YES(?,O(n^1)) 1112.47/297.07 YES(?,O(n^1)) 1112.47/297.07 1112.47/297.07 We are left with following problem, upon which TcT provides the 1112.47/297.07 certificate YES(?,O(n^1)). 1112.47/297.07 1112.47/297.07 Strict Trs: 1112.47/297.07 { 3(4(4(3(2(4(4(x1))))))) -> 3(5(5(2(4(4(2(0(2(2(x1)))))))))) 1112.47/297.07 , 3(4(4(4(x1)))) -> 5(1(0(3(3(5(2(3(3(2(x1)))))))))) 1112.47/297.07 , 3(5(4(2(0(3(x1)))))) -> 3(2(0(1(2(1(5(1(3(3(x1)))))))))) 1112.47/297.07 , 3(1(0(1(5(4(4(x1))))))) -> 3(0(4(3(3(3(3(2(0(5(x1)))))))))) 1112.47/297.07 , 3(2(3(1(2(4(4(x1))))))) -> 3(2(5(2(5(1(3(0(4(5(x1)))))))))) 1112.47/297.07 , 4(3(2(3(5(3(2(x1))))))) -> 4(5(1(5(2(0(1(1(5(2(x1)))))))))) 1112.47/297.07 , 4(4(0(4(4(0(x1)))))) -> 4(3(0(0(4(5(1(5(1(0(x1)))))))))) 1112.47/297.07 , 4(4(0(5(4(5(4(x1))))))) -> 2(0(2(4(3(3(2(1(5(4(x1)))))))))) 1112.47/297.07 , 4(5(4(2(4(1(2(x1))))))) -> 4(3(5(3(3(3(1(3(2(2(x1)))))))))) 1112.47/297.07 , 4(2(4(2(5(4(5(x1))))))) -> 0(5(1(5(4(3(4(1(3(5(x1)))))))))) 1112.47/297.07 , 5(3(4(4(4(0(5(x1))))))) -> 2(3(3(5(3(1(5(1(1(1(x1)))))))))) 1112.47/297.07 , 5(3(1(3(x1)))) -> 5(5(2(1(5(5(5(1(1(1(x1)))))))))) 1112.47/297.07 , 5(4(5(0(5(0(x1)))))) -> 3(3(3(2(1(1(0(4(2(0(x1)))))))))) 1112.47/297.07 , 5(4(1(3(4(5(4(x1))))))) -> 3(2(4(2(5(5(5(5(0(4(x1)))))))))) 1112.47/297.07 , 5(4(1(2(5(0(1(x1))))))) -> 3(3(4(3(4(0(3(0(0(1(x1)))))))))) 1112.47/297.07 , 5(4(0(1(4(1(4(x1))))))) -> 3(3(2(0(4(1(0(0(3(5(x1)))))))))) 1112.47/297.07 , 5(4(0(1(5(4(x1)))))) -> 5(4(3(2(1(1(0(3(3(1(x1)))))))))) 1112.47/297.07 , 5(0(3(2(4(5(4(x1))))))) -> 5(3(5(5(2(2(4(5(2(0(x1)))))))))) 1112.47/297.07 , 5(0(5(4(5(1(4(x1))))))) -> 2(1(0(0(0(5(1(5(5(2(x1)))))))))) 1112.47/297.07 , 5(0(1(1(5(4(5(x1))))))) -> 5(1(1(3(0(4(1(4(5(1(x1)))))))))) 1112.47/297.07 , 1(3(4(1(4(4(0(x1))))))) -> 2(0(4(3(3(0(0(4(2(0(x1)))))))))) 1112.47/297.07 , 1(4(4(2(1(4(4(x1))))))) -> 3(5(1(1(0(5(0(3(1(0(x1)))))))))) 1112.47/297.07 , 1(0(0(3(4(4(x1)))))) -> 0(2(2(1(3(3(0(0(3(3(x1)))))))))) 1112.47/297.07 , 0(4(0(5(0(x1))))) -> 0(4(2(2(2(4(0(4(3(3(x1)))))))))) 1112.47/297.07 , 0(4(0(2(2(4(4(x1))))))) -> 4(2(5(5(2(3(3(2(4(4(x1)))))))))) 1112.47/297.07 , 0(5(3(4(3(5(4(x1))))))) -> 0(3(1(5(1(3(3(5(3(3(x1)))))))))) 1112.47/297.07 , 0(5(5(3(2(3(2(x1))))))) -> 0(5(5(3(4(5(5(3(4(1(x1)))))))))) 1112.47/297.07 , 0(5(0(4(5(0(x1)))))) -> 0(0(2(3(0(2(0(0(1(0(x1)))))))))) 1112.47/297.07 , 0(5(0(4(1(3(1(x1))))))) -> 