YES(?,O(n^1)) 1144.95/297.07 YES(?,O(n^1)) 1144.95/297.07 1144.95/297.07 We are left with following problem, upon which TcT provides the 1144.95/297.07 certificate YES(?,O(n^1)). 1144.95/297.07 1144.95/297.07 Strict Trs: 1144.95/297.07 { 0(0(2(5(2(1(0(3(1(5(4(x1))))))))))) -> 1144.95/297.07 0(4(2(4(5(5(5(1(0(3(1(x1))))))))))) 1144.95/297.07 , 0(0(4(0(0(5(3(0(x1)))))))) -> 0(0(0(0(2(4(5(0(x1)))))))) 1144.95/297.07 , 0(1(2(x1))) -> 3(4(1(x1))) 1144.95/297.07 , 0(2(0(2(x1)))) -> 3(5(4(4(x1)))) 1144.95/297.07 , 0(2(5(4(4(1(3(4(2(x1))))))))) -> 0(0(4(5(4(5(4(2(2(x1))))))))) 1144.95/297.07 , 0(3(5(4(3(0(5(0(3(1(2(4(5(1(x1)))))))))))))) -> 1144.95/297.07 0(0(2(1(2(5(5(4(3(0(0(1(1(x1))))))))))))) 1144.95/297.07 , 0(4(2(4(1(5(0(4(0(3(4(3(1(2(x1)))))))))))))) -> 1144.95/297.07 0(0(5(4(0(4(0(1(2(2(0(0(0(1(x1)))))))))))))) 1144.95/297.07 , 0(5(4(5(1(1(2(5(3(0(4(5(3(5(4(3(x1)))))))))))))))) -> 1144.95/297.07 0(0(5(0(3(4(0(2(0(3(2(2(5(5(4(3(x1)))))))))))))))) 1144.95/297.07 , 1(0(4(5(x1)))) -> 1(5(4(5(x1)))) 1144.95/297.07 , 1(1(0(1(4(3(x1)))))) -> 1(1(4(2(3(3(x1)))))) 1144.95/297.07 , 1(2(4(1(4(4(3(1(4(x1))))))))) -> 1(1(5(5(5(2(4(3(2(x1))))))))) 1144.95/297.07 , 1(2(4(3(0(5(4(4(x1)))))))) -> 1(4(2(3(3(1(4(x1))))))) 1144.95/297.07 , 1(4(0(2(0(4(x1)))))) -> 1(4(4(2(4(5(x1)))))) 1144.95/297.07 , 2(2(1(0(4(x1))))) -> 1(5(4(2(5(x1))))) 1144.95/297.07 , 2(2(2(0(3(5(0(x1))))))) -> 0(5(2(4(4(5(0(x1))))))) 1144.95/297.07 , 2(2(3(2(2(0(2(2(2(3(0(2(4(x1))))))))))))) -> 1144.95/297.07 2(4(1(3(2(4(3(1(4(4(5(4(1(x1))))))))))))) 1144.95/297.07 , 2(3(1(2(5(0(5(3(2(2(5(1(2(1(5(0(4(1(x1)))))))))))))))))) -> 1144.95/297.07 1(1(5(3(3(1(1(5(4(4(5(2(2(3(5(2(5(5(1(x1))))))))))))))))))) 1144.95/297.07 , 2(3(3(1(2(4(5(4(3(2(5(0(4(2(2(3(x1)))))))))))))))) -> 1144.95/297.07 0(4(0(0(4(5(4(5(2(1(1(5(0(2(4(3(x1)))))))))))))))) 1144.95/297.07 , 2(4(4(1(0(3(3(2(5(5(0(3(5(4(4(3(3(1(3(3(x1)))))))))))))))))))) -> 1144.95/297.07 3(0(1(2(3(2(1(1(4(4(4(3(4(5(1(4(1(5(x1)))))))))))))))))) 1144.95/297.07 , 2(5(5(2(5(0(0(1(0(3(3(3(4(1(3(2(3(3(5(x1))))))))))))))))))) -> 1144.95/297.07 3(2(4(0(1(5(5(4(0(3(4(4(2(0(3(1(0(3(5(x1))))))))))))))))))) 1144.95/297.07 , 2(5(5(4(4(2(3(3(1(5(5(3(2(5(3(x1))))))))))))))) -> 1144.95/297.07 2(4(0(5(3(3(5(4(2(4(3(1(5(2(x1)))))))))))))) 