YES(?,O(n^1)) 1120.14/297.09 YES(?,O(n^1)) 1120.14/297.09 1120.14/297.09 We are left with following problem, upon which TcT provides the 1120.14/297.09 certificate YES(?,O(n^1)). 1120.14/297.09 1120.14/297.09 Strict Trs: 1120.14/297.09 { 1(0(4(0(x1)))) -> 2(2(2(3(3(1(5(5(2(0(x1)))))))))) 1120.14/297.09 , 1(0(4(0(4(0(5(x1))))))) -> 2(2(2(2(3(5(4(2(2(4(x1)))))))))) 1120.14/297.09 , 1(0(4(2(4(2(4(x1))))))) -> 1(2(0(0(4(4(2(2(2(2(x1)))))))))) 1120.14/297.09 , 1(0(5(0(4(3(4(x1))))))) -> 0(4(5(3(5(2(0(3(1(2(x1)))))))))) 1120.14/297.09 , 1(0(5(5(0(4(2(x1))))))) -> 1(0(2(1(5(4(5(2(0(2(x1)))))))))) 1120.14/297.09 , 1(4(2(5(2(x1))))) -> 4(3(5(0(2(2(0(0(5(3(x1)))))))))) 1120.14/297.09 , 1(2(4(4(2(4(0(x1))))))) -> 0(2(4(2(3(0(4(3(4(3(x1)))))))))) 1120.14/297.09 , 1(5(4(0(1(1(x1)))))) -> 4(3(4(4(0(0(0(5(3(3(x1)))))))))) 1120.14/297.09 , 0(1(1(1(3(0(1(x1))))))) -> 4(2(2(3(3(0(4(0(0(3(x1)))))))))) 1120.14/297.09 , 0(0(5(1(2(5(1(x1))))))) -> 0(1(2(4(3(5(0(1(3(3(x1)))))))))) 1120.14/297.09 , 0(0(5(0(4(0(5(x1))))))) -> 0(5(5(3(5(3(0(5(2(5(x1)))))))))) 1120.14/297.09 , 0(0(5(5(5(0(5(x1))))))) -> 0(1(2(3(5(3(0(0(4(1(x1)))))))))) 1120.14/297.09 , 0(4(1(2(5(0(5(x1))))))) -> 2(0(1(5(1(5(0(2(0(5(x1)))))))))) 1120.14/297.09 , 0(4(1(5(5(x1))))) -> 2(4(2(0(2(4(3(0(1(5(x1)))))))))) 1120.14/297.09 , 0(4(2(4(2(3(4(x1))))))) -> 2(0(0(0(5(5(2(0(4(4(x1)))))))))) 1120.14/297.09 , 0(3(1(0(3(1(1(x1))))))) -> 0(3(5(3(5(4(4(5(4(0(x1)))))))))) 1120.14/297.09 , 0(5(0(1(1(3(x1)))))) -> 0(2(5(3(4(3(1(0(1(3(x1)))))))))) 1120.14/297.09 , 0(5(0(3(5(2(0(x1))))))) -> 2(2(3(3(1(4(2(2(0(2(x1)))))))))) 1120.14/297.09 , 0(5(0(5(2(5(x1)))))) -> 4(2(0(0(2(5(1(3(4(1(x1)))))))))) 1120.14/297.09 , 4(1(3(0(4(0(x1)))))) -> 5(0(1(2(3(1(2(3(5(2(x1)))))))))) 1120.14/297.09 , 2(1(1(4(4(1(4(x1))))))) -> 4(2(4(3(4(3(5(4(5(4(x1)))))))))) 1120.14/297.09 , 2(4(1(3(1(4(x1)))))) -> 5(5(3(4(3(2(1(4(4(4(x1)))))))))) 1120.14/297.09 , 2(4(0(1(0(4(x1)))))) -> 0(2(3(3(3(3(5(0(2(5(x1)))))))))) 1120.14/297.09 , 2(4(2(3(3(4(1(x1))))))) -> 4(4(3(5(4(0(2(2(4(4(x1)))))))))) 1120.14/297.09 , 2(5(2(5(4(0(x1)))))) -> 4(2(5(3(5(5(2(2(3(0(x1)))))))))) 1120.14/297.09 , 3(1(0(3(0(x1))))) -> 3(2(2(2(4(3(3(5(2(0(x1)))))))))) 1120.14/297.09 , 3(4(0(5(2(3(5(x1))))))) -> 