0(0(1(2(3(4(5(3(0(0(x1)))))))))) 1112.47/297.07 , 0(1(3(0(5(4(4(x1))))))) -> 0(1(3(3(3(4(5(0(3(5(x1)))))))))) 1112.47/297.07 , 0(0(3(5(1(4(x1)))))) -> 0(4(1(1(5(2(5(3(3(0(x1)))))))))) 1112.47/297.07 , 0(0(3(1(5(4(3(x1))))))) -> 2(1(5(0(2(5(3(3(0(3(x1)))))))))) 1112.47/297.07 , 0(0(3(0(5(4(4(x1))))))) -> 5(5(1(3(3(1(2(0(4(2(x1)))))))))) 1112.47/297.07 , 2(5(3(2(1(3(5(x1))))))) -> 5(3(3(4(3(4(5(5(1(1(x1)))))))))) 1112.47/297.07 , 2(1(1(5(4(1(0(x1))))))) -> 1(5(5(1(2(1(5(3(3(0(x1)))))))))) } 1112.47/297.07 Obligation: 1112.47/297.07 derivational complexity 1112.47/297.07 Answer: 1112.47/297.07 YES(?,O(n^1)) 1112.47/297.07 1112.47/297.07 The problem is match-bounded by 2. The enriched problem is 1112.47/297.07 compatible with the following automaton. 1112.47/297.07 { 3_0(1) -> 1 1112.47/297.07 , 3_1(1) -> 26 1112.47/297.07 , 3_1(2) -> 1 1112.47/297.07 , 3_1(2) -> 18 1112.47/297.07 , 3_1(2) -> 26 1112.47/297.07 , 3_1(2) -> 34 1112.47/297.07 , 3_1(2) -> 64 1112.47/297.07 , 3_1(2) -> 78 1112.47/297.07 , 3_1(2) -> 86 1112.47/297.07 , 3_1(2) -> 121 1112.47/297.07 , 3_1(2) -> 147 1112.47/297.07 , 3_1(9) -> 70 1112.47/297.07 , 3_1(10) -> 18 1112.47/297.07 , 3_1(14) -> 13 1112.47/297.07 , 3_1(15) -> 14 1112.47/297.07 , 3_1(18) -> 17 1112.47/297.07 , 3_1(25) -> 25 1112.47/297.07 , 3_1(26) -> 25 1112.47/297.07 , 3_1(29) -> 28 1112.47/297.07 , 3_1(30) -> 29 1112.47/297.07 , 3_1(31) -> 30 1112.47/297.07 , 3_1(32) -> 31 1112.47/297.07 , 3_1(34) -> 78 1112.47/297.07 , 3_1(39) -> 38 1112.47/297.07 , 3_1(41) -> 25 1112.47/297.07 , 3_1(49) -> 41 1112.47/297.07 , 3_1(55) -> 147 1112.47/297.07 , 3_1(56) -> 201 1112.47/297.07 , 3_1(61) -> 60 1112.47/297.07 , 3_1(62) -> 61 1112.47/297.07 , 3_1(67) -> 66 1112.47/297.07 , 3_1(68) -> 67 1112.47/297.07 , 3_1(69) -> 68 1112.47/297.07 , 3_1(71) -> 25 1112.47/297.07 , 3_1(76) -> 75 1112.47/297.07 , 3_1(79) -> 57 1112.47/297.07 , 3_1(80) -> 79 1112.47/297.07 , 3_1(82) -> 81 1112.47/297.07 , 3_1(86) -> 121 1112.47/297.07 , 3_1(91) -> 2 1112.47/297.07 , 3_1(92) -> 91 1112.47/297.07 , 3_1(105) -> 104 1112.47/297.07 , 3_1(108) -> 107 1112.47/297.07 , 3_1(115) -> 25 1112.47/297.07 , 3_1(116) -> 115 1112.47/297.07 , 3_1(121) -> 120 1112.47/297.07 , 3_1(122) -> 11 1112.47/297.07 , 3_1(135) -> 134 1112.47/297.07 , 3_1(141) -> 140 1112.47/297.07 , 3_1(142) -> 141 1112.47/297.07 , 3_1(151) -> 150 1112.47/297.07 , 3_1(152) -> 151 1112.47/297.07 , 3_1(164) -> 163 1112.47/297.07 , 3_1(165) -> 164 1112.47/297.07 , 3_1(167) -> 71 1112.47/297.07 , 3_1(171) -> 170 1112.47/297.07 , 3_1(172) -> 171 1112.47/297.07 , 3_1(174) -> 173 1112.47/297.07 , 3_1(178) -> 177 1112.47/297.07 , 3_1(181) -> 180 1112.47/297.07 , 3_1(187) -> 186 1112.47/297.07 , 3_1(190) -> 189 1112.47/297.07 , 3_1(192) -> 191 1112.47/297.07 , 3_1(193) -> 192 1112.47/297.07 , 3_1(194) -> 193 1112.47/297.07 , 3_1(201) -> 200 1112.47/297.07 , 3_1(206) -> 205 1112.47/297.07 , 3_1(207) -> 206 1112.47/297.07 , 3_1(209) -> 208 1112.47/297.07 , 3_1(210) -> 209 1112.47/297.07 , 3_1(212) -> 122 1112.47/297.07 , 3_1(214) -> 213 1112.47/297.07 , 4_0(1) -> 1 1112.47/297.07 , 4_1(1) -> 65 1112.47/297.07 , 4_1(2) -> 96 1112.47/297.07 , 4_1(6) -> 5 1112.47/297.07 , 4_1(7) -> 6 1112.47/297.07 , 4_1(10) -> 96 1112.47/297.07 , 4_1(24) -> 76 1112.47/297.07 , 4_1(25) -> 159 1112.47/297.07 , 4_1(28) -> 27 1112.47/297.07 , 4_1(34) -> 40 1112.47/297.07 , 4_1(41) -> 1 1112.47/297.07 , 4_1(41) -> 40 1112.47/297.07 , 4_1(41) -> 56 1112.47/297.07 , 4_1(41) -> 65 1112.47/297.07 , 4_1(41) -> 103 1112.47/297.07 , 4_1(41) -> 166 1112.47/297.07 , 4_1(52) -> 51 1112.47/297.07 , 4_1(60) -> 59 1112.47/297.07 , 4_1(65) -> 166 1112.47/297.07 , 4_1(75) -> 74 1112.47/297.07 , 4_1(77) -> 76 1112.47/297.07 , 4_1(86) -> 178 1112.47/297.07 , 4_1(97) -> 96 1112.47/297.07 , 4_1(98) -> 19 1112.47/297.07 , 4_1(104) -> 91 1112.47/297.07 , 4_1(106) -> 105 1112.47/297.07 , 4_1(112) -> 111 1112.47/297.07 , 4_1(115) -> 11 1112.47/297.07 , 4_1(127) -> 126 1112.47/297.07 , 4_1(137) -> 136 1112.47/297.07 , 4_1(139) -> 138 1112.47/297.07 , 4_1(140) -> 58 1112.47/297.07 , 4_1(154) -> 71 1112.47/297.07 , 4_1(158) -> 157 1112.47/297.07 , 4_1(175) -> 174 1112.47/297.07 , 4_1(188) -> 187 1112.47/297.07 , 4_1(195) -> 194 1112.47/297.07 , 4_1(213) -> 212 1112.47/297.07 , 4_1(215) -> 214 1112.47/297.07 , 5_0(1) -> 1 1112.47/297.07 , 5_1(1) -> 34 1112.47/297.07 , 5_1(2) -> 48 1112.47/297.07 , 5_1(3) -> 2 1112.47/297.07 , 5_1(4) -> 3 1112.47/297.07 , 5_1(10) -> 48 1112.47/297.07 , 5_1(11) -> 1 1112.47/297.07 , 5_1(11) -> 10 1112.47/297.07 , 5_1(11) -> 26 1112.47/297.07 , 5_1(11) -> 34 1112.47/297.07 , 5_1(11) -> 56 1112.47/297.07 , 5_1(11) -> 64 1112.47/297.07 , 5_1(11) -> 190 1112.47/297.07 , 5_1(16) -> 15 1112.47/297.07 , 5_1(24) -> 23 1112.47/297.07 , 5_1(25) -> 172 1112.47/297.07 , 5_1(35) -> 