YES(?,O(n^1)) 1123.19/297.09 YES(?,O(n^1)) 1123.19/297.09 1123.19/297.09 We are left with following problem, upon which TcT provides the 1123.19/297.09 certificate YES(?,O(n^1)). 1123.19/297.09 1123.19/297.09 Strict Trs: 1123.19/297.09 { 0(0(0(2(0(3(0(5(1(0(5(0(5(1(0(4(3(x1))))))))))))))))) -> 1123.19/297.09 0(0(1(4(5(0(0(2(0(0(1(1(3(2(5(3(x1)))))))))))))))) 1123.19/297.09 , 0(0(1(1(x1)))) -> 2(2(1(3(x1)))) 1123.19/297.09 , 0(1(2(4(3(4(2(1(1(0(4(5(4(0(4(5(4(5(3(4(1(x1))))))))))))))))))))) 1123.19/297.09 -> 1123.19/297.09 2(4(0(1(5(0(1(2(3(0(4(1(4(1(5(3(4(1(5(0(2(x1))))))))))))))))))))) 1123.19/297.09 , 0(4(2(4(1(1(5(3(0(2(2(0(5(1(5(x1))))))))))))))) -> 1123.19/297.09 1(1(0(0(3(5(5(1(1(2(5(3(5(5(x1)))))))))))))) 1123.19/297.09 , 0(4(5(2(1(2(0(1(x1)))))))) -> 0(1(5(4(2(5(0(0(x1)))))))) 1123.19/297.09 , 0(5(1(3(5(4(4(0(5(1(2(0(0(5(3(x1))))))))))))))) -> 1123.19/297.09 0(4(0(0(3(4(3(3(5(0(4(3(3(1(3(x1))))))))))))))) 1123.19/297.09 , 1(0(3(3(1(4(3(3(5(0(4(2(4(3(4(2(0(2(x1)))))))))))))))))) -> 1123.19/297.09 1(0(5(1(0(2(0(0(4(0(2(5(0(2(5(2(2(2(x1)))))))))))))))))) 1123.19/297.09 , 1(3(1(1(0(4(x1)))))) -> 1(3(0(2(0(4(x1)))))) 1123.19/297.09 , 1(4(0(4(x1)))) -> 1(2(3(1(x1)))) 1123.19/297.09 , 1(4(0(4(0(4(0(2(2(5(5(3(1(1(0(0(3(x1))))))))))))))))) -> 1123.19/297.09 1(1(0(0(3(4(4(4(4(4(2(3(3(1(0(4(3(x1))))))))))))))))) 1123.19/297.09 , 2(2(5(1(1(3(5(4(0(5(5(2(4(1(4(4(1(x1))))))))))))))))) -> 1123.19/297.09 4(1(1(2(3(3(1(1(4(5(3(1(3(2(4(0(2(x1))))))))))))))))) 1123.19/297.09 , 2(4(2(0(0(1(3(4(2(1(5(2(2(0(4(1(x1)))))))))))))))) -> 1123.19/297.09 3(2(2(3(4(1(2(1(0(3(1(2(3(2(1(1(x1)))))))))))))))) 1123.19/297.09 , 2(4(2(1(5(5(0(1(0(4(2(2(2(3(4(1(0(4(x1)))))))))))))))))) -> 1123.19/297.09 2(1(3(2(1(2(2(5(1(1(3(5(4(4(5(5(5(x1))))))))))))))))) 1123.19/297.09 , 2(4(4(5(4(4(3(x1))))))) -> 2(4(2(3(4(2(2(x1))))))) 1123.19/297.09 , 3(0(0(2(1(1(3(1(5(0(5(1(0(5(x1)))))))))))))) -> 1123.19/297.09 5(1(0(1(2(2(1(3(3(1(0(2(5(x1))))))))))))) 1123.19/297.09 , 3(0(4(4(4(5(3(1(2(5(0(4(x1)))))))))))) -> 1123.19/297.09 5(3(3(0(3(5(1(0(0(1(0(x1))))))))))) 1123.19/297.09 , 3(4(3(1(1(x1))))) -> 3(4(0(3(1(x1))))) 1123.19/297.09 , 4(0(5(5(3(2(1(0(0(0(x1)))))))))) -> 