YES(?,O(n^1)) 1039.06/297.08 YES(?,O(n^1)) 1039.06/297.08 1039.06/297.08 We are left with following problem, upon which TcT provides the 1039.06/297.08 certificate YES(?,O(n^1)). 1039.06/297.08 1039.06/297.08 Strict Trs: 1039.06/297.08 { 0(1(2(2(3(0(4(4(x1)))))))) -> 0(4(5(0(3(4(0(4(x1)))))))) 1039.06/297.08 , 0(1(4(4(3(2(0(4(1(4(3(4(4(1(5(3(4(4(x1)))))))))))))))))) -> 1039.06/297.08 0(2(4(2(3(1(0(1(1(1(3(0(2(4(4(1(1(2(x1)))))))))))))))))) 1039.06/297.08 , 0(2(2(2(0(5(2(5(4(x1))))))))) -> 0(0(0(3(4(3(0(1(0(x1))))))))) 1039.06/297.08 , 1(1(4(1(0(1(0(3(3(4(4(1(5(4(0(4(4(5(5(3(x1)))))))))))))))))))) -> 1039.06/297.08 1(3(0(3(2(2(4(4(2(0(3(3(4(0(3(0(4(3(4(0(x1)))))))))))))))))))) 1039.06/297.08 , 2(0(3(3(3(4(1(1(0(4(4(0(3(3(3(0(0(1(5(3(x1)))))))))))))))))))) -> 1039.06/297.08 5(3(3(1(4(0(4(5(4(4(4(2(4(3(1(1(1(5(4(x1))))))))))))))))))) 1039.06/297.08 , 2(1(1(3(4(3(1(1(5(x1))))))))) -> 1(0(2(3(1(0(5(1(5(x1))))))))) 1039.06/297.08 , 2(2(0(0(2(1(0(5(3(2(2(1(4(0(5(x1))))))))))))))) -> 1039.06/297.08 0(0(3(5(3(0(4(3(1(3(0(2(5(5(x1)))))))))))))) 1039.06/297.08 , 2(3(3(2(1(5(0(5(0(1(3(3(2(5(1(5(0(3(0(5(x1)))))))))))))))))))) -> 1039.06/297.08 3(4(0(2(5(5(2(4(2(4(3(1(1(4(4(5(5(3(5(x1))))))))))))))))))) 1039.06/297.08 , 2(4(5(0(1(1(3(3(5(3(0(0(x1)))))))))))) -> 1039.06/297.08 4(4(2(2(1(0(4(0(1(3(2(0(x1)))))))))))) 1039.06/297.08 , 3(0(0(4(2(5(5(1(3(0(2(3(3(5(1(4(5(x1))))))))))))))))) -> 1039.06/297.08 3(4(0(1(0(5(5(3(1(4(0(3(5(3(2(2(5(x1))))))))))))))))) 1039.06/297.08 , 3(3(2(2(3(3(4(0(0(0(2(5(0(5(3(0(0(1(1(4(x1)))))))))))))))))))) -> 1039.06/297.08 3(1(1(0(3(3(5(4(2(2(1(0(1(1(0(5(0(3(4(0(x1)))))))))))))))))))) 1039.06/297.08 , 4(2(4(1(0(5(0(4(1(0(3(0(2(5(4(3(5(3(5(3(x1)))))))))))))))))))) -> 1039.06/297.08 4(2(5(4(4(2(4(5(0(0(3(1(5(0(2(0(2(2(1(x1))))))))))))))))))) 1039.06/297.08 , 4(4(3(0(3(1(5(3(5(1(3(1(5(3(x1)))))))))))))) -> 1039.06/297.08 0(2(4(5(0(0(0(5(1(0(5(4(4(x1))))))))))))) 1039.06/297.08 , 5(1(1(4(1(5(3(0(4(3(2(5(4(1(3(3(5(x1))))))))))))))))) -> 1039.06/297.08 5(0(1(0(4(0(2(4(5(1(5(4(1(5(3(3(5(x1))))))))))))))))) 1039.06/297.08 , 5(4(0(4(3(3(1(2(5(3(0(x1))))))))))) -> 1039.06/297.08 5(5(2(5(3(1(5(0(3(5(2(x1))))))))))) } 1039.06/297.08 Obligation: 1039.06/297.08 derivational complexity 1039.06/297.08 Answer: 1039.06/297.08 YES(?,O(n^1)) 1039.06/297.08 1039.06/297.08 The problem is match-bounded by 1. The enriched problem is 1039.06/297.08 compatible with the following automaton. 