YES(?,O(n^1)) 1142.04/297.07 YES(?,O(n^1)) 1142.04/297.07 1142.04/297.07 We are left with following problem, upon which TcT provides the 1142.04/297.07 certificate YES(?,O(n^1)). 1142.04/297.07 1142.04/297.07 Strict Trs: 1142.04/297.07 { 3(4(5(x1))) -> 3(2(3(2(1(5(3(5(2(2(x1)))))))))) 1142.04/297.07 , 3(4(5(3(x1)))) -> 3(2(3(2(1(4(1(0(3(2(x1)))))))))) 1142.04/297.07 , 3(4(5(0(0(x1))))) -> 4(3(3(1(2(5(0(4(3(0(x1)))))))))) 1142.04/297.07 , 3(4(0(5(0(1(x1)))))) -> 3(2(1(3(1(0(0(4(0(1(x1)))))))))) 1142.04/297.07 , 3(5(0(5(x1)))) -> 3(2(1(4(3(3(2(0(1(5(x1)))))))))) 1142.04/297.07 , 3(0(4(5(3(3(x1)))))) -> 4(2(0(5(4(2(1(0(0(3(x1)))))))))) 1142.04/297.07 , 4(3(5(0(5(5(x1)))))) -> 4(3(2(5(2(5(2(1(3(5(x1)))))))))) 1142.04/297.07 , 4(0(4(5(4(1(x1)))))) -> 4(4(3(1(1(1(4(0(1(1(x1)))))))))) 1142.04/297.07 , 4(0(5(5(x1)))) -> 3(3(2(2(2(0(3(5(3(5(x1)))))))))) 1142.04/297.07 , 4(0(5(0(5(4(5(x1))))))) -> 1(2(1(3(2(2(5(3(5(5(x1)))))))))) 1142.04/297.07 , 5(3(5(5(5(4(1(x1))))))) -> 0(1(2(0(4(3(2(5(4(1(x1)))))))))) 1142.04/297.07 , 5(4(5(4(1(x1))))) -> 1(5(3(4(1(0(4(2(0(1(x1)))))))))) 1142.04/297.07 , 5(4(5(5(3(3(4(x1))))))) -> 1(5(0(2(3(4(1(3(0(0(x1)))))))))) 1142.04/297.07 , 5(5(3(4(x1)))) -> 1(1(4(4(1(4(3(4(2(2(x1)))))))))) 1142.04/297.07 , 5(5(0(1(0(0(x1)))))) -> 5(0(4(2(4(4(2(2(4(0(x1)))))))))) 1142.04/297.07 , 5(2(3(5(2(x1))))) -> 5(2(2(1(2(0(5(2(2(2(x1)))))))))) 1142.04/297.07 , 2(3(4(3(4(5(3(x1))))))) -> 0(1(5(2(3(5(0(1(2(2(x1)))))))))) 1142.04/297.07 , 2(3(5(1(0(x1))))) -> 2(1(2(5(1(1(5(4(2(0(x1)))))))))) 1142.04/297.07 , 1(5(5(2(2(5(5(x1))))))) -> 1(0(4(2(5(3(1(5(1(5(x1)))))))))) 1142.04/297.07 , 1(2(3(5(4(4(x1)))))) -> 4(0(2(0(4(0(3(2(2(4(x1)))))))))) 1142.04/297.07 , 1(0(0(5(2(3(4(x1))))))) -> 2(4(1(4(5(3(2(1(0(4(x1)))))))))) 1142.04/297.07 , 0(4(5(3(x1)))) -> 4(0(3(2(3(1(1(5(0(5(x1)))))))))) 1142.04/297.07 , 0(5(4(3(4(5(x1)))))) -> 1(5(0(2(2(3(4(3(2(5(x1)))))))))) 1142.04/297.07 , 0(5(4(5(2(0(x1)))))) -> 0(2(2(5(3(3(2(2(2(0(x1)))))))))) 1142.04/297.07 , 0(5(4(1(x1)))) -> 0(1(4(1(5(1(2(2(0(1(x1)))))))))) 1142.04/297.07 , 0(5(5(5(2(3(3(x1))))))) -> 1(0(1(3(0(5(4(2(4(2(x1)))))))))) 1142.04/297.07 , 0(5(5(1(1(3(x1)))))) -> 0(5(0(3(2(1(4(1(4(2(x1)))))))))) 