19 1112.47/297.07 , 5_1(37) -> 36 1112.47/297.07 , 5_1(41) -> 34 1112.47/297.07 , 5_1(42) -> 41 1112.47/297.07 , 5_1(44) -> 43 1112.47/297.07 , 5_1(48) -> 133 1112.47/297.07 , 5_1(53) -> 52 1112.47/297.07 , 5_1(55) -> 54 1112.47/297.07 , 5_1(65) -> 64 1112.47/297.07 , 5_1(66) -> 49 1112.47/297.07 , 5_1(72) -> 71 1112.47/297.07 , 5_1(74) -> 73 1112.47/297.07 , 5_1(81) -> 80 1112.47/297.07 , 5_1(83) -> 90 1112.47/297.07 , 5_1(84) -> 83 1112.47/297.07 , 5_1(85) -> 216 1112.47/297.07 , 5_1(86) -> 139 1112.47/297.07 , 5_1(87) -> 11 1112.47/297.07 , 5_1(90) -> 89 1112.47/297.07 , 5_1(97) -> 127 1112.47/297.07 , 5_1(100) -> 99 1112.47/297.07 , 5_1(101) -> 100 1112.47/297.07 , 5_1(102) -> 101 1112.47/297.07 , 5_1(103) -> 102 1112.47/297.07 , 5_1(114) -> 195 1112.47/297.07 , 5_1(123) -> 122 1112.47/297.07 , 5_1(124) -> 123 1112.47/297.07 , 5_1(132) -> 131 1112.47/297.07 , 5_1(146) -> 145 1112.47/297.07 , 5_1(161) -> 160 1112.47/297.07 , 5_1(162) -> 161 1112.47/297.07 , 5_1(169) -> 168 1112.47/297.07 , 5_1(173) -> 72 1112.47/297.07 , 5_1(176) -> 175 1112.47/297.07 , 5_1(177) -> 176 1112.47/297.07 , 5_1(189) -> 188 1112.47/297.07 , 5_1(198) -> 197 1112.47/297.07 , 5_1(200) -> 199 1112.47/297.07 , 5_1(202) -> 128 1112.47/297.07 , 5_1(205) -> 204 1112.47/297.07 , 5_1(216) -> 215 1112.47/297.07 , 5_1(218) -> 217 1112.47/297.07 , 5_1(219) -> 218 1112.47/297.07 , 5_2(222) -> 172 1112.47/297.07 , 5_2(223) -> 222 1112.47/297.07 , 5_2(226) -> 225 1112.47/297.07 , 5_2(227) -> 226 1112.47/297.07 , 5_2(228) -> 227 1112.47/297.07 , 5_2(237) -> 34 1112.47/297.07 , 5_2(237) -> 139 1112.47/297.07 , 5_2(238) -> 237 1112.47/297.07 , 5_2(241) -> 240 1112.47/297.07 , 5_2(242) -> 241 1112.47/297.07 , 5_2(243) -> 242 1112.47/297.07 , 1_0(1) -> 1 1112.47/297.07 , 1_1(1) -> 86 1112.47/297.07 , 1_1(2) -> 86 1112.47/297.07 , 1_1(3) -> 86 1112.47/297.07 , 1_1(11) -> 86 1112.47/297.07 , 1_1(12) -> 11 1112.47/297.07 , 1_1(18) -> 69 1112.47/297.07 , 1_1(19) -> 86 1112.47/297.07 , 1_1(21) -> 20 1112.47/297.07 , 1_1(23) -> 22 1112.47/297.07 , 1_1(25) -> 24 1112.47/297.07 , 1_1(26) -> 24 1112.47/297.07 , 1_1(34) -> 63 1112.47/297.07 , 1_1(38) -> 37 1112.47/297.07 , 1_1(41) -> 86 1112.47/297.07 , 1_1(42) -> 86 1112.47/297.07 , 1_1(43) -> 42 1112.47/297.07 , 1_1(47) -> 46 1112.47/297.07 , 1_1(48) -> 47 1112.47/297.07 , 1_1(54) -> 53 1112.47/297.07 , 1_1(56) -> 55 1112.47/297.07 , 