YES(?,O(n^1)) 1109.13/297.08 YES(?,O(n^1)) 1109.13/297.08 1109.13/297.08 We are left with following problem, upon which TcT provides the 1109.13/297.08 certificate YES(?,O(n^1)). 1109.13/297.08 1109.13/297.08 Strict Trs: 1109.13/297.08 { 0(1(0(5(0(4(x1)))))) -> 0(1(5(5(1(x1))))) 1109.13/297.08 , 0(1(1(2(3(x1))))) -> 0(1(3(3(4(x1))))) 1109.13/297.08 , 0(4(0(0(3(1(4(1(2(x1))))))))) -> 2(5(3(2(2(1(2(2(x1)))))))) 1109.13/297.08 , 1(0(5(5(1(2(4(x1))))))) -> 2(5(4(5(1(1(4(x1))))))) 1109.13/297.08 , 1(1(1(3(3(0(0(1(2(2(5(1(4(4(4(5(4(3(4(1(x1)))))))))))))))))))) -> 1109.13/297.08 3(4(0(2(1(0(4(1(0(3(1(4(0(3(4(2(0(5(x1)))))))))))))))))) 1109.13/297.08 , 1(2(3(2(1(4(5(2(5(4(5(x1))))))))))) -> 1109.13/297.08 2(1(2(4(2(2(3(0(2(1(x1)))))))))) 1109.13/297.08 , 1(4(2(1(4(x1))))) -> 1(1(1(0(x1)))) 1109.13/297.08 , 1(4(5(1(4(x1))))) -> 5(5(5(2(x1)))) 1109.13/297.08 , 1(5(4(3(4(4(3(3(4(5(4(1(5(5(0(1(4(0(2(x1))))))))))))))))))) -> 1109.13/297.08 0(4(3(3(2(2(0(5(1(0(4(4(3(2(3(5(4(2(x1)))))))))))))))))) 1109.13/297.08 , 1(5(5(5(3(2(0(1(3(4(0(2(5(0(0(3(4(3(x1)))))))))))))))))) -> 1109.13/297.08 5(4(3(1(4(2(4(5(4(5(0(3(1(0(2(2(1(3(x1)))))))))))))))))) 1109.13/297.08 , 2(0(5(2(5(x1))))) -> 2(2(3(2(1(x1))))) 1109.13/297.08 , 2(4(0(0(0(3(3(3(3(0(0(4(x1)))))))))))) -> 1109.13/297.08 2(0(0(2(0(4(4(3(1(0(2(x1))))))))))) 1109.13/297.08 , 3(0(3(1(2(0(1(2(2(4(0(4(x1)))))))))))) -> 1109.13/297.08 0(4(1(4(3(2(0(2(5(4(3(3(x1)))))))))))) 1109.13/297.08 , 3(0(3(4(3(3(5(1(0(4(5(0(0(0(2(2(1(4(x1)))))))))))))))))) -> 1109.13/297.08 0(1(5(5(0(1(5(0(5(0(0(4(0(4(3(4(x1)))))))))))))))) 1109.13/297.08 , 3(2(0(3(1(4(3(1(0(5(5(1(3(4(2(1(5(4(3(x1))))))))))))))))))) -> 1109.13/297.08 3(0(3(1(1(3(0(4(1(1(2(1(5(2(0(0(4(2(3(x1))))))))))))))))))) 1109.13/297.08 , 4(0(2(5(2(1(1(2(0(1(2(1(x1)))))))))))) -> 1109.13/297.08 0(2(0(0(0(1(0(1(5(2(1(x1))))))))))) 1109.13/297.08 , 4(0(2(5(4(3(5(x1))))))) -> 1(1(3(5(1(5(x1)))))) 1109.13/297.08 , 4(1(1(5(1(4(3(3(0(3(0(5(4(1(0(4(2(1(4(1(x1)))))))))))))))))))) -> 1109.13/297.08 4(3(4(5(3(1(1(4(1(3(0(2(0(2(5(1(1(3(1(x1))))))))))))))))))) 1109.13/297.08 , 4(2(0(4(2(2(5(0(5(3(5(x1))))))))))) -> 1109.13/297.08 4(5(2(5(1(2(4(5(4(3(3(5(x1)))))))))))) 1109.13/297.08 , 4(2(5(1(1(3(1(3(2(5(5(4(3(5(5(4(x1)))))))))))))))) -> 1109.13/297.08 4(2(2(5(1(0(2(5(1(0(3(0(3(5(3(x1))))))))))))))) 1109.13/297.08 , 4(3(4(5(2(4(4(5(4(3(4(3(x1)))))))))))) -> 1109.13/297.08 2(5(3(0(2(5(2(4(4(1(3(x1))))))))))) 1109.13/297.08 , 5(4(2(4(0(4(1(4(4(2(0(1(3(4(1(3(5(4(4(4(x1)))))))))))))))))))) -> 1109.13/297.08 