 189 1107.74/297.17 , 5_1(58) -> 57 1107.74/297.17 , 5_1(62) -> 61 1107.74/297.17 , 5_1(63) -> 62 1107.74/297.17 , 5_1(69) -> 68 1107.74/297.17 , 5_1(73) -> 72 1107.74/297.17 , 5_1(75) -> 74 1107.74/297.17 , 5_1(76) -> 16 1107.74/297.17 , 5_1(80) -> 79 1107.74/297.17 , 5_1(81) -> 76 1107.74/297.17 , 5_1(86) -> 85 1107.74/297.17 , 5_1(95) -> 94 1107.74/297.17 , 5_1(103) -> 102 1107.74/297.17 , 5_1(107) -> 106 1107.74/297.17 , 5_1(108) -> 107 1107.74/297.17 , 5_1(111) -> 110 1107.74/297.17 , 5_1(117) -> 5 1107.74/297.17 , 5_1(124) -> 123 1107.74/297.17 , 5_1(129) -> 16 1107.74/297.17 , 5_1(147) -> 40 1107.74/297.17 , 5_1(153) -> 152 1107.74/297.17 , 5_1(154) -> 153 1107.74/297.17 , 5_1(159) -> 158 1107.74/297.17 , 5_1(166) -> 165 1107.74/297.17 , 5_1(167) -> 166 1107.74/297.17 , 5_1(173) -> 172 1107.74/297.17 , 5_1(174) -> 16 1107.74/297.17 , 5_1(176) -> 175 1107.74/297.17 , 5_1(178) -> 177 1107.74/297.17 , 5_1(183) -> 182 1107.74/297.17 , 5_1(186) -> 185 1107.74/297.17 , 5_1(187) -> 186 1107.74/297.17 , 5_1(189) -> 16 1107.74/297.17 , 5_1(199) -> 198 1107.74/297.17 , 5_1(209) -> 208 1107.74/297.17 , 5_1(215) -> 214 1107.74/297.17 , 5_1(219) -> 218 1107.74/297.17 , 5_1(222) -> 16 1107.74/297.17 , 5_1(223) -> 222 1107.74/297.17 , 5_2(242) -> 3 1107.74/297.17 , 5_2(242) -> 20 } 1107.74/297.17 1107.74/297.17 Hurray, we answered YES(?,O(n^1)) 1108.54/297.71 EOF