1_1(57) -> 86 1112.47/297.07 , 1_1(63) -> 46 1112.47/297.07 , 1_1(64) -> 63 1112.47/297.07 , 1_1(70) -> 69 1112.47/297.07 , 1_1(72) -> 86 1112.47/297.07 , 1_1(73) -> 72 1112.47/297.07 , 1_1(78) -> 77 1112.47/297.07 , 1_1(83) -> 82 1112.47/297.07 , 1_1(85) -> 84 1112.47/297.07 , 1_1(86) -> 85 1112.47/297.07 , 1_1(89) -> 88 1112.47/297.07 , 1_1(94) -> 93 1112.47/297.07 , 1_1(95) -> 94 1112.47/297.07 , 1_1(113) -> 112 1112.47/297.07 , 1_1(115) -> 2 1112.47/297.07 , 1_1(116) -> 86 1112.47/297.07 , 1_1(118) -> 117 1112.47/297.07 , 1_1(119) -> 118 1112.47/297.07 , 1_1(128) -> 57 1112.47/297.07 , 1_1(133) -> 132 1112.47/297.07 , 1_1(134) -> 12 1112.47/297.07 , 1_1(138) -> 137 1112.47/297.07 , 1_1(143) -> 3 1112.47/297.07 , 1_1(144) -> 143 1112.47/297.07 , 1_1(150) -> 149 1112.47/297.07 , 1_1(168) -> 167 1112.47/297.07 , 1_1(170) -> 169 1112.47/297.07 , 1_1(185) -> 179 1112.47/297.07 , 1_1(191) -> 71 1112.47/297.07 , 1_1(196) -> 154 1112.47/297.07 , 1_1(197) -> 196 1112.47/297.07 , 1_1(199) -> 221 1112.47/297.07 , 1_1(208) -> 87 1112.47/297.07 , 1_1(211) -> 210 1112.47/297.07 , 1_1(217) -> 1 1112.47/297.07 , 1_1(217) -> 10 1112.47/297.07 , 1_1(220) -> 219 1112.47/297.07 , 1_2(116) -> 245 1112.47/297.07 , 1_2(192) -> 230 1112.47/297.07 , 1_2(225) -> 224 1112.47/297.07 , 1_2(229) -> 228 1112.47/297.07 , 1_2(230) -> 229 1112.47/297.07 , 1_2(240) -> 239 1112.47/297.07 , 1_2(244) -> 243 1112.47/297.07 , 1_2(245) -> 244 1112.47/297.07 , 0_0(1) -> 1 1112.47/297.07 , 0_1(1) -> 56 1112.47/297.07 , 0_1(9) -> 8 1112.47/297.07 , 0_1(11) -> 103 1112.47/297.07 , 0_1(13) -> 12 1112.47/297.07 , 0_1(20) -> 19 1112.47/297.07 , 0_1(25) -> 153 1112.47/297.07 , 0_1(26) -> 207 1112.47/297.07 , 0_1(27) -> 2 1112.47/297.07 , 0_1(34) -> 33 1112.47/297.07 , 0_1(40) -> 39 1112.47/297.07 , 0_1(41) -> 56 1112.47/297.07 , 0_1(46) -> 45 1112.47/297.07 , 0_1(50) -> 49 1112.47/297.07 , 0_1(51) -> 50 1112.47/297.07 , 0_1(55) -> 184 1112.47/297.07 , 0_1(56) -> 190 1112.47/297.07 , 0_1(58) -> 57 1112.47/297.07 , 0_1(65) -> 103 1112.47/297.07 , 0_1(71) -> 1 1112.47/297.07 , 0_1(71) -> 33 1112.47/297.07 , 0_1(71) -> 55 1112.47/297.07 , 0_1(71) -> 56 1112.47/297.07 , 0_1(71) -> 65 1112.47/297.07 , 0_1(71) -> 86 1112.47/297.07 , 0_1(71) -> 96 1112.47/297.07 , 0_1(71) -> 103 1112.47/297.07 , 0_1(71) -> 109 1112.47/297.07 , 0_1(71) -> 113 1112.47/297.07 , 0_1(71) -> 190 1112.47/297.07 , 0_1(78) -> 