5(4(4(2(2(1(4(4(5(1(4(5(4(5(2(2(0(3(x1)))))))))))))))))) 1109.13/297.08 , 5(4(4(5(3(5(2(2(3(4(0(2(0(3(2(5(4(3(x1)))))))))))))))))) -> 1109.13/297.08 5(4(0(5(1(1(1(1(3(2(0(0(3(5(0(1(3(x1))))))))))))))))) 1109.13/297.08 , 5(4(5(4(2(5(0(1(5(4(x1)))))))))) -> 0(0(1(2(1(2(3(2(2(x1))))))))) 1109.13/297.08 , 5(5(4(1(1(1(3(2(2(5(1(2(3(5(4(x1))))))))))))))) -> 1109.13/297.08 5(5(0(3(1(2(0(2(0(2(0(4(1(2(x1)))))))))))))) } 1109.13/297.08 Obligation: 1109.13/297.08 derivational complexity 1109.13/297.08 Answer: 1109.13/297.08 YES(?,O(n^1)) 1109.13/297.08 1109.13/297.08 The problem is match-bounded by 2. The enriched problem is 1109.13/297.08 compatible with the following automaton. 1109.13/297.08 { 0_0(1) -> 1 1109.13/297.08 , 0_1(1) -> 44 1109.13/297.08 , 0_1(2) -> 1 1109.13/297.08 , 0_1(2) -> 5 1109.13/297.08 , 0_1(2) -> 7 1109.13/297.08 , 0_1(2) -> 34 1109.13/297.08 , 0_1(2) -> 44 1109.13/297.08 , 0_1(2) -> 60 1109.13/297.08 , 0_1(2) -> 77 1109.13/297.08 , 0_1(2) -> 129 1109.13/297.08 , 0_1(14) -> 90 1109.13/297.08 , 0_1(20) -> 19 1109.13/297.08 , 0_1(23) -> 22 1109.13/297.08 , 0_1(26) -> 25 1109.13/297.08 , 0_1(30) -> 29 1109.13/297.08 , 0_1(34) -> 33 1109.13/297.08 , 0_1(41) -> 40 1109.13/297.08 , 0_1(52) -> 51 1109.13/297.08 , 0_1(55) -> 54 1109.13/297.08 , 0_1(61) -> 118 1109.13/297.08 , 0_1(71) -> 70 1109.13/297.08 , 0_1(74) -> 73 1109.13/297.08 , 0_1(76) -> 198 1109.13/297.08 , 0_1(77) -> 186 1109.13/297.08 , 0_1(83) -> 8 1109.13/297.08 , 0_1(84) -> 83 1109.13/297.08 , 0_1(86) -> 85 1109.13/297.08 , 0_1(95) -> 94 1109.13/297.08 , 0_1(99) -> 4 1109.13/297.08 , 0_1(101) -> 100 1109.13/297.08 , 0_1(102) -> 101 1109.13/297.08 , 0_1(104) -> 103 1109.13/297.08 , 0_1(105) -> 18 1109.13/297.08 , 0_1(110) -> 109 1109.13/297.08 , 0_1(118) -> 117 1109.13/297.08 , 0_1(119) -> 118 1109.13/297.08 , 0_1(122) -> 121 1109.13/297.08 , 0_1(123) -> 122 1109.13/297.08 , 0_1(124) -> 123 1109.13/297.08 , 0_1(126) -> 125 1109.13/297.08 , 0_1(130) -> 44 1109.13/297.08 , 0_1(140) -> 139 1109.13/297.08 , 0_1(142) -> 141 1109.13/297.08 , 0_1(160) -> 159 1109.13/297.08 , 0_1(164) -> 163 1109.13/297.08 , 0_1(166) -> 165 1109.13/297.08 , 0_1(168) -> 10 1109.13/297.08 , 0_1(187) -> 62 1109.13/297.08 , 0_1(195) -> 194 1109.13/297.08 , 0_1(196) -> 195 1109.13/297.08 , 0_1(199) -> 2 1109.13/297.08 , 0_1(204) -> 46 1109.13/297.08 , 0_1(208) -> 207 1109.13/297.08 , 0_1(210) -> 209 1109.13/297.08 , 0_1(212) -> 211 1109.13/297.08 , 1_0(1) -> 1 1109.13/297.08 , 1_1(1) -> 5 1109.13/297.08 , 1_1(3) -> 2 1109.13/297.08 , 1_1(7) -> 17 1109.13/297.08 , 1_1(9) -> 5 1109.13/297.08 , 1_1(13) -> 12 1109.13/297.08 , 1_1(14) -> 213 1109.13/297.08 , 1_1(16) -> 5 1109.13/297.08 , 1_1(17) -> 16 1109.13/297.08 , 1_1(22) -> 21 1109.13/297.08 , 1_1(25) -> 24 1109.13/297.08 , 1_1(28) -> 27 1109.13/297.08 , 1_1(34) -> 129 1109.13/297.08 , 1_1(35) -> 8 1109.13/297.08 , 1_1(42) -> 1 1109.13/297.08 , 1_1(42) -> 5 1109.13/297.08 , 1_1(42) -> 7 1109.13/297.08 , 1_1(42) -> 17 1109.13/297.08 , 1_1(43) -> 42 1109.13/297.08 , 1_1(44) -> 43 1109.13/297.08 , 1_1(45) -> 5 1109.13/297.08 , 1_1(46) -> 126 1109.13/297.08 , 1_1(47) -> 5 1109.13/297.08 , 1_1(54) -> 53 1109.13/297.08 , 1_1(62) -> 76 1109.13/297.08 , 1_1(64) -> 63 1109.13/297.08 , 1_1(73) -> 72 1109.13/297.08 , 1_1(77) -> 76 1109.13/297.08 , 1_1(90) -> 89 1109.13/297.08 , 1_1(91) -> 47 1109.13/297.08 , 1_1(107) -> 106 1109.13/297.08 , 1_1(108) -> 107 1109.13/297.08 , 1_1(112) -> 111 1109.13/297.08 , 1_1(113) -> 112 1109.13/297.08 , 1_1(115) -> 114 1109.13/297.08 , 1_1(120) -> 213 1109.13/297.08 , 1_1(125) -> 124 1109.13/297.08 , 1_1(127) -> 126 1109.13/297.08 , 1_1(130) -> 76 1109.13/297.08 , 1_1(135) -> 134 1109.13/297.08 , 1_1(136) -> 135 1109.13/297.08 , 1_1(138) -> 137 1109.13/297.08 , 1_1(145) -> 144 1109.13/297.08 , 1_1(146) -> 145 1109.13/297.08 , 1_1(147) -> 5 1109.13/297.08 , 1_1(150) -> 149 1109.13/297.08 , 1_1(159) -> 158 1109.13/297.08 , 1_1(163) -> 162 1109.13/297.08 , 1_1(176) -> 175 1109.13/297.08 , 1_1(180) -> 179 1109.13/297.08 , 1_1(189) -> 188 1109.13/297.08 , 1_1(190) -> 189 1109.13/297.08 , 1_1(191) -> 190 1109.13/297.08 , 1_1(192) -> 191 1109.13/297.08 , 1_1(200) -> 199 1109.13/297.08 , 1_1(202) -> 201 1109.13/297.08 , 1_1(206) -> 205 1109.13/297.08 , 1_2(9) -> 82 1109.13/297.08 , 2_0(1) -> 1 1109.13/297.08 , 2_1(1) -> 14 1109.13/297.08 , 2_1(5) -> 41 1109.13/297.08 , 2_1(8) -> 1 1109.13/297.08 , 2_1(8) -> 5 1109.13/297.08 , 2_1(8) -> 7 1109.13/297.08 , 2_1(8) -> 14 1109.13/297.08 , 2_1(8) -> 32 1109.13/297.08 , 2_1(8) -> 43 1109.13/297.08 , 2_1(8) -> 44 1109.13/297.08 , 2_1(8) -> 104 1109.13/297.08 , 2_1(8) -> 213 1109.13/297.08 , 2_1(11) -> 10 1109.13/297.08 , 2_1(12) -> 11 1109.13/297.08 , 2_1(14) -> 13 1109.13/297.08 , 2_1(21) -> 20 1109.13/297.08 , 2_1(33) -> 32 1109.13/297.08 , 2_1(36) -> 35 1109.13/297.08 , 2_1(38) -> 37 1109.13/297.08 , 2_1(39) -> 38 1109.13/297.08 , 2_1(41) -> 74 1109.13/297.08 , 2_1(47) -> 14 1109.13/297.08 , 2_1(50) -> 49 1109.13/297.08 , 2_1(51) -> 50 1109.13/297.08 , 2_1(59) -> 58 1109.13/297.08 , 2_1(62) -> 120 1109.13/297.08 , 2_1(66) -> 