1123.19/297.09 1(4(3(3(4(3(3(1(0(0(x1)))))))))) 1123.19/297.09 , 4(1(5(2(4(0(1(1(0(1(x1)))))))))) -> 1123.19/297.09 0(1(0(2(5(0(5(3(5(4(x1)))))))))) 1123.19/297.09 , 4(3(0(2(5(3(1(2(3(x1))))))))) -> 4(1(1(0(0(0(5(3(x1)))))))) 1123.19/297.09 , 4(4(1(4(0(0(1(3(x1)))))))) -> 4(1(2(3(4(2(5(3(x1)))))))) 1123.19/297.09 , 4(5(2(2(5(1(5(0(4(0(1(1(x1)))))))))))) -> 1123.19/297.09 4(1(1(4(3(2(2(3(5(2(1(3(x1)))))))))))) 1123.19/297.09 , 5(4(2(2(4(2(1(1(0(5(1(5(2(4(0(1(3(5(x1)))))))))))))))))) -> 1123.19/297.09 5(1(2(2(3(1(5(2(5(1(1(3(4(2(4(0(5(5(x1)))))))))))))))))) 1123.19/297.09 , 5(4(2(3(0(4(3(2(2(2(4(1(x1)))))))))))) -> 1123.19/297.09 5(1(0(2(4(4(4(5(1(4(1(x1))))))))))) 1123.19/297.09 , 5(5(4(2(0(2(3(x1))))))) -> 5(2(4(1(2(3(3(x1))))))) } 1123.19/297.09 Obligation: 1123.19/297.09 derivational complexity 1123.19/297.09 Answer: 1123.19/297.09 YES(?,O(n^1)) 1123.19/297.09 1123.19/297.09 The problem is match-bounded by 2. The enriched problem is 1123.19/297.09 compatible with the following automaton. 1123.19/297.09 { 0_0(1) -> 1 1123.19/297.09 , 0_1(1) -> 59 1123.19/297.09 , 0_1(2) -> 1 1123.19/297.09 , 0_1(2) -> 58 1123.19/297.09 , 0_1(2) -> 59 1123.19/297.09 , 0_1(2) -> 88 1123.19/297.09 , 0_1(2) -> 89 1123.19/297.09 , 0_1(2) -> 204 1123.19/297.09 , 0_1(3) -> 2 1123.19/297.09 , 0_1(7) -> 6 1123.19/297.09 , 0_1(8) -> 7 1123.19/297.09 , 0_1(10) -> 9 1123.19/297.09 , 0_1(11) -> 10 1123.19/297.09 , 0_1(15) -> 178 1123.19/297.09 , 0_1(23) -> 22 1123.19/297.09 , 0_1(26) -> 25 1123.19/297.09 , 0_1(30) -> 29 1123.19/297.09 , 0_1(40) -> 39 1123.19/297.09 , 0_1(41) -> 59 1123.19/297.09 , 0_1(43) -> 42 1123.19/297.09 , 0_1(44) -> 43 1123.19/297.09 , 0_1(52) -> 198 1123.19/297.09 , 0_1(54) -> 2 1123.19/297.09 , 0_1(59) -> 58 1123.19/297.09 , 0_1(60) -> 59 1123.19/297.09 , 0_1(61) -> 60 1123.19/297.09 , 0_1(62) -> 61 1123.19/297.09 , 0_1(68) -> 67 1123.19/297.09 , 0_1(71) -> 41 1123.19/297.09 , 0_1(74) -> 73 1123.19/297.09 , 0_1(76) -> 75 1123.19/297.09 , 0_1(77) -> 76 1123.19/297.09 , 0_1(79) -> 78 1123.19/297.09 , 0_1(82) -> 81 1123.19/297.09 , 0_1(87) -> 86 1123.19/297.09 , 0_1(89) -> 88 1123.19/297.09 , 0_1(90) -> 164 1123.19/297.09 , 0_1(101) -> 100 