3(3(5(0(0(2(2(3(3(5(x1)))))))))) 1120.14/297.09 , 3(4(2(0(5(1(2(x1))))))) -> 3(3(3(3(3(2(0(1(5(3(x1)))))))))) 1120.14/297.09 , 3(4(2(4(2(5(x1)))))) -> 3(5(2(2(0(5(2(4(3(2(x1)))))))))) 1120.14/297.09 , 5(0(1(4(3(x1))))) -> 3(5(4(2(2(0(4(3(3(0(x1)))))))))) 1120.14/297.09 , 5(4(3(2(4(0(x1)))))) -> 5(0(1(2(0(2(2(3(0(2(x1)))))))))) 1120.14/297.09 , 5(5(0(4(0(3(x1)))))) -> 5(2(2(2(2(2(4(4(3(2(x1)))))))))) 1120.14/297.09 , 5(5(5(5(2(x1))))) -> 5(2(2(0(3(3(1(5(0(0(x1)))))))))) } 1120.14/297.09 Obligation: 1120.14/297.09 derivational complexity 1120.14/297.09 Answer: 1120.14/297.09 YES(?,O(n^1)) 1120.14/297.09 1120.14/297.09 The problem is match-bounded by 2. The enriched problem is 1120.14/297.09 compatible with the following automaton. 1120.14/297.09 { 1_0(1) -> 1 1120.14/297.09 , 1_1(1) -> 89 1120.14/297.09 , 1_1(7) -> 6 1120.14/297.09 , 1_1(17) -> 1 1120.14/297.09 , 1_1(17) -> 89 1120.14/297.09 , 1_1(25) -> 33 1120.14/297.09 , 1_1(36) -> 35 1120.14/297.09 , 1_1(48) -> 186 1120.14/297.09 , 1_1(49) -> 122 1120.14/297.09 , 1_1(62) -> 75 1120.14/297.09 , 1_1(70) -> 26 1120.14/297.09 , 1_1(76) -> 89 1120.14/297.09 , 1_1(83) -> 103 1120.14/297.09 , 1_1(91) -> 90 1120.14/297.09 , 1_1(93) -> 92 1120.14/297.09 , 1_1(109) -> 150 1120.14/297.09 , 1_1(121) -> 120 1120.14/297.09 , 1_1(125) -> 124 1120.14/297.09 , 1_1(131) -> 130 1120.14/297.09 , 1_1(132) -> 89 1120.14/297.09 , 1_1(134) -> 133 1120.14/297.09 , 1_1(137) -> 136 1120.14/297.09 , 1_1(151) -> 150 1120.14/297.09 , 1_1(210) -> 209 1120.14/297.09 , 1_2(220) -> 219 1120.14/297.09 , 0_0(1) -> 1 1120.14/297.09 , 0_1(1) -> 10 1120.14/297.09 , 0_1(2) -> 10 1120.14/297.09 , 0_1(10) -> 211 1120.14/297.09 , 0_1(16) -> 108 1120.14/297.09 , 0_1(17) -> 10 1120.14/297.09 , 0_1(19) -> 18 1120.14/297.09 , 0_1(20) -> 19 1120.14/297.09 , 0_1(25) -> 40 1120.14/297.09 , 0_1(26) -> 1 1120.14/297.09 , 0_1(26) -> 10 1120.14/297.09 , 0_1(26) -> 15 1120.14/297.09 , 0_1(26) -> 25 1120.14/297.09 , 0_1(26) -> 33 1120.14/297.09 , 0_1(26) -> 69 1120.14/297.09 , 0_1(26) -> 89 1120.14/297.09 , 0_1(26) -> 96 1120.14/297.09 , 0_1(26) -> 211 1120.14/297.09 , 0_1(32) -> 31 1120.14/297.09 , 0_1(34) -> 17 1120.14/297.09 , 0_1(41) -> 10 1120.14/297.09 , 0_1(42) -> 10 1120.14/297.09 , 0_1(44) -> 43 1120.14/297.09 , 0_1(47) -> 46 1120.14/297.09 , 0_1(48) -> 47 1120.14/297.09 , 0_1(49) -> 69 1120.14/297.09 , 0_1(54) -> 53 1120.14/297.09 , 0_1(59) -> 58 1120.14/297.09 , 0_1(60) -> 59 1120.14/297.09 , 0_1(61) -> 60 1120.14/297.09 , 0_1(67) -> 66 1120.14/297.09 , 0_1(69) -> 68 1120.14/297.09 , 0_1(75) -> 74 1120.14/297.09 , 0_1(81) -> 80 1120.14/297.09 , 0_1(82) -> 156 1120.14/297.09 , 0_1(83) -> 96 1120.14/297.09 , 0_1(87) -> 86 1120.14/297.09 , 0_1(88) -> 87 1120.14/297.09 , 0_1(89) -> 102 1120.14/297.09 , 0_1(90) -> 2 1120.14/297.09 , 0_1(95) -> 94 1120.14/297.09 , 0_1(99) -> 98 1120.14/297.09 , 0_1(103) -> 102 1120.14/297.09 , 0_1(104) -> 90 1120.14/297.09 , 0_1(105) -> 104 1120.14/297.09 , 0_1(109) -> 108 1120.14/297.09 , 0_1(122) -> 121 1120.14/297.09 , 0_1(127) -> 63 1120.14/297.09 , 0_1(128) -> 127 1120.14/297.09 , 0_1(133) -> 132 1120.14/297.09 , 0_1(139) -> 80 1120.14/297.09 , 0_1(161) -> 160 1120.14/297.09 , 0_1(169) -> 10 1120.14/297.09 , 0_1(177) -> 176 1120.14/297.09 , 0_1(178) -> 177 1120.14/297.09 , 0_1(186) -> 185 1120.14/297.09 , 0_1(190) -> 189 1120.14/297.09 , 0_1(197) -> 196 1120.14/297.09 , 0_1(199) -> 135 1120.14/297.09 , 0_1(202) -> 10 1120.14/297.09 , 0_1(207) -> 203 1120.14/297.09 , 0_2(215) -> 214 1120.14/297.09 , 0_2(219) -> 218 1120.14/297.09 , 4_0(1) -> 1 1120.14/297.09 , 4_1(1) -> 16 1120.14/297.09 , 4_1(8) -> 37 1120.14/297.09 , 4_1(10) -> 116 1120.14/297.09 , 4_1(14) -> 13 1120.14/297.09 , 4_1(16) -> 109 1120.14/297.09 , 4_1(17) -> 16 1120.14/297.09 , 4_1(21) -> 20 1120.14/297.09 , 4_1(22) -> 21 1120.14/297.09 , 4_1(27) -> 26 1120.14/297.09 , 4_1(38) -> 37 1120.14/297.09 , 4_1(41) -> 1 1120.14/297.09 , 4_1(41) -> 10 1120.14/297.09 , 4_1(41) -> 15 1120.14/297.09 , 4_1(41) -> 25 1120.14/297.09 , 4_1(41) -> 82 1120.14/297.09 , 4_1(41) -> 89 1120.14/297.09 , 4_1(41) -> 96 1120.14/297.09 , 4_1(41) -> 102 1120.14/297.09 , 4_1(41) -> 103 1120.14/297.09 , 4_1(49) -> 56 1120.14/297.09 , 4_1(51) -> 50 1120.14/297.09 , 4_1(55) -> 54 1120.14/297.09 , 4_1(57) -> 42 1120.14/297.09 , 4_1(58) -> 57 1120.14/297.09 , 4_1(68) -> 67 1120.14/297.09 , 4_1(72) -> 71 1120.14/297.09 , 4_1(76) -> 16 1120.14/297.09 , 4_1(89) -> 88 1120.14/297.09 , 4_1(97) -> 2 1120.14/297.09 , 4_1(101) -> 100 