1144.95/297.07 , 4(0(2(2(3(2(4(2(5(5(5(3(3(x1))))))))))))) -> 1144.95/297.07 4(0(5(0(4(0(4(2(4(4(2(5(3(x1))))))))))))) 1144.95/297.07 , 4(2(3(5(4(5(1(4(3(0(4(1(x1)))))))))))) -> 1144.95/297.07 3(2(0(2(2(1(3(1(1(x1))))))))) 1144.95/297.07 , 5(2(5(0(0(2(2(5(1(2(2(2(x1)))))))))))) -> 1144.95/297.07 5(0(3(1(0(1(0(1(5(5(3(x1))))))))))) 1144.95/297.07 , 5(5(4(1(0(1(5(3(5(5(x1)))))))))) -> 1144.95/297.07 3(4(3(4(4(4(0(4(2(5(x1)))))))))) } 1144.95/297.07 Obligation: 1144.95/297.07 derivational complexity 1144.95/297.07 Answer: 1144.95/297.07 YES(?,O(n^1)) 1144.95/297.07 1144.95/297.07 The problem is match-bounded by 2. The enriched problem is 1144.95/297.07 compatible with the following automaton. 1144.95/297.07 { 0_0(1) -> 1 1144.95/297.07 , 0_1(1) -> 17 1144.95/297.07 , 0_1(2) -> 1 1144.95/297.07 , 0_1(2) -> 17 1144.95/297.07 , 0_1(2) -> 25 1144.95/297.07 , 0_1(2) -> 26 1144.95/297.07 , 0_1(2) -> 60 1144.95/297.07 , 0_1(2) -> 137 1144.95/297.07 , 0_1(10) -> 9 1144.95/297.07 , 0_1(11) -> 45 1144.95/297.07 , 0_1(12) -> 2 1144.95/297.07 , 0_1(13) -> 12 1144.95/297.07 , 0_1(14) -> 13 1144.95/297.07 , 0_1(15) -> 175 1144.95/297.07 , 0_1(34) -> 33 1144.95/297.07 , 0_1(35) -> 34 1144.95/297.07 , 0_1(38) -> 37 1144.95/297.07 , 0_1(40) -> 39 1144.95/297.07 , 0_1(44) -> 43 1144.95/297.07 , 0_1(45) -> 44 1144.95/297.07 , 0_1(46) -> 36 1144.95/297.07 , 0_1(49) -> 48 1144.95/297.07 , 0_1(51) -> 50 1144.95/297.07 , 0_1(97) -> 3 1144.95/297.07 , 0_1(98) -> 97 1144.95/297.07 , 0_1(107) -> 106 1144.95/297.07 , 0_1(108) -> 18 1144.95/297.07 , 0_1(125) -> 124 1144.95/297.07 , 0_1(130) -> 129 1144.95/297.07 , 0_1(135) -> 134 1144.95/297.07 , 0_1(138) -> 137 1144.95/297.07 , 0_1(139) -> 74 1144.95/297.07 , 0_1(150) -> 149 1144.95/297.07 , 0_1(152) -> 151 1144.95/297.07 , 0_1(154) -> 153 1144.95/297.07 , 0_1(160) -> 123 1144.95/297.07 , 0_1(165) -> 164 1144.95/297.07 , 0_1(168) -> 167 1144.95/297.07 , 0_1(170) -> 169 1144.95/297.07 , 1_0(1) -> 1 1144.95/297.07 , 1_1(1) -> 11 1144.95/297.07 , 1_1(9) -> 8 1144.95/297.07 , 1_1(11) -> 35 1144.95/297.07 , 1_1(16) -> 122 1144.95/297.07 , 1_1(20) -> 70 1144.95/297.07 , 1_1(28) -> 27 1144.95/297.07 , 1_1(41) -> 40 1144.95/297.07 , 1_1(58) -> 1 1144.95/297.07 , 1_1(58) -> 11 1144.95/297.07 , 1_1(58) -> 25 