1123.19/297.09 , 0_1(102) -> 59 1123.19/297.09 , 0_1(124) -> 123 1123.19/297.09 , 0_1(147) -> 146 1123.19/297.09 , 0_1(155) -> 154 1123.19/297.09 , 0_1(158) -> 157 1123.19/297.09 , 0_1(162) -> 161 1123.19/297.09 , 0_1(163) -> 162 1123.19/297.09 , 0_1(171) -> 54 1123.19/297.09 , 0_1(174) -> 173 1123.19/297.09 , 0_1(177) -> 104 1123.19/297.09 , 0_1(178) -> 177 1123.19/297.09 , 0_2(214) -> 213 1123.19/297.09 , 0_2(216) -> 215 1123.19/297.09 , 1_0(1) -> 1 1123.19/297.09 , 1_1(1) -> 91 1123.19/297.09 , 1_1(2) -> 41 1123.19/297.09 , 1_1(4) -> 3 1123.19/297.09 , 1_1(12) -> 11 1123.19/297.09 , 1_1(13) -> 12 1123.19/297.09 , 1_1(16) -> 18 1123.19/297.09 , 1_1(24) -> 23 1123.19/297.09 , 1_1(27) -> 26 1123.19/297.09 , 1_1(32) -> 31 1123.19/297.09 , 1_1(34) -> 33 1123.19/297.09 , 1_1(38) -> 37 1123.19/297.09 , 1_1(41) -> 1 1123.19/297.09 , 1_1(41) -> 18 1123.19/297.09 , 1_1(41) -> 59 1123.19/297.09 , 1_1(41) -> 88 1123.19/297.09 , 1_1(41) -> 89 1123.19/297.09 , 1_1(41) -> 91 1123.19/297.09 , 1_1(41) -> 163 1123.19/297.09 , 1_1(41) -> 197 1123.19/297.09 , 1_1(42) -> 41 1123.19/297.09 , 1_1(48) -> 47 1123.19/297.09 , 1_1(49) -> 48 1123.19/297.09 , 1_1(54) -> 2 1123.19/297.09 , 1_1(58) -> 170 1123.19/297.09 , 1_1(59) -> 163 1123.19/297.09 , 1_1(60) -> 91 1123.19/297.09 , 1_1(73) -> 72 1123.19/297.09 , 1_1(90) -> 18 1123.19/297.09 , 1_1(91) -> 129 1123.19/297.09 , 1_1(100) -> 99 1123.19/297.09 , 1_1(102) -> 129 1123.19/297.09 , 1_1(103) -> 102 1123.19/297.09 , 1_1(104) -> 103 1123.19/297.09 , 1_1(108) -> 107 1123.19/297.09 , 1_1(109) -> 108 1123.19/297.09 , 1_1(113) -> 112 1123.19/297.09 , 1_1(121) -> 120 1123.19/297.09 , 1_1(123) -> 122 1123.19/297.09 , 1_1(126) -> 125 1123.19/297.09 , 1_1(130) -> 17 1123.19/297.09 , 1_1(133) -> 132 1123.19/297.09 , 1_1(137) -> 136 1123.19/297.09 , 1_1(138) -> 137 1123.19/297.09 , 1_1(145) -> 18 1123.19/297.09 , 1_1(146) -> 145 1123.19/297.09 , 1_1(148) -> 147 1123.19/297.09 , 1_1(151) -> 150 1123.19/297.09 , 1_1(154) -> 153 1123.19/297.09 , 1_1(161) -> 160 1123.19/297.09 , 1_1(189) -> 188 1123.19/297.09 , 1_1(193) -> 192 1123.19/297.09 , 1_1(194) -> 193 1123.19/297.09 , 1_1(204) -> 203 1123.19/297.09 , 1_1(207) -> 206 