YES(?,O(n^1)) 1116.92/297.09 YES(?,O(n^1)) 1116.92/297.09 1116.92/297.09 We are left with following problem, upon which TcT provides the 1116.92/297.09 certificate YES(?,O(n^1)). 1116.92/297.09 1116.92/297.09 Strict Trs: 1116.92/297.09 { 0(0(1(1(x1)))) -> 0(2(1(x1))) 1116.92/297.09 , 0(0(3(3(0(0(x1)))))) -> 0(0(4(0(4(0(x1)))))) 1116.92/297.09 , 0(1(4(3(5(3(0(4(1(1(2(3(3(1(4(0(5(2(3(x1))))))))))))))))))) -> 1116.92/297.09 0(3(0(0(5(4(5(0(4(0(2(2(1(4(0(0(0(4(x1)))))))))))))))))) 1116.92/297.09 , 0(2(5(2(4(3(4(0(4(3(x1)))))))))) -> 0(3(5(3(1(3(4(0(3(x1))))))))) 1116.92/297.09 , 0(3(1(5(2(3(1(5(x1)))))))) -> 0(3(3(5(3(5(1(5(x1)))))))) 1116.92/297.09 , 1(1(2(0(2(4(1(1(3(3(3(5(1(3(x1)))))))))))))) -> 1116.92/297.09 5(1(3(4(5(1(1(0(3(4(0(2(0(x1))))))))))))) 1116.92/297.09 , 1(3(2(1(5(1(1(0(5(2(2(x1))))))))))) -> 1116.92/297.09 1(0(2(5(4(2(2(0(5(3(x1)))))))))) 1116.92/297.09 , 1(4(0(0(5(2(2(5(2(2(3(0(2(5(x1)))))))))))))) -> 1116.92/297.09 1(5(4(2(3(0(1(3(0(3(2(2(0(5(x1)))))))))))))) 1116.92/297.09 , 1(4(5(3(1(1(1(0(3(2(x1)))))))))) -> 1(3(2(5(3(5(2(1(x1)))))))) 1116.92/297.09 , 1(5(5(2(1(0(x1)))))) -> 1(5(4(3(1(0(x1)))))) 1116.92/297.09 , 2(2(0(2(0(0(5(3(2(3(2(0(3(2(x1)))))))))))))) -> 1116.92/297.09 4(5(1(5(3(3(3(4(4(2(0(4(x1)))))))))))) 1116.92/297.09 , 2(2(4(1(3(4(1(x1))))))) -> 5(2(4(5(3(x1))))) 1116.92/297.09 , 2(4(0(4(5(3(3(3(2(0(x1)))))))))) -> 0(3(1(5(4(5(5(0(x1)))))))) 1116.92/297.09 , 2(5(5(1(5(1(2(0(2(1(3(3(4(x1))))))))))))) -> 1116.92/297.09 3(1(1(1(2(5(2(1(4(0(0(4(4(x1))))))))))))) 1116.92/297.09 , 3(0(0(2(2(0(4(4(0(x1))))))))) -> 2(5(5(0(2(0(2(0(x1)))))))) 1116.92/297.09 , 3(0(1(3(1(5(1(4(2(x1))))))))) -> 1(1(2(4(2(4(1(0(2(x1))))))))) 1116.92/297.09 , 3(0(4(4(0(2(4(4(4(x1))))))))) -> 2(5(5(0(3(3(4(x1))))))) 1116.92/297.09 , 3(1(5(1(5(0(4(2(x1)))))))) -> 3(1(4(5(0(5(2(x1))))))) 1116.92/297.09 , 3(2(4(0(1(0(0(2(0(1(3(x1))))))))))) -> 1116.92/297.09 2(4(0(3(5(5(1(3(3(x1))))))))) 1116.92/297.09 , 3(4(1(1(3(1(1(1(5(4(3(4(1(x1))))))))))))) -> 1116.92/297.09 3(4(0(0(3(5(3(5(0(4(4(4(x1)))))))))))) 1116.92/297.09 , 4(0(3(4(2(2(x1)))))) -> 4(5(2(2(3(x1))))) 1116.92/297.09 , 4(0(4(2(2(0(4(2(1(4(1(4(x1)))))))))))) -> 1116.92/297.09 4(5(0(5(4(5(5(4(x1)))))))) 1116.92/297.09 , 4(2(1(0(0(4(4(4(3(0(5(1(3(1(2(3(5(1(0(2(x1)))))))))))))))))))) -> 1116.92/297.09 4(4(1(4(5(0(4(2(4(5(2(3(4(2(2(5(5(1(x1)))))))))))))))))) 1116.92/297.09 , 4(2(3(5(4(2(5(5(1(1(4(4(0(4(1(0(x1)))))))))))))))) -> 1116.92/297.09 4(1(2(5(4(0(5(3(2(5(0(4(2(4(0(x1))))))))))))))) 1116.92/297.09 , 4(3(5(4(3(4(0(0(4(2(5(0(x1)))))))))))) -> 1116.92/297.09 4(0(2(0(3(3(3(5(3(1(2(4(x1)))))))))))) 1116.92/297.09 , 4(4(1(0(1(3(3(1(4(1(2(x1))))))))))) -> 1116.92/297.09 3(1(2(4(4(4(2(1(2(2(x1)))))))))) 1116.92/297.09 , 4(4(4(1(4(5(2(2(0(1(4(5(2(2(1(4(5(0(0(4(x1)))))))))))))))))))) -> 1116.92/297.09 2(1(2(1(4(0(4(5(3(2(5(0(3(2(0(2(2(5(1(4(x1)))))))))))))))))))) 1116.92/297.09 , 5(0(3(4(0(0(0(4(3(4(2(4(3(3(2(0(4(x1))))))))))))))))) -> 1116.92/297.09 5(2(3(3(1(2(0(4(3(0(1(5(5(2(3(4(x1)))))))))))))))) 1116.92/297.09 , 5(3(2(0(4(1(4(1(4(2(5(2(3(4(4(4(3(2(5(2(4(x1))))))))))))))))))))) 1116.92/297.09 -> 5(0(4(3(0(0(2(1(5(4(4(2(5(3(4(3(0(5(5(x1))))))))))))))))))) 1116.92/297.09 , 5(5(4(4(0(5(5(2(4(0(5(1(2(3(2(4(0(x1))))))))))))))))) -> 1116.92/297.09 0(3(2(0(4(3(1(2(4(5(3(3(0(1(1(5(1(3(x1)))))))))))))))))) } 1116.92/297.09 Obligation: 1116.92/297.09 derivational complexity 1116.92/297.09 Answer: 1116.92/297.09 YES(?,O(n^1)) 1116.92/297.09 1116.92/297.09 The problem is match-bounded by 1. The enriched problem is 1116.92/297.09 compatible with the following automaton. 1116.92/297.09 { 0_0(1) -> 1 1116.92/297.09 , 0_1(1) -> 7 1116.92/297.09 , 0_1(2) -> 1 1116.92/297.09 , 0_1(2) -> 7 1116.92/297.09 , 0_1(2) -> 26 1116.92/297.09 , 0_1(2) -> 32 1116.92/297.09 , 0_1(2) -> 102 1116.92/297.09 , 0_1(2) -> 103 1116.92/297.09 , 0_1(2) -> 125 1116.92/297.09 , 0_1(2) -> 152 1116.92/297.09 , 0_1(2) -> 210 1116.92/297.09 , 0_1(4) -> 2 1116.92/297.09 , 0_1(5) -> 21 1116.92/297.09 , 0_1(6) -> 5 1116.92/297.09 , 0_1(9) -> 8 1116.92/297.09 , 0_1(10) -> 9 1116.92/297.09 , 0_1(14) -> 13 1116.92/297.09 , 0_1(16) -> 15 1116.92/297.09 , 0_1(21) -> 20 1116.92/297.09 , 0_1(27) -> 26 1116.92/297.09 , 0_1(32) -> 62 1116.92/297.09 , 0_1(35) -> 7 1116.92/297.09 , 0_1(40) -> 39 1116.92/297.09 , 0_1(43) -> 42 1116.92/297.09 , 0_1(44) -> 7 1116.92/297.09 , 0_1(45) -> 44 1116.92/297.09 , 0_1(51) -> 50 1116.92/297.09 , 0_1(56) -> 55 1116.92/297.09 , 0_1(59) -> 58 1116.92/297.09 , 0_1(63) -> 7 1116.92/297.09 , 0_1(82) -> 7 1116.92/297.09 , 0_1(91) -> 90 1116.92/297.09 , 0_1(92) -> 91 1116.92/297.09 , 0_1(93) -> 7 1116.92/297.09 , 0_1(96) -> 95 1116.92/297.09 , 0_1(103) -> 102 1116.92/297.09 , 0_1(107) -> 106 1116.92/297.09 , 0_1(109) -> 