1039.06/297.08 { 0_0(1) -> 1 1039.06/297.08 , 0_1(1) -> 31 1039.06/297.08 , 0_1(2) -> 1 1039.06/297.08 , 0_1(2) -> 8 1039.06/297.08 , 0_1(2) -> 24 1039.06/297.08 , 0_1(2) -> 31 1039.06/297.08 , 0_1(2) -> 121 1039.06/297.08 , 0_1(2) -> 161 1039.06/297.08 , 0_1(5) -> 4 1039.06/297.08 , 0_1(8) -> 7 1039.06/297.08 , 0_1(14) -> 13 1039.06/297.08 , 0_1(19) -> 18 1039.06/297.08 , 0_1(25) -> 2 1039.06/297.08 , 0_1(26) -> 25 1039.06/297.08 , 0_1(30) -> 29 1039.06/297.08 , 0_1(34) -> 33 1039.06/297.08 , 0_1(41) -> 40 1039.06/297.08 , 0_1(45) -> 44 1039.06/297.08 , 0_1(47) -> 46 1039.06/297.08 , 0_1(48) -> 136 1039.06/297.08 , 0_1(51) -> 31 1039.06/297.08 , 0_1(55) -> 54 1039.06/297.08 , 0_1(67) -> 32 1039.06/297.08 , 0_1(71) -> 70 1039.06/297.08 , 0_1(77) -> 76 1039.06/297.08 , 0_1(82) -> 81 1039.06/297.08 , 0_1(84) -> 31 1039.06/297.08 , 0_1(86) -> 85 1039.06/297.08 , 0_1(101) -> 31 1039.06/297.08 , 0_1(106) -> 105 1039.06/297.08 , 0_1(108) -> 107 1039.06/297.08 , 0_1(112) -> 111 1039.06/297.08 , 0_1(118) -> 117 1039.06/297.08 , 0_1(124) -> 123 1039.06/297.08 , 0_1(132) -> 131 1039.06/297.08 , 0_1(135) -> 134 1039.06/297.08 , 0_1(144) -> 143 1039.06/297.08 , 0_1(145) -> 144 1039.06/297.08 , 0_1(149) -> 148 1039.06/297.08 , 0_1(151) -> 150 1039.06/297.08 , 0_1(155) -> 154 1039.06/297.08 , 0_1(156) -> 155 1039.06/297.08 , 0_1(157) -> 156 1039.06/297.08 , 0_1(160) -> 159 1039.06/297.08 , 0_1(162) -> 50 1039.06/297.08 , 0_1(164) -> 163 1039.06/297.08 , 0_1(166) -> 165 1039.06/297.08 , 0_1(181) -> 180 1039.06/297.08 , 1_0(1) -> 1 1039.06/297.08 , 1_1(1) -> 153 1039.06/297.08 , 1_1(13) -> 12 1039.06/297.08 , 1_1(15) -> 14 1039.06/297.08 , 1_1(16) -> 15 1039.06/297.08 , 1_1(17) -> 16 1039.06/297.08 , 1_1(23) -> 22 1039.06/297.08 , 1_1(24) -> 23 1039.06/297.08 , 1_1(31) -> 30 1039.06/297.08 , 1_1(32) -> 1 1039.06/297.08 , 1_1(32) -> 24 1039.06/297.08 , 1_1(32) -> 152 1039.06/297.08 , 1_1(32) -> 153 1039.06/297.08 , 1_1(51) -> 153 1039.06/297.08 , 1_1(53) -> 52 1039.06/297.08 , 1_1(64) -> 63 1039.06/297.08 , 1_1(65) -> 64 1039.06/297.08 , 1_1(66) -> 65 1039.06/297.08 , 1_1(70) -> 69 1039.06/297.08 , 1_1(73) -> 72 1039.06/297.08 , 1_1(80) -> 79 1039.06/297.08 , 1_1(84) -> 153 1039.06/297.08 , 1_1(95) -> 94 1039.06/297.08 , 1_1(96) -> 95 1039.06/297.08 , 1_1(100) -> 108 1039.06/297.08 , 1_1(105) -> 104 1039.06/297.08 , 1_1(109) -> 108 1039.06/297.08 , 1_1(111) -> 86 1039.06/297.08 , 1_1(116) -> 115 1039.06/297.08 , 1_1(122) -> 84 1039.06/297.08 , 1_1(123) -> 122 1039.06/297.08 , 1_1(131) -> 130 