1123.19/297.09 , 1_2(21) -> 20 1123.19/297.09 , 1_2(211) -> 210 1123.19/297.09 , 1_2(212) -> 18 1123.19/297.09 , 2_0(1) -> 1 1123.19/297.09 , 2_1(1) -> 40 1123.19/297.09 , 2_1(9) -> 8 1123.19/297.09 , 2_1(15) -> 14 1123.19/297.09 , 2_1(17) -> 1 1123.19/297.09 , 2_1(17) -> 40 1123.19/297.09 , 2_1(17) -> 58 1123.19/297.09 , 2_1(17) -> 59 1123.19/297.09 , 2_1(18) -> 17 1123.19/297.09 , 2_1(28) -> 27 1123.19/297.09 , 2_1(40) -> 85 1123.19/297.09 , 2_1(41) -> 40 1123.19/297.09 , 2_1(50) -> 49 1123.19/297.09 , 2_1(53) -> 155 1123.19/297.09 , 2_1(57) -> 56 1123.19/297.09 , 2_1(71) -> 155 1123.19/297.09 , 2_1(75) -> 74 1123.19/297.09 , 2_1(80) -> 79 1123.19/297.09 , 2_1(83) -> 82 1123.19/297.09 , 2_1(85) -> 84 1123.19/297.09 , 2_1(88) -> 87 1123.19/297.09 , 2_1(90) -> 41 1123.19/297.09 , 2_1(97) -> 96 1123.19/297.09 , 2_1(103) -> 40 1123.19/297.09 , 2_1(105) -> 104 1123.19/297.09 , 2_1(115) -> 114 1123.19/297.09 , 2_1(116) -> 40 1123.19/297.09 , 2_1(117) -> 116 1123.19/297.09 , 2_1(118) -> 117 1123.19/297.09 , 2_1(122) -> 121 1123.19/297.09 , 2_1(127) -> 126 1123.19/297.09 , 2_1(129) -> 128 1123.19/297.09 , 2_1(132) -> 131 1123.19/297.09 , 2_1(134) -> 133 1123.19/297.09 , 2_1(135) -> 134 1123.19/297.09 , 2_1(143) -> 22 1123.19/297.09 , 2_1(149) -> 148 1123.19/297.09 , 2_1(150) -> 149 1123.19/297.09 , 2_1(172) -> 171 1123.19/297.09 , 2_1(179) -> 103 1123.19/297.09 , 2_1(183) -> 182 1123.19/297.09 , 2_1(184) -> 183 1123.19/297.09 , 2_1(186) -> 146 1123.19/297.09 , 2_1(187) -> 186 1123.19/297.09 , 2_1(191) -> 190 1123.19/297.09 , 2_1(197) -> 196 1123.19/297.09 , 2_1(199) -> 147 1123.19/297.09 , 2_1(205) -> 145 1123.19/297.09 , 2_1(208) -> 207 1123.19/297.09 , 2_2(19) -> 9 1123.19/297.09 , 2_2(20) -> 19 1123.19/297.09 , 2_2(209) -> 58 1123.19/297.09 , 2_2(209) -> 161 1123.19/297.09 , 2_2(210) -> 209 1123.19/297.09 , 2_2(215) -> 214 1123.19/297.09 , 3_0(1) -> 1 1123.19/297.09 , 3_1(1) -> 16 1123.19/297.09 , 3_1(2) -> 16 1123.19/297.09 , 3_1(14) -> 13 1123.19/297.09 , 3_1(16) -> 208 1123.19/297.09 , 3_1(18) -> 70 1123.19/297.09 , 3_1(29) -> 28 1123.19/297.09 , 3_1(36) -> 35 1123.19/297.09 , 3_1(39) -> 41 1123.19/297.09 , 3_1(41) -> 90 1123.19/297.09 , 3_1(42) -> 16 1123.19/297.09 , 3_1(45) -> 44 1123.19/297.09 , 3_1(52) -> 51 1123.19/297.09 , 3_1(63) -> 62 1123.19/297.09 , 3_1(65) -> 64 1123.19/297.09 , 3_1(66) -> 65 1123.19/297.09 , 3_1(70) -> 69 1123.19/297.09 , 3_1(86) -> 41 1123.19/297.09 , 3_1(90) -> 168 1123.19/297.09 , 3_1(91) -> 90 1123.19/297.09 , 3_1(98) -> 97 1123.19/297.09 , 3_1(99) -> 98 1123.19/297.09 , 3_1(106) -> 105 1123.19/297.09 , 3_1(107) -> 106 1123.19/297.09 , 3_1(112) -> 111 1123.19/297.09 , 3_1(114) -> 113 1123.19/297.09 , 3_1(116) -> 1 1123.19/297.09 , 3_1(116) -> 16 1123.19/297.09 , 3_1(116) -> 40 1123.19/297.09 , 3_1(119) -> 118 1123.19/297.09 , 3_1(125) -> 124 1123.19/297.09 , 3_1(128) -> 127 1123.19/297.09 , 3_1(129) -> 90 1123.19/297.09 , 3_1(131) -> 130 1123.19/297.09 , 3_1(139) -> 138 1123.19/297.09 , 3_1(144) -> 143 1123.19/297.09 , 3_1(152) -> 151 1123.19/297.09 , 3_1(153) -> 152 1123.19/297.09 , 3_1(156) -> 145 1123.19/297.09 , 3_1(157) -> 156 1123.19/297.09 , 3_1(159) -> 158 1123.19/297.09 , 3_1(166) -> 165 1123.19/297.09 , 3_1(167) -> 166 1123.19/297.09 , 3_1(169) -> 168 1123.19/297.09 , 3_1(170) -> 169 1123.19/297.09 , 3_1(176) -> 175 1123.19/297.09 , 3_1(180) -> 179 1123.19/297.09 , 3_1(182) -> 181 1123.19/297.09 , 3_1(185) -> 184 1123.19/297.09 , 3_1(188) -> 187 1123.19/297.09 , 3_1(195) -> 194 1123.19/297.09 , 3_2(2) -> 211 1123.19/297.09 , 3_2(13) -> 21 1123.19/297.09 , 3_2(41) -> 211 1123.19/297.09 , 3_2(42) -> 211 1123.19/297.09 , 3_2(54) -> 211 1123.19/297.09 , 3_2(104) -> 211 1123.19/297.09 , 3_2(213) -> 212 1123.19/297.09 , 4_0(1) -> 1 1123.19/297.09 , 4_1(1) -> 89 1123.19/297.09 , 4_1(4) -> 89 1123.19/297.09 , 4_1(5) -> 4 1123.19/297.09 , 4_1(14) -> 180 1123.19/297.09 , 4_1(16) -> 101 1123.19/297.09 , 4_1(22) -> 17 1123.19/297.09 , 4_1(31) -> 30 1123.19/297.09 , 4_1(33) -> 32 1123.19/297.09 , 4_1(37) -> 36 1123.19/297.09 , 4_1(39) -> 115 1123.19/297.09 , 4_1(41) -> 89 1123.19/297.09 , 4_1(44) -> 101 1123.19/297.09 , 4_1(54) -> 89 1123.19/297.09 , 4_1(56) -> 55 1123.19/297.09 , 4_1(60) -> 2 1123.19/297.09 , 4_1(64) -> 63 1123.19/297.09 , 4_1(69) -> 68 1123.19/297.09 , 4_1(78) -> 77 1123.19/297.09 , 4_1(85) -> 144 1123.19/297.09 , 