108 1116.92/297.09 , 0_1(115) -> 114 1116.92/297.09 , 0_1(116) -> 115 1116.92/297.09 , 0_1(121) -> 120 1116.92/297.09 , 0_1(123) -> 69 1116.92/297.09 , 0_1(131) -> 130 1116.92/297.09 , 0_1(146) -> 145 1116.92/297.09 , 0_1(151) -> 150 1116.92/297.09 , 0_1(153) -> 68 1116.92/297.09 , 0_1(155) -> 154 1116.92/297.09 , 0_1(171) -> 170 1116.92/297.09 , 0_1(177) -> 176 1116.92/297.09 , 0_1(180) -> 179 1116.92/297.09 , 0_1(188) -> 187 1116.92/297.09 , 0_1(191) -> 190 1116.92/297.09 , 0_1(195) -> 33 1116.92/297.09 , 0_1(198) -> 197 1116.92/297.09 , 0_1(199) -> 198 1116.92/297.09 , 0_1(210) -> 209 1116.92/297.09 , 0_1(212) -> 211 1116.92/297.09 , 0_1(221) -> 220 1116.92/297.09 , 1_0(1) -> 1 1116.92/297.09 , 1_1(1) -> 3 1116.92/297.09 , 1_1(3) -> 3 1116.92/297.09 , 1_1(4) -> 183 1116.92/297.09 , 1_1(6) -> 183 1116.92/297.09 , 1_1(7) -> 67 1116.92/297.09 , 1_1(19) -> 18 1116.92/297.09 , 1_1(24) -> 23 1116.92/297.09 , 1_1(27) -> 112 1116.92/297.09 , 1_1(32) -> 31 1116.92/297.09 , 1_1(34) -> 33 1116.92/297.09 , 1_1(38) -> 37 1116.92/297.09 , 1_1(39) -> 38 1116.92/297.09 , 1_1(44) -> 1 1116.92/297.09 , 1_1(44) -> 3 1116.92/297.09 , 1_1(44) -> 27 1116.92/297.09 , 1_1(44) -> 31 1116.92/297.09 , 1_1(44) -> 112 1116.92/297.09 , 1_1(44) -> 183 1116.92/297.09 , 1_1(46) -> 3 1116.92/297.09 , 1_1(57) -> 56 1116.92/297.09 , 1_1(70) -> 69 1116.92/297.09 , 1_1(78) -> 8 1116.92/297.09 , 1_1(83) -> 82 1116.92/297.09 , 1_1(84) -> 83 1116.92/297.09 , 1_1(85) -> 84 1116.92/297.09 , 1_1(89) -> 88 1116.92/297.09 , 1_1(93) -> 3 1116.92/297.09 , 1_1(97) -> 44 1116.92/297.09 , 1_1(102) -> 101 1116.92/297.09 , 1_1(111) -> 222 1116.92/297.09 , 1_1(113) -> 112 1116.92/297.09 , 1_1(122) -> 165 1116.92/297.09 , 1_1(128) -> 127 1116.92/297.09 , 1_1(142) -> 68 1116.92/297.09 , 1_1(152) -> 160 1116.92/297.09 , 1_1(166) -> 165 1116.92/297.09 , 1_1(167) -> 93 1116.92/297.09 , 1_1(169) -> 168 1116.92/297.09 , 1_1(186) -> 185 1116.92/297.09 , 1_1(192) -> 191 1116.92/297.09 , 1_1(201) -> 200 1116.92/297.09 , 1_1(211) -> 3 1116.92/297.09 , 1_1(215) -> 214 1116.92/297.09 , 1_1(222) -> 221 1116.92/297.09 , 2_0(1) -> 1 1116.92/297.09 , 2_1(1) -> 103 1116.92/297.09 , 2_1(3) -> 2 1116.92/297.09 , 2_1(5) -> 76 1116.92/297.09 , 2_1(6) -> 152 1116.92/297.09 , 2_1(7) -> 43 1116.92/297.09 , 2_1(17) -> 16 1116.92/297.09 , 2_1(18) -> 17 1116.92/297.09 , 2_1(27) -> 122 