65 1109.13/297.08 , 2_1(75) -> 74 1109.13/297.08 , 2_1(76) -> 75 1109.13/297.08 , 2_1(77) -> 120 1109.13/297.08 , 2_1(78) -> 8 1109.13/297.08 , 2_1(85) -> 84 1109.13/297.08 , 2_1(94) -> 93 1109.13/297.08 , 2_1(96) -> 95 1109.13/297.08 , 2_1(114) -> 113 1109.13/297.08 , 2_1(117) -> 116 1109.13/297.08 , 2_1(120) -> 13 1109.13/297.08 , 2_1(121) -> 2 1109.13/297.08 , 2_1(130) -> 14 1109.13/297.08 , 2_1(141) -> 140 1109.13/297.08 , 2_1(143) -> 142 1109.13/297.08 , 2_1(148) -> 147 1109.13/297.08 , 2_1(151) -> 150 1109.13/297.08 , 2_1(156) -> 130 1109.13/297.08 , 2_1(157) -> 156 1109.13/297.08 , 2_1(161) -> 160 1109.13/297.08 , 2_1(169) -> 168 1109.13/297.08 , 2_1(171) -> 170 1109.13/297.08 , 2_1(174) -> 173 1109.13/297.08 , 2_1(175) -> 174 1109.13/297.08 , 2_1(185) -> 184 1109.13/297.08 , 2_1(186) -> 185 1109.13/297.08 , 2_1(194) -> 193 1109.13/297.08 , 2_1(201) -> 200 1109.13/297.08 , 2_1(203) -> 202 1109.13/297.08 , 2_1(207) -> 206 1109.13/297.08 , 2_1(209) -> 208 1109.13/297.08 , 2_1(211) -> 210 1109.13/297.08 , 2_2(79) -> 32 1109.13/297.08 , 2_2(80) -> 79 1109.13/297.08 , 2_2(82) -> 81 1109.13/297.08 , 3_0(1) -> 1 1109.13/297.08 , 3_1(1) -> 77 1109.13/297.08 , 3_1(5) -> 146 1109.13/297.08 , 3_1(6) -> 3 1109.13/297.08 , 3_1(7) -> 6 1109.13/297.08 , 3_1(10) -> 9 1109.13/297.08 , 3_1(13) -> 203 1109.13/297.08 , 3_1(15) -> 43 1109.13/297.08 , 3_1(18) -> 1 1109.13/297.08 , 3_1(18) -> 5 1109.13/297.08 , 3_1(18) -> 77 1109.13/297.08 , 3_1(27) -> 26 1109.13/297.08 , 3_1(31) -> 30 1109.13/297.08 , 3_1(34) -> 155 1109.13/297.08 , 3_1(40) -> 39 1109.13/297.08 , 3_1(41) -> 78 1109.13/297.08 , 3_1(47) -> 77 1109.13/297.08 , 3_1(48) -> 47 1109.13/297.08 , 3_1(49) -> 48 1109.13/297.08 , 3_1(58) -> 57 1109.13/297.08 , 3_1(60) -> 59 1109.13/297.08 , 3_1(62) -> 77 1109.13/297.08 , 3_1(63) -> 62 1109.13/297.08 , 3_1(72) -> 71 1109.13/297.08 , 3_1(77) -> 98 1109.13/297.08 , 3_1(89) -> 88 1109.13/297.08 , 3_1(93) -> 92 1109.13/297.08 , 3_1(106) -> 105 1109.13/297.08 , 3_1(109) -> 108 1109.13/297.08 , 3_1(128) -> 43 1109.13/297.08 , 3_1(130) -> 77 1109.13/297.08 , 3_1(131) -> 130 1109.13/297.08 , 3_1(134) -> 133 1109.13/297.08 , 3_1(139) -> 138 1109.13/297.08 , 3_1(155) -> 154 1109.13/297.08 , 3_1(165) -> 164 1109.13/297.08 , 3_1(167) -> 166 1109.13/297.08 , 3_1(193) -> 192 1109.13/297.08 , 3_1(197) -> 196 1109.13/297.08 , 3_1(205) -> 204 1109.13/297.08 , 3_2(81) -> 80 1109.13/297.08 , 4_0(1) -> 1 1109.13/297.08 , 4_1(1) -> 7 1109.13/297.08 , 4_1(2) -> 7 1109.13/297.08 , 4_1(6) -> 104 1109.13/297.08 , 