1120.14/297.09 , 4_1(109) -> 151 1120.14/297.09 , 4_1(114) -> 113 1120.14/297.09 , 4_1(115) -> 114 1120.14/297.09 , 4_1(119) -> 118 1120.14/297.09 , 4_1(126) -> 125 1120.14/297.09 , 4_1(132) -> 16 1120.14/297.09 , 4_1(139) -> 144 1120.14/297.09 , 4_1(140) -> 63 1120.14/297.09 , 4_1(142) -> 141 1120.14/297.09 , 4_1(145) -> 144 1120.14/297.09 , 4_1(148) -> 147 1120.14/297.09 , 4_1(157) -> 41 1120.14/297.09 , 4_1(160) -> 159 1120.14/297.09 , 4_1(173) -> 172 1120.14/297.09 , 4_1(192) -> 206 1120.14/297.09 , 4_1(193) -> 192 1120.14/297.09 , 4_1(194) -> 187 1120.14/297.09 , 4_1(198) -> 197 1120.14/297.09 , 4_2(213) -> 212 1120.14/297.09 , 4_2(217) -> 216 1120.14/297.09 , 2_0(1) -> 1 1120.14/297.09 , 2_1(1) -> 25 1120.14/297.09 , 2_1(2) -> 1 1120.14/297.09 , 2_1(2) -> 10 1120.14/297.09 , 2_1(2) -> 87 1120.14/297.09 , 2_1(2) -> 89 1120.14/297.09 , 2_1(2) -> 96 1120.14/297.09 , 2_1(2) -> 108 1120.14/297.09 , 2_1(3) -> 2 1120.14/297.09 , 2_1(4) -> 3 1120.14/297.09 , 2_1(10) -> 9 1120.14/297.09 , 2_1(11) -> 4 1120.14/297.09 , 2_1(15) -> 14 1120.14/297.09 , 2_1(16) -> 15 1120.14/297.09 , 2_1(18) -> 17 1120.14/297.09 , 2_1(23) -> 22 1120.14/297.09 , 2_1(24) -> 23 1120.14/297.09 , 2_1(25) -> 24 1120.14/297.09 , 2_1(26) -> 25 1120.14/297.09 , 2_1(31) -> 30 1120.14/297.09 , 2_1(35) -> 34 1120.14/297.09 , 2_1(39) -> 126 1120.14/297.09 , 2_1(40) -> 39 1120.14/297.09 , 2_1(41) -> 25 1120.14/297.09 , 2_1(45) -> 44 1120.14/297.09 , 2_1(46) -> 45 1120.14/297.09 , 2_1(50) -> 26 1120.14/297.09 , 2_1(52) -> 51 1120.14/297.09 , 2_1(57) -> 25 1120.14/297.09 , 2_1(62) -> 179 1120.14/297.09 , 2_1(63) -> 41 1120.14/297.09 , 2_1(64) -> 63 1120.14/297.09 , 2_1(70) -> 25 1120.14/297.09 , 2_1(71) -> 70 1120.14/297.09 , 2_1(83) -> 82 1120.14/297.09 , 2_1(90) -> 25 1120.14/297.09 , 2_1(96) -> 95 1120.14/297.09 , 2_1(97) -> 25 1120.14/297.09 , 2_1(98) -> 97 1120.14/297.09 , 2_1(100) -> 99 1120.14/297.09 , 2_1(108) -> 107 1120.14/297.09 , 2_1(109) -> 162 1120.14/297.09 , 2_1(110) -> 25 1120.14/297.09 , 2_1(129) -> 128 1120.14/297.09 , 2_1(132) -> 25 1120.14/297.09 , 2_1(135) -> 134 1120.14/297.09 , 2_1(138) -> 137 1120.14/297.09 , 2_1(140) -> 25 1120.14/297.09 , 2_1(150) -> 149 1120.14/297.09 , 2_1(162) -> 161 1120.14/297.09 , 2_1(163) -> 