1144.95/297.07 , 1_1(58) -> 26 1144.95/297.07 , 1_1(58) -> 35 1144.95/297.07 , 1_1(58) -> 60 1144.95/297.07 , 1_1(58) -> 70 1144.95/297.07 , 1_1(59) -> 58 1144.95/297.07 , 1_1(73) -> 11 1144.95/297.07 , 1_1(74) -> 11 1144.95/297.07 , 1_1(75) -> 74 1144.95/297.07 , 1_1(80) -> 79 1144.95/297.07 , 1_1(82) -> 122 1144.95/297.07 , 1_1(85) -> 84 1144.95/297.07 , 1_1(86) -> 85 1144.95/297.07 , 1_1(104) -> 103 1144.95/297.07 , 1_1(105) -> 104 1144.95/297.07 , 1_1(106) -> 136 1144.95/297.07 , 1_1(109) -> 108 1144.95/297.07 , 1_1(113) -> 112 1144.95/297.07 , 1_1(114) -> 113 1144.95/297.07 , 1_1(121) -> 120 1144.95/297.07 , 1_1(126) -> 125 1144.95/297.07 , 1_1(137) -> 136 1144.95/297.07 , 1_1(148) -> 147 1144.95/297.07 , 1_1(149) -> 11 1144.95/297.07 , 1_1(163) -> 162 1144.95/297.07 , 1_1(167) -> 166 1144.95/297.07 , 1_1(169) -> 168 1144.95/297.07 , 1_1(171) -> 170 1144.95/297.07 , 1_2(42) -> 177 1144.95/297.07 , 1_2(73) -> 179 1144.95/297.07 , 1_2(110) -> 181 1144.95/297.07 , 2_0(1) -> 1 1144.95/297.07 , 2_1(1) -> 26 1144.95/297.07 , 2_1(4) -> 3 1144.95/297.07 , 2_1(15) -> 14 1144.95/297.07 , 2_1(16) -> 16 1144.95/297.07 , 2_1(18) -> 26 1144.95/297.07 , 2_1(20) -> 107 1144.95/297.07 , 2_1(26) -> 25 1144.95/297.07 , 2_1(27) -> 12 1144.95/297.07 , 2_1(29) -> 28 1144.95/297.07 , 2_1(42) -> 41 1144.95/297.07 , 2_1(43) -> 42 1144.95/297.07 , 2_1(50) -> 49 1144.95/297.07 , 2_1(53) -> 52 1144.95/297.07 , 2_1(54) -> 53 1144.95/297.07 , 2_1(56) -> 107 1144.95/297.07 , 2_1(57) -> 60 1144.95/297.07 , 2_1(61) -> 60 1144.95/297.07 , 2_1(65) -> 64 1144.95/297.07 , 2_1(67) -> 26 1144.95/297.07 , 2_1(68) -> 67 1144.95/297.07 , 2_1(72) -> 71 1144.95/297.07 , 2_1(73) -> 1 1144.95/297.07 , 2_1(73) -> 16 1144.95/297.07 , 2_1(73) -> 25 1144.95/297.07 , 2_1(73) -> 26 1144.95/297.07 , 2_1(73) -> 53 1144.95/297.07 , 2_1(77) -> 76 1144.95/297.07 , 2_1(81) -> 14 1144.95/297.07 , 2_1(91) -> 90 1144.95/297.07 , 2_1(92) -> 91 1144.95/297.07 , 2_1(95) -> 94 1144.95/297.07 , 2_1(103) -> 102 1144.95/297.07 , 2_1(110) -> 109 1144.95/297.07 , 2_1(112) -> 111 1144.95/297.07 , 2_1(123) -> 18 1144.95/297.07 , 2_1(134) -> 133 1144.95/297.07 , 2_1(145) -> 144 1144.95/297.07 , 2_1(149) -> 26 1144.95/297.07 , 2_1(156) -> 155 1144.95/297.07 , 2_1(159) -> 158 1144.95/297.07 , 2_1(161) -> 160 1144.95/297.07 , 2_1(162) -> 161 1144.95/297.07 , 2_1(180) -> 26 1144.95/297.07 , 3_0(1) -> 1 1144.95/297.07 , 3_1(1) -> 57 1144.95/297.07 , 3_1(11) -> 10 1144.95/297.07 , 3_1(16) -> 138 1144.95/297.07 , 3_1(18) -> 1 1144.95/297.07 , 3_1(18) -> 16 1144.95/297.07 , 3_1(18) -> 17 1144.95/297.07 , 3_1(18) -> 20 1144.95/297.07 , 3_1(18) -> 26 1144.95/297.07 , 3_1(18) -> 45 1144.95/297.07 , 3_1(18) -> 54 1144.95/297.07 , 3_1(18) -> 59 1144.95/297.07 , 3_1(18) -> 107 1144.95/297.07 , 3_1(26) -> 66 1144.95/297.07 , 3_1(33) -> 32 1144.95/297.07 , 3_1(35) -> 163 1144.95/297.07 , 3_1(47) -> 46 1144.95/297.07 , 3_1(52) -> 51 1144.95/297.07 , 3_1(57) -> 61 1144.95/297.07 , 3_1(69) -> 68 1144.95/297.07 , 3_1(70) -> 69 1144.95/297.07 , 3_1(73) -> 57 1144.95/297.07 , 3_1(76) -> 75 1144.95/297.07 , 3_1(79) -> 78 1144.95/297.07 , 3_1(83) -> 62 1144.95/297.07 , 3_1(84) -> 83 1144.95/297.07 , 3_1(93) -> 92 1144.95/297.07 , 3_1(111) -> 110 1144.95/297.07 , 3_1(118) -> 117 1144.95/297.07 , 3_1(122) -> 10 1144.95/297.07 , 3_1(131) -> 130 1144.95/297.07 , 3_1(136) -> 135 1144.95/297.07 , 3_1(141) -> 140 1144.95/297.07 , 3_1(142) -> 141 1144.95/297.07 , 3_1(147) -> 146 1144.95/297.07 , 3_1(166) -> 165 1144.95/297.07 , 3_1(172) -> 11 1144.95/297.07 , 3_1(180) -> 1 1144.95/297.07 , 3_2(176) -> 39 1144.95/297.07 , 3_2(178) -> 45 1144.95/297.07 , 3_2(180) -> 18 1144.95/297.07 , 4_0(1) -> 1 1144.95/297.07 , 4_1(1) -> 20 1144.95/297.07 , 4_1(3) -> 2 1144.95/297.07 , 4_1(5) -> 4 1144.95/297.07 , 4_1(11) -> 18 1144.95/297.07 , 4_1(14) -> 67 1144.95/297.07 , 4_1(15) -> 72 1144.95/297.07 , 4_1(16) -> 15 1144.95/297.07 , 4_1(20) -> 19 1144.95/297.07 , 4_1(21) -> 12 1144.95/297.07 , 4_1(23) -> 22 1144.95/297.07 , 4_1(25) -> 24 1144.95/297.07 , 4_1(32) -> 31 1144.95/297.07 , 4_1(37) -> 36 1144.95/297.07 , 4_1(39) -> 38 1144.95/297.07 , 4_1(48) -> 47 1144.95/297.07 , 4_1(57) -> 56 1144.95/297.07 , 4_1(60) -> 59 1144.95/297.07 , 4_1(66) -> 65 1144.95/297.07 , 4_1(67) -> 58 1144.95/297.07 , 4_1(71) -> 154 1144.95/297.07 , 4_1(73) -> 20 1144.95/297.07 , 4_1(74) -> 73 1144.95/297.07 , 4_1(78) -> 77 1144.95/297.07 , 4_1(81) -> 80 1144.95/297.07 , 4_1(82) -> 81 1144.95/297.07 , 4_1(88) -> 87 1144.95/297.07 , 4_1(89) -> 88 1144.95/297.07 , 4_1(99) -> 