1142.04/297.07 , 0(5(5(1(0(x1))))) -> 0(2(4(5(3(1(5(1(4(0(x1)))))))))) 1142.04/297.07 , 0(5(5(1(0(5(x1)))))) -> 1(2(0(2(5(4(3(1(1(5(x1)))))))))) 1142.04/297.07 , 0(1(2(5(2(3(5(x1))))))) -> 4(4(3(1(4(0(5(1(5(5(x1)))))))))) 1142.04/297.07 , 0(0(5(3(5(3(0(x1))))))) -> 0(2(5(0(2(4(3(1(0(0(x1)))))))))) 1142.04/297.07 , 0(0(5(0(4(0(1(x1))))))) -> 5(1(4(4(2(0(3(3(4(1(x1)))))))))) 1142.04/297.07 , 0(0(5(0(5(5(x1)))))) -> 1(1(3(4(3(0(2(4(5(2(x1)))))))))) } 1142.04/297.07 Obligation: 1142.04/297.07 derivational complexity 1142.04/297.07 Answer: 1142.04/297.07 YES(?,O(n^1)) 1142.04/297.07 1142.04/297.07 The problem is match-bounded by 2. The enriched problem is 1142.04/297.07 compatible with the following automaton. 1142.04/297.07 { 3_0(1) -> 1 1142.04/297.07 , 3_1(1) -> 43 1142.04/297.07 , 3_1(2) -> 1 1142.04/297.07 , 3_1(2) -> 43 1142.04/297.07 , 3_1(2) -> 49 1142.04/297.07 , 3_1(2) -> 78 1142.04/297.07 , 3_1(2) -> 103 1142.04/297.07 , 3_1(2) -> 192 1142.04/297.07 , 3_1(4) -> 3 1142.04/297.07 , 3_1(8) -> 7 1142.04/297.07 , 3_1(9) -> 131 1142.04/297.07 , 3_1(10) -> 13 1142.04/297.07 , 3_1(15) -> 14 1142.04/297.07 , 3_1(16) -> 15 1142.04/297.07 , 3_1(22) -> 21 1142.04/297.07 , 3_1(24) -> 23 1142.04/297.07 , 3_1(31) -> 30 1142.04/297.07 , 3_1(32) -> 31 1142.04/297.07 , 3_1(35) -> 49 1142.04/297.07 , 3_1(40) -> 186 1142.04/297.07 , 3_1(41) -> 89 1142.04/297.07 , 3_1(51) -> 50 1142.04/297.07 , 3_1(57) -> 2 1142.04/297.07 , 3_1(62) -> 61 1142.04/297.07 , 3_1(66) -> 65 1142.04/297.07 , 3_1(70) -> 69 1142.04/297.07 , 3_1(76) -> 75 1142.04/297.07 , 3_1(78) -> 192 1142.04/297.07 , 3_1(80) -> 79 1142.04/297.07 , 3_1(87) -> 86 1142.04/297.07 , 3_1(95) -> 94 1142.04/297.07 , 3_1(101) -> 131 1142.04/297.07 , 3_1(112) -> 111 1142.04/297.07 , 3_1(125) -> 124 1142.04/297.07 , 3_1(136) -> 135 1142.04/297.07 , 3_1(139) -> 127 1142.04/297.07 , 3_1(141) -> 140 1142.04/297.07 , 3_1(146) -> 145 1142.04/297.07 , 3_1(148) -> 147 1142.04/297.07 , 3_1(152) -> 151 1142.04/297.07 , 3_1(153) -> 152 1142.04/297.07 , 3_1(159) -> 158 1142.04/297.07 , 3_1(166) -> 165 1142.04/297.07 , 3_1(172) -> 171 1142.04/297.07 , 3_1(179) -> 178 1142.04/297.07 , 3_1(192) -> 191 1142.04/297.07 , 