1116.92/297.09 , 2_1(42) -> 96 1116.92/297.09 , 2_1(43) -> 60 1116.92/297.09 , 2_1(44) -> 2 1116.92/297.09 , 2_1(46) -> 45 1116.92/297.09 , 2_1(49) -> 48 1116.92/297.09 , 2_1(50) -> 49 1116.92/297.09 , 2_1(54) -> 53 1116.92/297.09 , 2_1(61) -> 60 1116.92/297.09 , 2_1(62) -> 61 1116.92/297.09 , 2_1(64) -> 63 1116.92/297.09 , 2_1(68) -> 43 1116.92/297.09 , 2_1(77) -> 33 1116.92/297.09 , 2_1(86) -> 85 1116.92/297.09 , 2_1(88) -> 87 1116.92/297.09 , 2_1(93) -> 1 1116.92/297.09 , 2_1(93) -> 6 1116.92/297.09 , 2_1(93) -> 27 1116.92/297.09 , 2_1(93) -> 92 1116.92/297.09 , 2_1(93) -> 121 1116.92/297.09 , 2_1(98) -> 97 1116.92/297.09 , 2_1(100) -> 99 1116.92/297.09 , 2_1(103) -> 166 1116.92/297.09 , 2_1(104) -> 194 1116.92/297.09 , 2_1(122) -> 69 1116.92/297.09 , 2_1(133) -> 132 1116.92/297.09 , 2_1(136) -> 135 1116.92/297.09 , 2_1(139) -> 138 1116.92/297.09 , 2_1(140) -> 139 1116.92/297.09 , 2_1(142) -> 122 1116.92/297.09 , 2_1(143) -> 142 1116.92/297.09 , 2_1(149) -> 148 1116.92/297.09 , 2_1(154) -> 153 1116.92/297.09 , 2_1(161) -> 83 1116.92/297.09 , 2_1(165) -> 164 1116.92/297.09 , 2_1(168) -> 167 1116.92/297.09 , 2_1(175) -> 174 1116.92/297.09 , 2_1(179) -> 178 1116.92/297.09 , 2_1(181) -> 180 1116.92/297.09 , 2_1(182) -> 181 1116.92/297.09 , 2_1(187) -> 186 1116.92/297.09 , 2_1(200) -> 199 1116.92/297.09 , 2_1(205) -> 204 1116.92/297.09 , 2_1(211) -> 8 1116.92/297.09 , 2_1(216) -> 215 1116.92/297.09 , 3_0(1) -> 1 1116.92/297.09 , 3_1(1) -> 27 1116.92/297.09 , 3_1(2) -> 27 1116.92/297.09 , 3_1(6) -> 104 1116.92/297.09 , 3_1(8) -> 2 1116.92/297.09 , 3_1(23) -> 22 1116.92/297.09 , 3_1(25) -> 24 1116.92/297.09 , 3_1(27) -> 113 1116.92/297.09 , 3_1(28) -> 8 1116.92/297.09 , 3_1(30) -> 29 1116.92/297.09 , 3_1(35) -> 34 1116.92/297.09 , 3_1(41) -> 40 1116.92/297.09 , 3_1(44) -> 27 1116.92/297.09 , 3_1(55) -> 54 1116.92/297.09 , 3_1(58) -> 57 1116.92/297.09 , 3_1(59) -> 96 1116.92/297.09 , 3_1(60) -> 59 1116.92/297.09 , 3_1(63) -> 44 1116.92/297.09 , 3_1(66) -> 65 1116.92/297.09 , 3_1(67) -> 53 1116.92/297.09 , 3_1(68) -> 59 1116.92/297.09 , 3_1(72) -> 71 1116.92/297.09 , 3_1(73) -> 72 1116.92/297.09 , 3_1(74) -> 73 1116.92/297.09 , 3_1(82) -> 1 1116.92/297.09 , 3_1(82) -> 6 1116.92/297.09 , 3_1(82) -> 27 1116.92/297.09 , 3_1(82) -> 92 1116.92/297.09 , 3_1(82) -> 103 1116.92/297.09 , 3_1(82) -> 104 1116.92/297.09 , 3_1(82) -> 139 