25 1120.14/297.09 , 2_1(167) -> 166 1120.14/297.09 , 2_1(168) -> 167 1120.14/297.09 , 2_1(169) -> 25 1120.14/297.09 , 2_1(170) -> 169 1120.14/297.09 , 2_1(171) -> 170 1120.14/297.09 , 2_1(172) -> 171 1120.14/297.09 , 2_1(179) -> 178 1120.14/297.09 , 2_1(180) -> 179 1120.14/297.09 , 2_1(185) -> 184 1120.14/297.09 , 2_1(188) -> 187 1120.14/297.09 , 2_1(189) -> 188 1120.14/297.09 , 2_1(192) -> 191 1120.14/297.09 , 2_1(195) -> 194 1120.14/297.09 , 2_1(196) -> 195 1120.14/297.09 , 2_1(200) -> 199 1120.14/297.09 , 2_1(201) -> 200 1120.14/297.09 , 2_1(202) -> 132 1120.14/297.09 , 2_1(203) -> 202 1120.14/297.09 , 2_1(204) -> 203 1120.14/297.09 , 2_1(205) -> 204 1120.14/297.09 , 2_1(206) -> 205 1120.14/297.09 , 2_2(212) -> 87 1120.14/297.09 , 2_2(214) -> 213 1120.14/297.09 , 2_2(216) -> 215 1120.14/297.09 , 3_0(1) -> 1 1120.14/297.09 , 3_1(1) -> 49 1120.14/297.09 , 3_1(2) -> 49 1120.14/297.09 , 3_1(5) -> 4 1120.14/297.09 , 3_1(6) -> 5 1120.14/297.09 , 3_1(8) -> 174 1120.14/297.09 , 3_1(10) -> 168 1120.14/297.09 , 3_1(12) -> 11 1120.14/297.09 , 3_1(17) -> 49 1120.14/297.09 , 3_1(18) -> 49 1120.14/297.09 , 3_1(25) -> 193 1120.14/297.09 , 3_1(26) -> 49 1120.14/297.09 , 3_1(29) -> 28 1120.14/297.09 , 3_1(33) -> 32 1120.14/297.09 , 3_1(40) -> 201 1120.14/297.09 , 3_1(42) -> 41 1120.14/297.09 , 3_1(49) -> 62 1120.14/297.09 , 3_1(53) -> 52 1120.14/297.09 , 3_1(56) -> 55 1120.14/297.09 , 3_1(65) -> 64 1120.14/297.09 , 3_1(66) -> 65 1120.14/297.09 , 3_1(70) -> 26 1120.14/297.09 , 3_1(73) -> 72 1120.14/297.09 , 3_1(78) -> 77 1120.14/297.09 , 3_1(80) -> 79 1120.14/297.09 , 3_1(83) -> 181 1120.14/297.09 , 3_1(84) -> 71 1120.14/297.09 , 3_1(86) -> 85 1120.14/297.09 , 3_1(88) -> 131 1120.14/297.09 , 3_1(102) -> 101 1120.14/297.09 , 3_1(110) -> 26 1120.14/297.09 , 3_1(112) -> 111 1120.14/297.09 , 3_1(118) -> 117 1120.14/297.09 , 3_1(120) -> 119 1120.14/297.09 , 3_1(123) -> 3 1120.14/297.09 , 3_1(124) -> 123 1120.14/297.09 , 3_1(136) -> 135 1120.14/297.09 , 3_1(139) -> 138 1120.14/297.09 , 3_1(141) -> 140 1120.14/297.09 , 3_1(143) -> 142 1120.14/297.09 , 3_1(147) -> 146 1120.14/297.09 , 3_1(149) -> 148 1120.14/297.09 , 3_1(152) -> 50 1120.14/297.09 , 3_1(153) -> 152 1120.14/297.09 , 3_1(154) -> 153 1120.14/297.09 , 3_1(155) -> 