3_1(193) -> 90 1142.04/297.07 , 3_1(195) -> 194 1142.04/297.07 , 3_2(199) -> 192 1142.04/297.07 , 3_2(201) -> 200 1142.04/297.07 , 3_2(205) -> 204 1142.04/297.07 , 3_2(208) -> 49 1142.04/297.07 , 3_2(208) -> 69 1142.04/297.07 , 3_2(212) -> 211 1142.04/297.07 , 3_2(213) -> 212 1142.04/297.07 , 4_0(1) -> 1 1142.04/297.07 , 4_1(1) -> 78 1142.04/297.07 , 4_1(9) -> 95 1142.04/297.07 , 4_1(10) -> 163 1142.04/297.07 , 4_1(11) -> 6 1142.04/297.07 , 4_1(14) -> 1 1142.04/297.07 , 4_1(14) -> 21 1142.04/297.07 , 4_1(14) -> 22 1142.04/297.07 , 4_1(14) -> 28 1142.04/297.07 , 4_1(14) -> 29 1142.04/297.07 , 4_1(14) -> 43 1142.04/297.07 , 4_1(14) -> 78 1142.04/297.07 , 4_1(14) -> 103 1142.04/297.07 , 4_1(14) -> 138 1142.04/297.07 , 4_1(14) -> 192 1142.04/297.07 , 4_1(21) -> 20 1142.04/297.07 , 4_1(22) -> 103 1142.04/297.07 , 4_1(28) -> 27 1142.04/297.07 , 4_1(29) -> 78 1142.04/297.07 , 4_1(30) -> 23 1142.04/297.07 , 4_1(39) -> 38 1142.04/297.07 , 4_1(50) -> 14 1142.04/297.07 , 4_1(55) -> 54 1142.04/297.07 , 4_1(63) -> 103 1142.04/297.07 , 4_1(71) -> 78 1142.04/297.07 , 4_1(75) -> 74 1142.04/297.07 , 4_1(81) -> 80 1142.04/297.07 , 4_1(84) -> 83 1142.04/297.07 , 4_1(88) -> 87 1142.04/297.07 , 4_1(91) -> 90 1142.04/297.07 , 4_1(92) -> 91 1142.04/297.07 , 4_1(94) -> 93 1142.04/297.07 , 4_1(98) -> 97 1142.04/297.07 , 4_1(100) -> 99 1142.04/297.07 , 4_1(101) -> 100 1142.04/297.07 , 4_1(122) -> 121 1142.04/297.07 , 4_1(130) -> 129 1142.04/297.07 , 4_1(132) -> 115 1142.04/297.07 , 4_1(134) -> 133 1142.04/297.07 , 4_1(147) -> 146 1142.04/297.07 , 4_1(155) -> 72 1142.04/297.07 , 4_1(162) -> 161 1142.04/297.07 , 4_1(169) -> 168 1142.04/297.07 , 4_1(170) -> 149 1142.04/297.07 , 4_1(178) -> 177 1142.04/297.07 , 4_1(180) -> 52 1142.04/297.07 , 4_1(186) -> 185 1142.04/297.07 , 4_1(188) -> 187 1142.04/297.07 , 4_1(189) -> 188 1142.04/297.07 , 4_1(194) -> 193 1142.04/297.07 , 4_1(198) -> 197 1142.04/297.07 , 4_2(211) -> 210 1142.04/297.07 , 5_0(1) -> 1 1142.04/297.07 , 5_1(1) -> 35 1142.04/297.07 , 5_1(2) -> 35 1142.04/297.07 , 5_1(7) -> 6 1142.04/297.07 , 5_1(9) -> 8 1142.04/297.07 , 5_1(10) -> 198 1142.04/297.07 , 5_1(19) -> 18 1142.04/297.07 , 5_1(34) -> 126 1142.04/297.07 , 5_1(35) -> 70 1142.04/297.07 , 5_1(38) -> 37 1142.04/297.07 , 5_1(45) -> 44 1142.04/297.07 , 5_1(47) -> 46 1142.04/297.07 , 5_1(49) -> 62 1142.04/297.07 , 5_1(69) -> 68 1142.04/297.07 , 5_1(78) -> 77 1142.04/297.07 , 5_1(79) -> 63 1142.04/297.07 , 5_1(83) -> 120 1142.04/297.07 , 5_1(95) -> 120 1142.04/297.07 , 5_1(96) -> 1 1142.04/297.07 , 5_1(96) -> 22 1142.04/297.07 , 5_1(96) -> 35 1142.04/297.07 , 5_1(96) -> 41 1142.04/297.07 , 5_1(96) -> 70 1142.04/297.07 , 5_1(96) -> 198 1142.04/297.07 , 5_1(109) -> 108 1142.04/297.07 , 5_1(110) -> 72 1142.04/297.07 , 5_1(113) -> 112 1142.04/297.07 , 5_1(118) -> 117 1142.04/297.07 , 5_1(124) -> 123 1142.04/297.07 , 5_1(135) -> 134 1142.04/297.07 , 5_1(144) -> 143 1142.04/297.07 , 5_1(151) -> 150 1142.04/297.07 , 5_1(157) -> 156 1142.04/297.07 , 5_1(161) -> 160 1142.04/297.07 , 5_1(164) -> 71 1142.04/297.07 , 5_1(171) -> 170 1142.04/297.07 , 5_1(174) -> 173 1142.04/297.07 , 5_1(177) -> 176 1142.04/297.07 , 5_1(182) -> 181 1142.04/297.07 , 5_1(183) -> 149 1142.04/297.07 , 5_2(164) -> 216 1142.04/297.07 , 5_2(204) -> 203 1142.04/297.07 , 5_2(206) -> 205 1142.04/297.07 , 2_0(1) -> 1 1142.04/297.07 , 2_1(1) -> 10 1142.04/297.07 , 2_1(2) -> 10 1142.04/297.07 , 2_1(3) -> 2 1142.04/297.07 , 2_1(5) -> 4 1142.04/297.07 , 2_1(9) -> 109 1142.04/297.07 , 2_1(10) -> 9 1142.04/297.07 , 2_1(14) -> 10 1142.04/297.07 , 2_1(18) -> 17 1142.04/297.07 , 2_1(22) -> 84 1142.04/297.07 , 2_1(28) -> 84 1142.04/297.07 , 2_1(33) -> 32 1142.04/297.07 , 2_1(35) -> 148 1142.04/297.07 , 2_1(36) -> 14 1142.04/297.07 , 2_1(40) -> 39 1142.04/297.07 , 2_1(44) -> 15 1142.04/297.07 , 2_1(46) -> 45 1142.04/297.07 , 2_1(48) -> 47 1142.04/297.07 , 2_1(57) -> 10 1142.04/297.07 , 2_1(58) -> 57 1142.04/297.07 , 2_1(59) -> 58 1142.04/297.07 , 2_1(60) -> 59 1142.04/297.07 , 2_1(63) -> 9 1142.04/297.07 , 2_1(64) -> 63 1142.04/297.07 , 2_1(67) -> 66 1142.04/297.07 , 2_1(68) -> 67 1142.04/297.07 , 2_1(73) -> 72 1142.04/297.07 , 2_1(77) -> 76 1142.04/297.07 , 2_1(78) -> 102 1142.04/297.07 , 2_1(84) -> 154 1142.04/297.07 , 2_1(86) -> 85 1142.04/297.07 , 2_1(96) -> 10 1142.04/297.07 , 2_1(99) -> 98 1142.04/297.07 , 2_1(102) -> 101 1142.04/297.07 , 2_1(103) -> 