114 1112.47/297.07 , 0_1(86) -> 109 1112.47/297.07 , 0_1(95) -> 142 1112.47/297.07 , 0_1(96) -> 95 1112.47/297.07 , 0_1(107) -> 106 1112.47/297.07 , 0_1(109) -> 108 1112.47/297.07 , 0_1(111) -> 110 1112.47/297.07 , 0_1(114) -> 113 1112.47/297.07 , 0_1(115) -> 56 1112.47/297.07 , 0_1(120) -> 119 1112.47/297.07 , 0_1(129) -> 128 1112.47/297.07 , 0_1(130) -> 129 1112.47/297.07 , 0_1(131) -> 130 1112.47/297.07 , 0_1(136) -> 135 1112.47/297.07 , 0_1(145) -> 144 1112.47/297.07 , 0_1(147) -> 146 1112.47/297.07 , 0_1(153) -> 152 1112.47/297.07 , 0_1(159) -> 158 1112.47/297.07 , 0_1(179) -> 71 1112.47/297.07 , 0_1(182) -> 181 1112.47/297.07 , 0_1(184) -> 183 1112.47/297.07 , 0_1(189) -> 106 1112.47/297.07 , 0_1(198) -> 202 1112.47/297.07 , 0_1(203) -> 202 1112.47/297.07 , 0_1(217) -> 56 1112.47/297.07 , 2_0(1) -> 1 1112.47/297.07 , 2_1(1) -> 10 1112.47/297.07 , 2_1(2) -> 9 1112.47/297.07 , 2_1(5) -> 4 1112.47/297.07 , 2_1(8) -> 7 1112.47/297.07 , 2_1(10) -> 9 1112.47/297.07 , 2_1(17) -> 16 1112.47/297.07 , 2_1(19) -> 2 1112.47/297.07 , 2_1(22) -> 21 1112.47/297.07 , 2_1(33) -> 32 1112.47/297.07 , 2_1(36) -> 35 1112.47/297.07 , 2_1(41) -> 2 1112.47/297.07 , 2_1(45) -> 44 1112.47/297.07 , 2_1(56) -> 97 1112.47/297.07 , 2_1(57) -> 1 1112.47/297.07 , 2_1(57) -> 24 1112.47/297.07 , 2_1(57) -> 34 1112.47/297.07 , 2_1(57) -> 56 1112.47/297.07 , 2_1(57) -> 65 1112.47/297.07 , 2_1(57) -> 86 1112.47/297.07 , 2_1(57) -> 166 1112.47/297.07 , 2_1(57) -> 190 1112.47/297.07 , 2_1(59) -> 58 1112.47/297.07 , 2_1(63) -> 62 1112.47/297.07 , 2_1(88) -> 87 1112.47/297.07 , 2_1(93) -> 92 1112.47/297.07 , 2_1(95) -> 211 1112.47/297.07 , 2_1(99) -> 98 1112.47/297.07 , 2_1(110) -> 91 1112.47/297.07 , 2_1(117) -> 116 1112.47/297.07 , 2_1(125) -> 124 1112.47/297.07 , 2_1(126) -> 125 1112.47/297.07 , 2_1(148) -> 71 1112.47/297.07 , 2_1(149) -> 148 1112.47/297.07 , 2_1(155) -> 154 1112.47/297.07 , 2_1(156) -> 155 1112.47/297.07 , 2_1(157) -> 156 1112.47/297.07 , 2_1(160) -> 41 1112.47/297.07 , 2_1(163) -> 162 1112.47/297.07 , 2_1(166) -> 165 1112.47/297.07 , 2_1(180) -> 179 1112.47/297.07 , 2_1(183) -> 182 1112.47/297.07 , 2_1(186) -> 185 1112.47/297.07 , 2_1(199) -> 198 1112.47/297.07 , 2_1(204) -> 203 1112.47/297.07 , 2_1(221) -> 220 1112.47/297.07 , 2_2(224) -> 223 1112.47/297.07 , 2_2(239) -> 238 } 1112.47/297.07 1112.47/297.07 Hurray, we answered YES(?,O(n^1)) 1113.55/297.93 EOF