4_1(91) -> 204 1123.19/297.09 , 4_1(92) -> 45 1123.19/297.09 , 4_1(93) -> 92 1123.19/297.09 , 4_1(94) -> 93 1123.19/297.09 , 4_1(95) -> 94 1123.19/297.09 , 4_1(96) -> 95 1123.19/297.09 , 4_1(102) -> 1 1123.19/297.09 , 4_1(102) -> 40 1123.19/297.09 , 4_1(102) -> 85 1123.19/297.09 , 4_1(102) -> 89 1123.19/297.09 , 4_1(102) -> 101 1123.19/297.09 , 4_1(110) -> 109 1123.19/297.09 , 4_1(120) -> 119 1123.19/297.09 , 4_1(141) -> 140 1123.19/297.09 , 4_1(142) -> 141 1123.19/297.09 , 4_1(164) -> 116 1123.19/297.09 , 4_1(165) -> 41 1123.19/297.09 , 4_1(168) -> 167 1123.19/297.09 , 4_1(181) -> 104 1123.19/297.09 , 4_1(196) -> 195 1123.19/297.09 , 4_1(198) -> 197 1123.19/297.09 , 4_1(200) -> 199 1123.19/297.09 , 4_1(201) -> 200 1123.19/297.09 , 4_1(202) -> 201 1123.19/297.09 , 4_1(206) -> 205 1123.19/297.09 , 4_2(60) -> 216 1123.19/297.09 , 5_0(1) -> 1 1123.19/297.09 , 5_1(1) -> 53 1123.19/297.09 , 5_1(6) -> 5 1123.19/297.09 , 5_1(16) -> 15 1123.19/297.09 , 5_1(17) -> 185 1123.19/297.09 , 5_1(25) -> 24 1123.19/297.09 , 5_1(35) -> 34 1123.19/297.09 , 5_1(39) -> 38 1123.19/297.09 , 5_1(41) -> 15 1123.19/297.09 , 5_1(46) -> 45 1123.19/297.09 , 5_1(47) -> 46 1123.19/297.09 , 5_1(51) -> 50 1123.19/297.09 , 5_1(52) -> 142 1123.19/297.09 , 5_1(53) -> 52 1123.19/297.09 , 5_1(55) -> 54 1123.19/297.09 , 5_1(58) -> 57 1123.19/297.09 , 5_1(60) -> 53 1123.19/297.09 , 5_1(67) -> 66 1123.19/297.09 , 5_1(72) -> 71 1123.19/297.09 , 5_1(81) -> 80 1123.19/297.09 , 5_1(84) -> 83 1123.19/297.09 , 5_1(85) -> 83 1123.19/297.09 , 5_1(89) -> 176 1123.19/297.09 , 5_1(90) -> 15 1123.19/297.09 , 5_1(91) -> 202 1123.19/297.09 , 5_1(102) -> 53 1123.19/297.09 , 5_1(111) -> 110 1123.19/297.09 , 5_1(136) -> 135 1123.19/297.09 , 5_1(140) -> 139 1123.19/297.09 , 5_1(145) -> 1 1123.19/297.09 , 5_1(145) -> 16 1123.19/297.09 , 5_1(145) -> 52 1123.19/297.09 , 5_1(145) -> 53 1123.19/297.09 , 5_1(145) -> 176 1123.19/297.09 , 5_1(160) -> 159 1123.19/297.09 , 5_1(173) -> 172 1123.19/297.09 , 5_1(175) -> 174 1123.19/297.09 , 5_1(190) -> 189 1123.19/297.09 , 5_1(192) -> 191 1123.19/297.09 , 5_1(203) -> 202 } 1123.19/297.09 1123.19/297.09 Hurray, we answered YES(?,O(n^1)) 1123.91/297.57 EOF