1116.92/297.09 , 3_1(93) -> 27 1116.92/297.09 , 3_1(104) -> 96 1116.92/297.09 , 3_1(109) -> 27 1116.92/297.09 , 3_1(110) -> 109 1116.92/297.09 , 3_1(117) -> 116 1116.92/297.09 , 3_1(119) -> 118 1116.92/297.09 , 3_1(137) -> 136 1116.92/297.09 , 3_1(142) -> 27 1116.92/297.09 , 3_1(148) -> 147 1116.92/297.09 , 3_1(153) -> 27 1116.92/297.09 , 3_1(156) -> 155 1116.92/297.09 , 3_1(157) -> 156 1116.92/297.09 , 3_1(158) -> 157 1116.92/297.09 , 3_1(160) -> 159 1116.92/297.09 , 3_1(174) -> 173 1116.92/297.09 , 3_1(178) -> 177 1116.92/297.09 , 3_1(184) -> 77 1116.92/297.09 , 3_1(185) -> 184 1116.92/297.09 , 3_1(190) -> 189 1116.92/297.09 , 3_1(197) -> 196 1116.92/297.09 , 3_1(207) -> 206 1116.92/297.09 , 3_1(209) -> 208 1116.92/297.09 , 3_1(214) -> 213 1116.92/297.09 , 3_1(219) -> 218 1116.92/297.09 , 3_1(220) -> 219 1116.92/297.09 , 4_0(1) -> 1 1116.92/297.09 , 4_1(1) -> 6 1116.92/297.09 , 4_1(2) -> 6 1116.92/297.09 , 4_1(5) -> 4 1116.92/297.09 , 4_1(6) -> 92 1116.92/297.09 , 4_1(7) -> 6 1116.92/297.09 , 4_1(12) -> 11 1116.92/297.09 , 4_1(15) -> 14 1116.92/297.09 , 4_1(20) -> 19 1116.92/297.09 , 4_1(21) -> 89 1116.92/297.09 , 4_1(26) -> 25 1116.92/297.09 , 4_1(27) -> 52 1116.92/297.09 , 4_1(36) -> 35 1116.92/297.09 , 4_1(42) -> 41 1116.92/297.09 , 4_1(44) -> 6 1116.92/297.09 , 4_1(48) -> 47 1116.92/297.09 , 4_1(51) -> 77 1116.92/297.09 , 4_1(53) -> 52 1116.92/297.09 , 4_1(67) -> 100 1116.92/297.09 , 4_1(68) -> 1 1116.92/297.09 , 4_1(68) -> 4 1116.92/297.09 , 4_1(68) -> 6 1116.92/297.09 , 4_1(68) -> 25 1116.92/297.09 , 4_1(68) -> 52 1116.92/297.09 , 4_1(68) -> 60 1116.92/297.09 , 4_1(68) -> 103 1116.92/297.09 , 4_1(68) -> 166 1116.92/297.09 , 4_1(75) -> 74 1116.92/297.09 , 4_1(76) -> 75 1116.92/297.09 , 4_1(80) -> 79 1116.92/297.09 , 4_1(82) -> 6 1116.92/297.09 , 4_1(90) -> 89 1116.92/297.09 , 4_1(92) -> 121 1116.92/297.09 , 4_1(93) -> 6 1116.92/297.09 , 4_1(99) -> 98 1116.92/297.09 , 4_1(101) -> 100 1116.92/297.09 , 4_1(105) -> 83 1116.92/297.09 , 4_1(108) -> 93 1116.92/297.09 , 4_1(114) -> 82 1116.92/297.09 , 4_1(125) -> 124 1116.92/297.09 , 4_1(127) -> 68 1116.92/297.09 , 4_1(129) -> 128 1116.92/297.09 , 4_1(132) -> 131 1116.92/297.09 , 4_1(134) -> 133 1116.92/297.09 , 4_1(138) -> 137 1116.92/297.09 , 4_1(142) -> 6 1116.92/297.09 , 4_1(145) -> 144 1116.92/297.09 , 4_1(152) -> 151 1116.92/297.09 , 4_1(162) -> 161 1116.92/297.09 , 