YES(?,O(n^1)) 1139.19/297.21 YES(?,O(n^1)) 1139.19/297.21 1139.19/297.21 We are left with following problem, upon which TcT provides the 1139.19/297.21 certificate YES(?,O(n^1)). 1139.19/297.21 1139.19/297.21 Strict Trs: 1139.19/297.21 { 0(0(0(3(x1)))) -> 4(2(4(0(2(5(3(3(4(5(x1)))))))))) 1139.19/297.21 , 0(2(1(x1))) -> 0(4(0(1(4(5(1(5(0(1(x1)))))))))) 1139.19/297.21 , 0(2(3(1(3(x1))))) -> 1(0(1(2(1(3(1(3(1(2(x1)))))))))) 1139.19/297.21 , 0(5(2(2(2(0(x1)))))) -> 2(5(4(3(0(2(5(1(2(1(x1)))))))))) 1139.19/297.21 , 0(5(2(2(2(1(0(x1))))))) -> 0(3(2(3(1(4(1(0(1(0(x1)))))))))) 1139.19/297.21 , 0(5(2(1(3(x1))))) -> 2(4(2(5(2(4(3(0(2(4(x1)))))))))) 1139.19/297.21 , 0(5(3(5(3(1(5(x1))))))) -> 0(1(3(4(0(1(4(5(1(5(x1)))))))))) 1139.19/297.21 , 0(3(4(5(3(x1))))) -> 2(0(2(5(1(2(4(4(5(5(x1)))))))))) 1139.19/297.21 , 2(0(0(5(2(0(x1)))))) -> 4(0(4(2(1(4(4(4(0(1(x1)))))))))) 1139.19/297.21 , 2(0(2(0(2(1(0(x1))))))) -> 2(0(2(3(4(2(4(4(4(0(x1)))))))))) 1139.19/297.21 , 2(0(5(3(0(2(x1)))))) -> 2(5(3(5(1(4(5(0(0(2(x1)))))))))) 1139.19/297.21 , 2(1(0(2(1(5(x1)))))) -> 2(5(4(1(3(2(2(5(4(5(x1)))))))))) 1139.19/297.21 , 2(1(3(1(0(x1))))) -> 0(1(4(5(1(5(5(2(3(0(x1)))))))))) 1139.19/297.21 , 2(4(5(5(1(3(5(x1))))))) -> 2(1(2(1(4(4(4(3(4(4(x1)))))))))) 1139.19/297.21 , 1(0(2(3(x1)))) -> 1(1(2(5(4(1(2(4(3(2(x1)))))))))) 1139.19/297.21 , 1(1(5(1(4(4(3(x1))))))) -> 1(0(3(4(4(1(0(2(5(5(x1)))))))))) 1139.19/297.21 , 1(1(3(x1))) -> 1(2(1(2(2(2(5(1(4(2(x1)))))))))) 1139.19/297.21 , 1(5(2(4(2(1(1(x1))))))) -> 4(4(1(4(1(4(3(1(0(3(x1)))))))))) 1139.19/297.21 , 1(3(2(3(0(5(3(x1))))))) -> 1(4(0(1(5(4(0(3(2(5(x1)))))))))) 1139.19/297.21 , 1(3(5(3(x1)))) -> 3(5(4(5(2(4(3(2(5(4(x1)))))))))) 1139.19/297.21 , 5(1(5(1(0(2(x1)))))) -> 4(5(0(0(4(3(1(1(0(4(x1)))))))))) 1139.19/297.21 , 3(0(0(5(5(2(1(x1))))))) -> 0(2(4(3(2(3(2(1(0(3(x1)))))))))) 1139.19/297.21 , 3(1(5(2(3(0(5(x1))))))) -> 5(3(4(0(4(5(2(0(0(4(x1)))))))))) } 1139.19/297.21 Obligation: 1139.19/297.21 derivational complexity 1139.19/297.21 Answer: 1139.19/297.21 YES(?,O(n^1)) 1139.19/297.21 1139.19/297.21 The problem is match-bounded by 2. The enriched problem is 1139.19/297.21 compatible with the following automaton. 