154 1120.14/297.09 , 3_1(158) -> 157 1120.14/297.09 , 3_1(164) -> 163 1120.14/297.09 , 3_1(168) -> 198 1120.14/297.09 , 3_1(169) -> 1 1120.14/297.09 , 3_1(169) -> 49 1120.14/297.09 , 3_1(169) -> 83 1120.14/297.09 , 3_1(174) -> 173 1120.14/297.09 , 3_1(175) -> 169 1120.14/297.09 , 3_1(181) -> 180 1120.14/297.09 , 3_1(182) -> 175 1120.14/297.09 , 3_1(183) -> 182 1120.14/297.09 , 3_1(184) -> 183 1120.14/297.09 , 3_1(202) -> 49 1120.14/297.09 , 3_1(208) -> 207 1120.14/297.09 , 3_1(209) -> 208 1120.14/297.09 , 3_2(218) -> 217 1120.14/297.09 , 5_0(1) -> 1 1120.14/297.09 , 5_1(1) -> 83 1120.14/297.09 , 5_1(8) -> 7 1120.14/297.09 , 5_1(9) -> 8 1120.14/297.09 , 5_1(13) -> 12 1120.14/297.09 , 5_1(16) -> 145 1120.14/297.09 , 5_1(25) -> 139 1120.14/297.09 , 5_1(27) -> 83 1120.14/297.09 , 5_1(28) -> 27 1120.14/297.09 , 5_1(30) -> 29 1120.14/297.09 , 5_1(37) -> 36 1120.14/297.09 , 5_1(39) -> 38 1120.14/297.09 , 5_1(40) -> 93 1120.14/297.09 , 5_1(41) -> 83 1120.14/297.09 , 5_1(43) -> 42 1120.14/297.09 , 5_1(49) -> 48 1120.14/297.09 , 5_1(62) -> 61 1120.14/297.09 , 5_1(74) -> 73 1120.14/297.09 , 5_1(76) -> 26 1120.14/297.09 , 5_1(77) -> 76 1120.14/297.09 , 5_1(79) -> 78 1120.14/297.09 , 5_1(82) -> 81 1120.14/297.09 , 5_1(85) -> 84 1120.14/297.09 , 5_1(92) -> 91 1120.14/297.09 , 5_1(94) -> 93 1120.14/297.09 , 5_1(106) -> 105 1120.14/297.09 , 5_1(107) -> 106 1120.14/297.09 , 5_1(111) -> 110 1120.14/297.09 , 5_1(113) -> 112 1120.14/297.09 , 5_1(116) -> 115 1120.14/297.09 , 5_1(117) -> 50 1120.14/297.09 , 5_1(130) -> 129 1120.14/297.09 , 5_1(132) -> 1 1120.14/297.09 , 5_1(132) -> 15 1120.14/297.09 , 5_1(132) -> 16 1120.14/297.09 , 5_1(132) -> 25 1120.14/297.09 , 5_1(132) -> 83 1120.14/297.09 , 5_1(132) -> 88 1120.14/297.09 , 5_1(132) -> 145 1120.14/297.09 , 5_1(144) -> 143 1120.14/297.09 , 5_1(146) -> 132 1120.14/297.09 , 5_1(156) -> 155 1120.14/297.09 , 5_1(159) -> 158 1120.14/297.09 , 5_1(163) -> 63 1120.14/297.09 , 5_1(165) -> 164 1120.14/297.09 , 5_1(166) -> 165 1120.14/297.09 , 5_1(176) -> 175 1120.14/297.09 , 5_1(187) -> 169 1120.14/297.09 , 5_1(191) -> 190 1120.14/297.09 , 5_1(211) -> 210 1120.14/297.09 , 5_2(146) -> 220 } 1120.14/297.09 1120.14/297.09 Hurray, we answered YES(?,O(n^1)) 1121.29/297.97 EOF