4_1(163) -> 162 1116.92/297.09 , 4_1(164) -> 163 1116.92/297.09 , 4_1(170) -> 169 1116.92/297.09 , 4_1(172) -> 171 1116.92/297.09 , 4_1(184) -> 6 1116.92/297.09 , 4_1(189) -> 188 1116.92/297.09 , 4_1(195) -> 6 1116.92/297.09 , 4_1(196) -> 195 1116.92/297.09 , 4_1(203) -> 202 1116.92/297.09 , 4_1(204) -> 203 1116.92/297.09 , 4_1(208) -> 207 1116.92/297.09 , 4_1(211) -> 6 1116.92/297.09 , 4_1(213) -> 212 1116.92/297.09 , 4_1(217) -> 216 1116.92/297.09 , 5_0(1) -> 1 1116.92/297.09 , 5_1(1) -> 32 1116.92/297.09 , 5_1(2) -> 66 1116.92/297.09 , 5_1(3) -> 141 1116.92/297.09 , 5_1(6) -> 126 1116.92/297.09 , 5_1(7) -> 81 1116.92/297.09 , 5_1(11) -> 10 1116.92/297.09 , 5_1(13) -> 12 1116.92/297.09 , 5_1(22) -> 8 1116.92/297.09 , 5_1(27) -> 51 1116.92/297.09 , 5_1(29) -> 28 1116.92/297.09 , 5_1(31) -> 30 1116.92/297.09 , 5_1(32) -> 210 1116.92/297.09 , 5_1(33) -> 1 1116.92/297.09 , 5_1(33) -> 3 1116.92/297.09 , 5_1(33) -> 32 1116.92/297.09 , 5_1(33) -> 51 1116.92/297.09 , 5_1(33) -> 81 1116.92/297.09 , 5_1(33) -> 103 1116.92/297.09 , 5_1(33) -> 166 1116.92/297.09 , 5_1(37) -> 36 1116.92/297.09 , 5_1(47) -> 46 1116.92/297.09 , 5_1(51) -> 32 1116.92/297.09 , 5_1(52) -> 44 1116.92/297.09 , 5_1(62) -> 105 1116.92/297.09 , 5_1(65) -> 64 1116.92/297.09 , 5_1(68) -> 32 1116.92/297.09 , 5_1(69) -> 68 1116.92/297.09 , 5_1(71) -> 70 1116.92/297.09 , 5_1(79) -> 78 1116.92/297.09 , 5_1(81) -> 80 1116.92/297.09 , 5_1(87) -> 86 1116.92/297.09 , 5_1(94) -> 93 1116.92/297.09 , 5_1(95) -> 94 1116.92/297.09 , 5_1(103) -> 107 1116.92/297.09 , 5_1(106) -> 105 1116.92/297.09 , 5_1(108) -> 32 1116.92/297.09 , 5_1(111) -> 110 1116.92/297.09 , 5_1(112) -> 111 1116.92/297.09 , 5_1(118) -> 117 1116.92/297.09 , 5_1(120) -> 119 1116.92/297.09 , 5_1(124) -> 123 1116.92/297.09 , 5_1(126) -> 125 1116.92/297.09 , 5_1(130) -> 129 1116.92/297.09 , 5_1(135) -> 134 1116.92/297.09 , 5_1(141) -> 140 1116.92/297.09 , 5_1(144) -> 143 1116.92/297.09 , 5_1(147) -> 146 1116.92/297.09 , 5_1(150) -> 149 1116.92/297.09 , 5_1(159) -> 158 1116.92/297.09 , 5_1(173) -> 172 1116.92/297.09 , 5_1(176) -> 175 1116.92/297.09 , 5_1(183) -> 182 1116.92/297.09 , 5_1(193) -> 192 1116.92/297.09 , 5_1(194) -> 193 1116.92/297.09 , 5_1(202) -> 201 1116.92/297.09 , 5_1(206) -> 205 1116.92/297.09 , 5_1(218) -> 217 } 1116.92/297.09 1116.92/297.09 Hurray, we answered YES(?,O(n^1)) 1117.77/297.60 EOF