1139.19/297.21 { 0_0(1) -> 1 1139.19/297.21 , 0_1(1) -> 44 1139.19/297.21 , 0_1(5) -> 4 1139.19/297.21 , 0_1(11) -> 1 1139.19/297.21 , 0_1(11) -> 28 1139.19/297.21 , 0_1(11) -> 36 1139.19/297.21 , 0_1(11) -> 44 1139.19/297.21 , 0_1(11) -> 83 1139.19/297.21 , 0_1(11) -> 93 1139.19/297.21 , 0_1(11) -> 136 1139.19/297.21 , 0_1(13) -> 12 1139.19/297.21 , 0_1(19) -> 18 1139.19/297.21 , 0_1(21) -> 20 1139.19/297.21 , 0_1(28) -> 83 1139.19/297.21 , 0_1(29) -> 18 1139.19/297.21 , 0_1(33) -> 32 1139.19/297.21 , 0_1(43) -> 42 1139.19/297.21 , 0_1(51) -> 50 1139.19/297.21 , 0_1(52) -> 158 1139.19/297.21 , 0_1(56) -> 55 1139.19/297.21 , 0_1(60) -> 29 1139.19/297.21 , 0_1(67) -> 2 1139.19/297.21 , 0_1(83) -> 82 1139.19/297.21 , 0_1(93) -> 135 1139.19/297.21 , 0_1(112) -> 111 1139.19/297.21 , 0_1(136) -> 135 1139.19/297.21 , 0_1(138) -> 137 1139.19/297.21 , 0_1(142) -> 141 1139.19/297.21 , 0_1(153) -> 152 1139.19/297.21 , 0_1(154) -> 153 1139.19/297.21 , 0_1(158) -> 170 1139.19/297.21 , 0_1(167) -> 166 1139.19/297.21 , 0_2(174) -> 173 1139.19/297.21 , 0_2(180) -> 83 1139.19/297.21 , 0_2(182) -> 181 1139.19/297.21 , 0_2(188) -> 187 1139.19/297.21 , 0_2(189) -> 44 1139.19/297.21 , 0_2(189) -> 50 1139.19/297.21 , 0_2(189) -> 83 1139.19/297.21 , 0_2(191) -> 190 1139.19/297.21 , 0_2(197) -> 196 1139.19/297.21 , 2_0(1) -> 1 1139.19/297.21 , 2_1(1) -> 28 1139.19/297.21 , 2_1(3) -> 2 1139.19/297.21 , 2_1(6) -> 5 1139.19/297.21 , 2_1(10) -> 143 1139.19/297.21 , 2_1(19) -> 36 1139.19/297.21 , 2_1(23) -> 22 1139.19/297.21 , 2_1(29) -> 1 1139.19/297.21 , 2_1(29) -> 28 1139.19/297.21 , 2_1(29) -> 36 1139.19/297.21 , 2_1(29) -> 44 1139.19/297.21 , 2_1(29) -> 51 1139.19/297.21 , 2_1(29) -> 135 1139.19/297.21 , 2_1(34) -> 33 1139.19/297.21 , 2_1(38) -> 37 1139.19/297.21 , 2_1(46) -> 45 1139.19/297.21 , 2_1(48) -> 47 1139.19/297.21 , 2_1(52) -> 51 1139.19/297.21 , 2_1(61) -> 60 1139.19/297.21 , 2_1(64) -> 63 1139.19/297.21 , 2_1(66) -> 112 1139.19/297.21 , 2_1(69) -> 68 1139.19/297.21 , 2_1(75) -> 74 1139.19/297.21 , 2_1(86) -> 85 1139.19/297.21 , 2_1(87) -> 86 1139.19/297.21 , 2_1(93) -> 92 1139.19/297.21 , 2_1(95) -> 94 1139.19/297.21 , 2_1(102) -> 101 1139.19/297.21 , 2_1(106) -> 105 1139.19/297.21 , 2_1(113) -> 20 1139.19/297.21 , 2_1(115) -> 114 1139.19/297.21 , 2_1(116) -> 115 1139.19/297.21 , 2_1(117) -> 116 1139.19/297.21 , 2_1(134) -> 163 1139.19/297.21 , 2_1(144) -> 28 1139.19/297.21 , 2_1(148) -> 147 1139.19/297.21 , 2_1(150) -> 85 1139.19/297.21 , 2_1(151) -> 150 1139.19/297.21 , 2_1(159) -> 11 1139.19/297.21 , 2_1(162) -> 161 1139.19/297.21 , 2_1(170) -> 169 1139.19/297.21 , 2_2(54) -> 128 1139.19/297.21 , 2_2(121) -> 120 1139.19/297.21 , 2_2(123) -> 122 1139.19/297.21 , 2_2(124) -> 123 1139.19/297.21 , 2_2(125) -> 124 1139.19/297.21 , 2_2(172) -> 171 1139.19/297.21 , 2_2(175) -> 174 1139.19/297.21 , 1_0(1) -> 1 1139.19/297.21 , 1_1(1) -> 19 1139.19/297.21 , 1_1(10) -> 59 1139.19/297.21 , 1_1(11) -> 19 1139.19/297.21 , 1_1(14) -> 13 1139.19/297.21 , 1_1(17) -> 16 1139.19/297.21 , 1_1(18) -> 41 1139.19/297.21 , 1_1(20) -> 1 1139.19/297.21 , 1_1(20) -> 19 1139.19/297.21 , 1_1(20) -> 43 1139.19/297.21 , 1_1(20) -> 44 1139.19/297.21 , 1_1(20) -> 83 1139.19/297.21 , 1_1(22) -> 21 1139.19/297.21 , 1_1(24) -> 23 1139.19/297.21 , 1_1(26) -> 25 1139.19/297.21 , 1_1(28) -> 27 1139.19/297.21 , 1_1(36) -> 35 1139.19/297.21 , 1_1(40) -> 39 1139.19/297.21 , 1_1(42) -> 41 1139.19/297.21 , 1_1(44) -> 43 1139.19/297.21 , 1_1(53) -> 11 1139.19/297.21 , 1_1(57) -> 56 1139.19/297.21 , 1_1(60) -> 19 1139.19/297.21 , 1_1(63) -> 62 1139.19/297.21 , 1_1(70) -> 69 1139.19/297.21 , 1_1(80) -> 79 1139.19/297.21 , 1_1(84) -> 31 1139.19/297.21 , 1_1(90) -> 89 1139.19/297.21 , 1_1(94) -> 29 1139.19/297.21 , 1_1(96) -> 95 1139.19/297.21 , 1_1(101) -> 20 1139.19/297.21 , 1_1(105) -> 104 1139.19/297.21 , 1_1(111) -> 110 1139.19/297.21 , 1_1(114) -> 113 1139.19/297.21 , 1_1(119) -> 118 1139.19/297.21 , 1_1(130) -> 129 1139.19/297.21 , 1_1(132) -> 131 1139.19/297.21 , 1_1(135) -> 134 1139.19/297.21 , 1_1(139) -> 138 1139.19/297.21 , 1_1(157) -> 156 1139.19/297.21 , 1_1(158) -> 157 1139.19/297.21 , 1_2(20) -> 188 1139.19/297.21 , 1_2(94) -> 197 1139.19/297.21 , 1_2(120) -> 19 1139.19/297.21 , 1_2(122) -> 121 1139.19/297.21 , 1_2(127) -> 126 1139.19/297.21 , 1_2(183) -> 182 1139.19/297.21 , 1_2(186) -> 185 1139.19/297.21 , 1_2(192) -> 191 1139.19/297.21 , 1_2(195) -> 194 1139.19/297.21 , 4_0(1) -> 1 1139.19/297.21 , 4_1(1) -> 52 1139.19/297.21 , 4_1(2) -> 1 1139.19/297.21 , 4_1(2) -> 10 1139.19/297.21 , 4_1(2) -> 19 1139.19/297.21 , 4_1(2) -> 28 1139.19/297.21 , 4_1(2) -> 44 1139.19/297.21 , 4_1(2) -> 58 1139.19/297.21 , 4_1(2) -> 59 1139.19/297.21 , 4_1(4) -> 3 1139.19/297.21 , 4_1(10) -> 9 1139.19/297.21 , 4_1(12) -> 11 1139.19/297.21 , 4_1(15) -> 14 1139.19/297.21 , 4_1(18) -> 72 1139.19/297.21 , 4_1(20) -> 77 1139.19/297.21 , 4_1(28) -> 119 1139.19/297.21 , 4_1(29) -> 52 1139.19/297.21 , 4_1(31) -> 30 1139.19/297.21 , 4_1(41) -> 40 1139.19/297.21 , 4_1(43) -> 40 1139.19/297.21 , 4_1(44) -> 77 1139.19/297.21 , 4_1(45) -> 29 1139.19/297.21 , 4_1(49) -> 48 1139.19/297.21 , 4_1(52) -> 100 1139.19/297.21 , 4_1(55) -> 54 1139.19/297.21 , 4_1(58) -> 57 1139.19/297.21 , 4_1(65) -> 64 1139.19/297.21 , 4_1(66) -> 65 1139.19/297.21 , 4_1(68) -> 67 1139.19/297.21 , 4_1(71) -> 70 1139.19/297.21 , 4_1(72) -> 71 1139.19/297.21 , 4_1(74) -> 73 1139.19/297.21 , 4_1(76) -> 75 1139.19/297.21 , 4_1(77) -> 76 1139.19/297.21 , 4_1(81) -> 80 1139.19/297.21 , 4_1(88) -> 53 1139.19/297.21 , 4_1(97) -> 96 1139.19/297.21 , 4_1(98) -> 97 1139.19/297.21 , 4_1(99) -> 98 1139.19/297.21 , 4_1(104) -> 103 1139.19/297.21 , 4_1(107) -> 106 1139.19/297.21 , 4_1(109) -> 108 1139.19/297.21 , 4_1(110) -> 109 1139.19/297.21 , 4_1(129) -> 2 1139.19/297.21 , 4_1(131) -> 130 1139.19/297.21 , 4_1(133) -> 132 1139.19/297.21 , 4_1(137) -> 20 1139.19/297.21 , 4_1(141) -> 140 1139.19/297.21 , 4_1(144) -> 29 1139.19/297.21 , 4_1(145) -> 52 1139.19/297.21 , 4_1(146) -> 145 1139.19/297.21 , 4_1(149) -> 148 1139.19/297.21 , 4_1(155) -> 154 1139.19/297.21 , 4_1(159) -> 52 1139.19/297.21 , 4_1(160) -> 159 1139.19/297.21 , 4_1(164) -> 52 1139.19/297.21 , 4_1(165) -> 29 1139.19/297.21 , 4_1(166) -> 165 1139.19/297.21 , 4_1(168) -> 167 1139.19/297.21 , 4_2(128) -> 127 1139.19/297.21 , 4_2(171) -> 82 1139.19/297.21 , 4_2(173) -> 172 1139.19/297.21 , 4_2(179) -> 178 1139.19/297.21 , 4_2(181) -> 180 1139.19/297.21 , 4_2(184) -> 183 1139.19/297.21 , 4_2(190) -> 189 1139.19/297.21 , 4_2(193) -> 192 1139.19/297.21 , 5_0(1) -> 1 1139.19/297.21 , 5_1(1) -> 10 1139.19/297.21 , 5_1(7) -> 6 1139.19/297.21 , 5_1(9) -> 87 1139.19/297.21 , 5_1(10) -> 66 1139.19/297.21 , 5_1(16) -> 15 1139.19/297.21 , 5_1(18) -> 17 1139.19/297.21 , 5_1(19) -> 58 1139.19/297.21 , 5_1(29) -> 151 1139.19/297.21 , 5_1(30) -> 29 1139.19/297.21 , 5_1(35) -> 34 1139.19/297.21 , 5_1(37) -> 10 1139.19/297.21 , 5_1(47) -> 46 1139.19/297.21 , 5_1(52) -> 151 1139.19/297.21 , 5_1(59) -> 58 1139.19/297.21 , 5_1(62) -> 61 1139.19/297.21 , 5_1(79) -> 78 1139.19/297.21 , 5_1(82) -> 81 1139.19/297.21 , 5_1(89) -> 88 1139.19/297.21 , 5_1(91) -> 90 1139.19/297.21 , 5_1(92) -> 91 1139.19/297.21 , 5_1(103) -> 102 1139.19/297.21 , 5_1(118) -> 117 1139.19/297.21 , 5_1(140) -> 139 1139.19/297.21 , 5_1(144) -> 10 1139.19/297.21 , 5_1(145) -> 144 1139.19/297.21 , 5_1(147) -> 146 1139.19/297.21 , 5_1(152) -> 2 1139.19/297.21 , 5_1(164) -> 1 1139.19/297.21 , 5_1(164) -> 136 1139.19/297.21 , 5_1(165) -> 10 1139.19/297.21 , 5_1(169) -> 168 1139.19/297.21 , 5_2(37) -> 179 1139.19/297.21 , 5_2(126) -> 125 1139.19/297.21 , 5_2(176) -> 175 1139.19/297.21 , 5_2(185) -> 184 1139.19/297.21 , 5_2(187) -> 186 1139.19/297.21 , 5_2(194) -> 193 1139.19/297.21 , 5_2(196) -> 195 1139.19/297.21 , 3_0(1) -> 1 1139.19/297.21 , 3_1(1) -> 136 1139.19/297.21 , 3_1(8) -> 7 1139.19/297.21 , 3_1(9) -> 8 1139.19/297.21 , 3_1(20) -> 93 1139.19/297.21 , 3_1(25) -> 24 1139.19/297.21 , 3_1(27) -> 26 1139.19/297.21 , 3_1(28) -> 107 1139.19/297.21 , 3_1(32) -> 31 1139.19/297.21 , 3_1(37) -> 11 1139.19/297.21 , 3_1(39) -> 38 1139.19/297.21 , 3_1(44) -> 93 1139.19/297.21 , 3_1(50) -> 49 1139.19/297.21 , 3_1(54) -> 53 1139.19/297.21 , 3_1(73) -> 61 1139.19/297.21 , 3_1(78) -> 30 1139.19/297.21 , 3_1(85) -> 84 1139.19/297.21 , 3_1(94) -> 93 1139.19/297.21 , 3_1(100) -> 99 1139.19/297.21 , 3_1(101) -> 93 1139.19/297.21 , 3_1(108) -> 21 1139.19/297.21 , 3_1(134) -> 133 1139.19/297.21 , 3_1(143) -> 142 1139.19/297.21 , 3_1(144) -> 1 1139.19/297.21 , 3_1(144) -> 19 1139.19/297.21 , 3_1(150) -> 149 1139.19/297.21 , 3_1(156) -> 155 1139.19/297.21 , 3_1(161) -> 160 1139.19/297.21 , 3_1(163) -> 162 1139.19/297.21 , 3_1(165) -> 164 1139.19/297.21 , 3_2(177) -> 176 1139.19/297.21 , 3_2(178) -> 177 } 1139.19/297.21 1139.19/297.21 Hurray, we answered YES(?,O(n^1)) 1140.04/298.10 EOF