102 1142.04/297.07 , 2_1(104) -> 96 1142.04/297.07 , 2_1(105) -> 104 1142.04/297.07 , 2_1(107) -> 106 1142.04/297.07 , 2_1(111) -> 110 1142.04/297.07 , 2_1(115) -> 1 1142.04/297.07 , 2_1(115) -> 10 1142.04/297.07 , 2_1(115) -> 29 1142.04/297.07 , 2_1(115) -> 40 1142.04/297.07 , 2_1(117) -> 116 1142.04/297.07 , 2_1(123) -> 122 1142.04/297.07 , 2_1(128) -> 127 1142.04/297.07 , 2_1(137) -> 136 1142.04/297.07 , 2_1(140) -> 139 1142.04/297.07 , 2_1(145) -> 86 1142.04/297.07 , 2_1(149) -> 71 1142.04/297.07 , 2_1(150) -> 149 1142.04/297.07 , 2_1(154) -> 153 1142.04/297.07 , 2_1(163) -> 162 1142.04/297.07 , 2_1(167) -> 166 1142.04/297.07 , 2_1(176) -> 175 1142.04/297.07 , 2_1(185) -> 184 1142.04/297.07 , 2_1(190) -> 189 1142.04/297.07 , 2_1(193) -> 10 1142.04/297.07 , 2_1(197) -> 196 1142.04/297.07 , 2_2(96) -> 207 1142.04/297.07 , 2_2(164) -> 207 1142.04/297.07 , 2_2(200) -> 199 1142.04/297.07 , 2_2(202) -> 201 1142.04/297.07 , 2_2(207) -> 206 1142.04/297.07 , 2_2(209) -> 208 1142.04/297.07 , 2_2(214) -> 213 1142.04/297.07 , 1_0(1) -> 1 1142.04/297.07 , 1_1(1) -> 29 1142.04/297.07 , 1_1(6) -> 5 1142.04/297.07 , 1_1(9) -> 114 1142.04/297.07 , 1_1(12) -> 11 1142.04/297.07 , 1_1(17) -> 16 1142.04/297.07 , 1_1(23) -> 3 1142.04/297.07 , 1_1(25) -> 24 1142.04/297.07 , 1_1(28) -> 137 1142.04/297.07 , 1_1(29) -> 56 1142.04/297.07 , 1_1(34) -> 179 1142.04/297.07 , 1_1(35) -> 34 1142.04/297.07 , 1_1(41) -> 40 1142.04/297.07 , 1_1(49) -> 48 1142.04/297.07 , 1_1(52) -> 51 1142.04/297.07 , 1_1(53) -> 52 1142.04/297.07 , 1_1(54) -> 53 1142.04/297.07 , 1_1(63) -> 1 1142.04/297.07 , 1_1(63) -> 22 1142.04/297.07 , 1_1(63) -> 29 1142.04/297.07 , 1_1(63) -> 34 1142.04/297.07 , 1_1(63) -> 35 1142.04/297.07 , 1_1(63) -> 41 1142.04/297.07 , 1_1(63) -> 70 1142.04/297.07 , 1_1(63) -> 77 1142.04/297.07 , 1_1(63) -> 78 1142.04/297.07 , 1_1(63) -> 103 1142.04/297.07 , 1_1(63) -> 144 1142.04/297.07 , 1_1(63) -> 182 1142.04/297.07 , 1_1(65) -> 64 1142.04/297.07 , 1_1(70) -> 182 1142.04/297.07 , 1_1(71) -> 34 1142.04/297.07 , 1_1(72) -> 71 1142.04/297.07 , 1_1(82) -> 81 1142.04/297.07 , 1_1(89) -> 88 1142.04/297.07 , 1_1(90) -> 63 1142.04/297.07 , 1_1(93) -> 92 1142.04/297.07 , 1_1(103) -> 174 1142.04/297.07 , 1_1(106) -> 105 1142.04/297.07 , 1_1(116) -> 115 1142.04/297.07 , 1_1(119) -> 118 1142.04/297.07 , 1_1(120) -> 119 1142.04/297.07 , 1_1(126) -> 125 1142.04/297.07 , 1_1(133) -> 132 1142.04/297.07 , 1_1(138) -> 137 1142.04/297.07 , 1_1(142) -> 141 1142.04/297.07 , 1_1(143) -> 142 1142.04/297.07 , 1_1(154) -> 157 1142.04/297.07 , 1_1(156) -> 155 1142.04/297.07 , 1_1(158) -> 121 1142.04/297.07 , 1_1(163) -> 169 1142.04/297.07 , 1_1(168) -> 167 1142.04/297.07 , 1_1(173) -> 172 1142.04/297.07 , 1_1(187) -> 96 1142.04/297.07 , 1_2(203) -> 202 1142.04/297.07 , 1_2(210) -> 209 1142.04/297.07 , 1_2(216) -> 215 1142.04/297.07 , 0_0(1) -> 1 1142.04/297.07 , 0_1(1) -> 22 1142.04/297.07 , 0_1(2) -> 22 1142.04/297.07 , 0_1(8) -> 107 1142.04/297.07 , 0_1(13) -> 12 1142.04/297.07 , 0_1(14) -> 22 1142.04/297.07 , 0_1(20) -> 19 1142.04/297.07 , 0_1(22) -> 41 1142.04/297.07 , 0_1(26) -> 25 1142.04/297.07 , 0_1(27) -> 26 1142.04/297.07 , 0_1(29) -> 28 1142.04/297.07 , 0_1(34) -> 33 1142.04/297.07 , 0_1(35) -> 144 1142.04/297.07 , 0_1(37) -> 36 1142.04/297.07 , 0_1(42) -> 41 1142.04/297.07 , 0_1(43) -> 42 1142.04/297.07 , 0_1(56) -> 55 1142.04/297.07 , 0_1(61) -> 60 1142.04/297.07 , 0_1(71) -> 1 1142.04/297.07 , 0_1(71) -> 10 1142.04/297.07 , 0_1(71) -> 22 1142.04/297.07 , 0_1(71) -> 35 1142.04/297.07 , 0_1(71) -> 41 1142.04/297.07 , 0_1(71) -> 62 1142.04/297.07 , 0_1(71) -> 68 1142.04/297.07 , 0_1(71) -> 144 1142.04/297.07 , 0_1(74) -> 73 1142.04/297.07 , 0_1(78) -> 138 1142.04/297.07 , 0_1(83) -> 82 1142.04/297.07 , 0_1(85) -> 79 1142.04/297.07 , 0_1(97) -> 96 1142.04/297.07 , 0_1(108) -> 107 1142.04/297.07 , 0_1(114) -> 113 1142.04/297.07 , 0_1(121) -> 63 1142.04/297.07 , 0_1(127) -> 14 1142.04/297.07 , 0_1(129) -> 128 1142.04/297.07 , 0_1(131) -> 130 1142.04/297.07 , 0_1(138) -> 25 1142.04/297.07 , 0_1(160) -> 159 1142.04/297.07 , 0_1(165) -> 164 1142.04/297.07 , 0_1(175) -> 64 1142.04/297.07 , 0_1(181) -> 180 1142.04/297.07 , 0_1(184) -> 183 1142.04/297.07 , 0_1(191) -> 190 1142.04/297.07 , 0_1(196) -> 195 1142.04/297.07 , 0_2(215) -> 214 } 1142.04/297.07 1142.04/297.07 Hurray, we answered YES(?,O(n^1)) 1143.10/297.90 EOF