98 1144.95/297.07 , 4_1(101) -> 100 1144.95/297.07 , 4_1(115) -> 114 1144.95/297.07 , 4_1(116) -> 115 1144.95/297.07 , 4_1(117) -> 116 1144.95/297.07 , 4_1(119) -> 118 1144.95/297.07 , 4_1(122) -> 121 1144.95/297.07 , 4_1(124) -> 123 1144.95/297.07 , 4_1(129) -> 128 1144.95/297.07 , 4_1(132) -> 131 1144.95/297.07 , 4_1(133) -> 132 1144.95/297.07 , 4_1(144) -> 143 1144.95/297.07 , 4_1(146) -> 145 1144.95/297.07 , 4_1(149) -> 1 1144.95/297.07 , 4_1(149) -> 20 1144.95/297.07 , 4_1(153) -> 152 1144.95/297.07 , 4_1(155) -> 154 1144.95/297.07 , 4_1(157) -> 156 1144.95/297.07 , 4_1(158) -> 157 1144.95/297.07 , 4_1(173) -> 172 1144.95/297.07 , 4_1(174) -> 173 1144.95/297.07 , 4_1(175) -> 174 1144.95/297.07 , 4_2(177) -> 176 1144.95/297.07 , 4_2(179) -> 178 1144.95/297.07 , 4_2(181) -> 180 1144.95/297.07 , 5_0(1) -> 1 1144.95/297.07 , 5_1(1) -> 16 1144.95/297.07 , 5_1(3) -> 16 1144.95/297.07 , 5_1(6) -> 5 1144.95/297.07 , 5_1(7) -> 6 1144.95/297.07 , 5_1(8) -> 7 1144.95/297.07 , 5_1(11) -> 96 1144.95/297.07 , 5_1(15) -> 58 1144.95/297.07 , 5_1(17) -> 16 1144.95/297.07 , 5_1(18) -> 82 1144.95/297.07 , 5_1(19) -> 18 1144.95/297.07 , 5_1(20) -> 55 1144.95/297.07 , 5_1(22) -> 21 1144.95/297.07 , 5_1(24) -> 23 1144.95/297.07 , 5_1(26) -> 148 1144.95/297.07 , 5_1(30) -> 29 1144.95/297.07 , 5_1(31) -> 30 1144.95/297.07 , 5_1(36) -> 12 1144.95/297.07 , 5_1(55) -> 54 1144.95/297.07 , 5_1(56) -> 55 1144.95/297.07 , 5_1(57) -> 159 1144.95/297.07 , 5_1(62) -> 59 1144.95/297.07 , 5_1(63) -> 62 1144.95/297.07 , 5_1(64) -> 63 1144.95/297.07 , 5_1(71) -> 2 1144.95/297.07 , 5_1(87) -> 86 1144.95/297.07 , 5_1(90) -> 89 1144.95/297.07 , 5_1(94) -> 93 1144.95/297.07 , 5_1(96) -> 95 1144.95/297.07 , 5_1(100) -> 99 1144.95/297.07 , 5_1(102) -> 101 1144.95/297.07 , 5_1(106) -> 105 1144.95/297.07 , 5_1(120) -> 119 1144.95/297.07 , 5_1(127) -> 126 1144.95/297.07 , 5_1(128) -> 127 1144.95/297.07 , 5_1(140) -> 139 1144.95/297.07 , 5_1(143) -> 142 1144.95/297.07 , 5_1(149) -> 16 1144.95/297.07 , 5_1(151) -> 150 1144.95/297.07 , 5_1(159) -> 171 1144.95/297.07 , 5_1(164) -> 1 1144.95/297.07 , 5_1(164) -> 16 1144.95/297.07 , 5_1(164) -> 148 1144.95/297.07 , 5_1(180) -> 16 } 1144.95/297.07 1144.95/297.07 Hurray, we answered YES(?,O(n^1)) 1145.63/297.57 EOF