1039.06/297.08 , 1_1(133) -> 132 1039.06/297.08 , 1_1(134) -> 133 1039.06/297.08 , 1_1(147) -> 146 1039.06/297.08 , 1_1(159) -> 158 1039.06/297.08 , 1_1(163) -> 162 1039.06/297.08 , 1_1(170) -> 169 1039.06/297.08 , 1_1(173) -> 172 1039.06/297.08 , 1_1(179) -> 178 1039.06/297.08 , 2_0(1) -> 1 1039.06/297.08 , 2_1(1) -> 24 1039.06/297.08 , 2_1(2) -> 24 1039.06/297.08 , 2_1(9) -> 2 1039.06/297.08 , 2_1(11) -> 10 1039.06/297.08 , 2_1(20) -> 19 1039.06/297.08 , 2_1(24) -> 121 1039.06/297.08 , 2_1(31) -> 110 1039.06/297.08 , 2_1(36) -> 35 1039.06/297.08 , 2_1(37) -> 36 1039.06/297.08 , 2_1(40) -> 39 1039.06/297.08 , 2_1(61) -> 60 1039.06/297.08 , 2_1(68) -> 67 1039.06/297.08 , 2_1(73) -> 82 1039.06/297.08 , 2_1(82) -> 121 1039.06/297.08 , 2_1(83) -> 82 1039.06/297.08 , 2_1(87) -> 86 1039.06/297.08 , 2_1(90) -> 89 1039.06/297.08 , 2_1(92) -> 91 1039.06/297.08 , 2_1(101) -> 24 1039.06/297.08 , 2_1(102) -> 24 1039.06/297.08 , 2_1(103) -> 102 1039.06/297.08 , 2_1(104) -> 103 1039.06/297.08 , 2_1(129) -> 128 1039.06/297.08 , 2_1(130) -> 129 1039.06/297.08 , 2_1(137) -> 101 1039.06/297.08 , 2_1(141) -> 140 1039.06/297.08 , 2_1(150) -> 149 1039.06/297.08 , 2_1(152) -> 151 1039.06/297.08 , 2_1(153) -> 152 1039.06/297.08 , 2_1(167) -> 166 1039.06/297.08 , 2_1(176) -> 175 1039.06/297.08 , 3_0(1) -> 1 1039.06/297.08 , 3_1(6) -> 5 1039.06/297.08 , 3_1(12) -> 11 1039.06/297.08 , 3_1(18) -> 17 1039.06/297.08 , 3_1(24) -> 100 1039.06/297.08 , 3_1(27) -> 26 1039.06/297.08 , 3_1(29) -> 28 1039.06/297.08 , 3_1(33) -> 32 1039.06/297.08 , 3_1(35) -> 34 1039.06/297.08 , 3_1(42) -> 41 1039.06/297.08 , 3_1(43) -> 42 1039.06/297.08 , 3_1(46) -> 45 1039.06/297.08 , 3_1(49) -> 48 1039.06/297.08 , 3_1(51) -> 50 1039.06/297.08 , 3_1(52) -> 51 1039.06/297.08 , 3_1(63) -> 62 1039.06/297.08 , 3_1(69) -> 68 1039.06/297.08 , 3_1(73) -> 100 1039.06/297.08 , 3_1(74) -> 25 1039.06/297.08 , 3_1(76) -> 75 1039.06/297.08 , 3_1(79) -> 78 1039.06/297.08 , 3_1(81) -> 80 1039.06/297.08 , 3_1(84) -> 1 1039.06/297.08 , 3_1(84) -> 24 1039.06/297.08 , 3_1(84) -> 174 1039.06/297.08 , 3_1(94) -> 93 1039.06/297.08 , 3_1(100) -> 174 1039.06/297.08 , 3_1(110) -> 109 1039.06/297.08 , 3_1(115) -> 114 1039.06/297.08 , 3_1(119) -> 118 1039.06/297.08 , 3_1(121) -> 120 1039.06/297.08 , 3_1(125) -> 124 1039.06/297.08 , 3_1(126) -> 125 1039.06/297.08 , 3_1(146) -> 145 1039.06/297.08 , 3_1(178) -> 177 1039.06/297.08 , 3_1(182) -> 181 1039.06/297.08 , 4_0(1) -> 1 1039.06/297.08 , 4_1(1) -> 8 1039.06/297.08 , 4_1(3) -> 2 1039.06/297.08 , 4_1(7) -> 6 1039.06/297.08 , 4_1(8) -> 161 1039.06/297.08 , 4_1(10) -> 9 1039.06/297.08 , 4_1(21) -> 20 1039.06/297.08 , 4_1(22) -> 21 1039.06/297.08 , 4_1(28) -> 27 1039.06/297.08 , 4_1(31) -> 49 1039.06/297.08 , 4_1(38) -> 37 1039.06/297.08 , 4_1(39) -> 38 1039.06/297.08 , 4_1(44) -> 43 1039.06/297.08 , 4_1(48) -> 47 1039.06/297.08 , 4_1(51) -> 8 1039.06/297.08 , 4_1(54) -> 53 1039.06/297.08 , 4_1(56) -> 55 1039.06/297.08 , 4_1(58) -> 57 1039.06/297.08 , 4_1(59) -> 58 1039.06/297.08 , 4_1(60) -> 59 1039.06/297.08 , 4_1(62) -> 61 1039.06/297.08 , 4_1(78) -> 77 1039.06/297.08 , 4_1(84) -> 8 1039.06/297.08 , 4_1(85) -> 84 1039.06/297.08 , 4_1(91) -> 90 1039.06/297.08 , 4_1(93) -> 92 1039.06/297.08 , 4_1(97) -> 96 1039.06/297.08 , 4_1(98) -> 97 1039.06/297.08 , 4_1(101) -> 1 1039.06/297.08 , 4_1(101) -> 8 1039.06/297.08 , 4_1(101) -> 24 1039.06/297.08 , 4_1(102) -> 101 1039.06/297.08 , 4_1(107) -> 106 1039.06/297.08 , 4_1(117) -> 116 1039.06/297.08 , 4_1(128) -> 127 1039.06/297.08 , 4_1(135) -> 2 1039.06/297.08 , 4_1(139) -> 138 1039.06/297.08 , 4_1(140) -> 139 1039.06/297.08 , 4_1(142) -> 141 1039.06/297.08 , 4_1(165) -> 164 1039.06/297.08 , 4_1(168) -> 167 1039.06/297.08 , 4_1(172) -> 171 1039.06/297.08 , 5_0(1) -> 1 1039.06/297.08 , 5_1(1) -> 73 1039.06/297.08 , 5_1(4) -> 3 1039.06/297.08 , 5_1(8) -> 66 1039.06/297.08 , 5_1(23) -> 71 1039.06/297.08 , 5_1(24) -> 182 1039.06/297.08 , 5_1(50) -> 1 1039.06/297.08 , 5_1(50) -> 24 1039.06/297.08 , 5_1(50) -> 66 1039.06/297.08 , 5_1(50) -> 73 1039.06/297.08 , 5_1(50) -> 110 1039.06/297.08 , 5_1(57) -> 56 1039.06/297.08 , 5_1(72) -> 71 1039.06/297.08 , 5_1(73) -> 83 1039.06/297.08 , 5_1(75) -> 74 1039.06/297.08 , 5_1(88) -> 87 1039.06/297.08 , 5_1(89) -> 88 1039.06/297.08 , 5_1(99) -> 98 1039.06/297.08 , 5_1(100) -> 99 1039.06/297.08 , 5_1(113) -> 112 1039.06/297.08 , 5_1(114) -> 113 1039.06/297.08 , 5_1(120) -> 119 1039.06/297.08 , 5_1(127) -> 126 1039.06/297.08 , 5_1(136) -> 135 1039.06/297.08 , 5_1(138) -> 137 1039.06/297.08 , 5_1(143) -> 142 1039.06/297.08 , 5_1(148) -> 147 1039.06/297.08 , 5_1(154) -> 10 1039.06/297.08 , 5_1(158) -> 157 1039.06/297.08 , 5_1(161) -> 160 1039.06/297.08 , 5_1(169) -> 168 1039.06/297.08 , 5_1(171) -> 170 1039.06/297.08 , 5_1(174) -> 173 1039.06/297.08 , 5_1(175) -> 50 1039.06/297.08 , 5_1(177) -> 176 1039.06/297.08 , 5_1(180) -> 179 } 1039.06/297.08 1039.06/297.08 Hurray, we answered YES(?,O(n^1)) 1039.89/297.63 EOF