4_1(14) -> 61 1109.13/297.08 , 4_1(15) -> 9 1109.13/297.08 , 4_1(18) -> 7 1109.13/297.08 , 4_1(19) -> 18 1109.13/297.08 , 4_1(24) -> 23 1109.13/297.08 , 4_1(29) -> 28 1109.13/297.08 , 4_1(32) -> 31 1109.13/297.08 , 4_1(37) -> 36 1109.13/297.08 , 4_1(47) -> 2 1109.13/297.08 , 4_1(56) -> 55 1109.13/297.08 , 4_1(57) -> 56 1109.13/297.08 , 4_1(62) -> 45 1109.13/297.08 , 4_1(65) -> 64 1109.13/297.08 , 4_1(67) -> 66 1109.13/297.08 , 4_1(69) -> 68 1109.13/297.08 , 4_1(76) -> 172 1109.13/297.08 , 4_1(87) -> 86 1109.13/297.08 , 4_1(88) -> 87 1109.13/297.08 , 4_1(92) -> 91 1109.13/297.08 , 4_1(96) -> 151 1109.13/297.08 , 4_1(98) -> 97 1109.13/297.08 , 4_1(103) -> 102 1109.13/297.08 , 4_1(111) -> 110 1109.13/297.08 , 4_1(120) -> 119 1109.13/297.08 , 4_1(130) -> 1 1109.13/297.08 , 4_1(130) -> 7 1109.13/297.08 , 4_1(130) -> 61 1109.13/297.08 , 4_1(132) -> 131 1109.13/297.08 , 4_1(137) -> 136 1109.13/297.08 , 4_1(152) -> 151 1109.13/297.08 , 4_1(154) -> 153 1109.13/297.08 , 4_1(172) -> 171 1109.13/297.08 , 4_1(173) -> 62 1109.13/297.08 , 4_1(177) -> 176 1109.13/297.08 , 4_1(178) -> 177 1109.13/297.08 , 4_1(181) -> 180 1109.13/297.08 , 4_1(183) -> 182 1109.13/297.08 , 4_1(213) -> 212 1109.13/297.08 , 5_0(1) -> 1 1109.13/297.08 , 5_1(1) -> 34 1109.13/297.08 , 5_1(4) -> 3 1109.13/297.08 , 5_1(5) -> 4 1109.13/297.08 , 5_1(7) -> 60 1109.13/297.08 , 5_1(9) -> 8 1109.13/297.08 , 5_1(14) -> 46 1109.13/297.08 , 5_1(16) -> 15 1109.13/297.08 , 5_1(41) -> 127 1109.13/297.08 , 5_1(42) -> 34 1109.13/297.08 , 5_1(45) -> 1 1109.13/297.08 , 5_1(45) -> 5 1109.13/297.08 , 5_1(45) -> 17 1109.13/297.08 , 5_1(45) -> 34 1109.13/297.08 , 5_1(45) -> 60 1109.13/297.08 , 5_1(45) -> 129 1109.13/297.08 , 5_1(46) -> 45 1109.13/297.08 , 5_1(53) -> 52 1109.13/297.08 , 5_1(61) -> 60 1109.13/297.08 , 5_1(68) -> 67 1109.13/297.08 , 5_1(70) -> 69 1109.13/297.08 , 5_1(76) -> 4 1109.13/297.08 , 5_1(77) -> 167 1109.13/297.08 , 5_1(97) -> 96 1109.13/297.08 , 5_1(100) -> 99 1109.13/297.08 , 5_1(116) -> 115 1109.13/297.08 , 5_1(129) -> 128 1109.13/297.08 , 5_1(133) -> 132 1109.13/297.08 , 5_1(144) -> 143 1109.13/297.08 , 5_1(147) -> 130 1109.13/297.08 , 5_1(149) -> 148 1109.13/297.08 , 5_1(153) -> 152 1109.13/297.08 , 5_1(158) -> 157 1109.13/297.08 , 5_1(162) -> 161 1109.13/297.08 , 5_1(170) -> 169 1109.13/297.08 , 5_1(179) -> 178 1109.13/297.08 , 5_1(182) -> 181 1109.13/297.08 , 5_1(184) -> 183 1109.13/297.08 , 5_1(188) -> 187 1109.13/297.08 , 5_1(198) -> 197 } 1109.13/297.08 1109.13/297.08 Hurray, we answered YES(?,O(n^1)) 1109.84/297.57 EOF