YES(?,O(n^1)) 1133.86/298.09 YES(?,O(n^1)) 1133.86/298.09 1133.86/298.09 We are left with following problem, upon which TcT provides the 1133.86/298.09 certificate YES(?,O(n^1)). 1133.86/298.09 1133.86/298.09 Strict Trs: 1133.86/298.09 { 0(0(5(2(2(0(x1)))))) -> 3(5(0(3(2(x1))))) 1133.86/298.09 , 0(1(2(2(x1)))) -> 3(3(2(x1))) 1133.86/298.09 , 0(4(4(2(5(4(5(0(3(5(3(4(3(1(4(1(2(1(0(x1))))))))))))))))))) -> 1133.86/298.09 3(0(4(0(2(0(5(3(2(5(3(4(4(3(4(4(3(4(x1)))))))))))))))))) 1133.86/298.09 , 0(5(1(5(4(0(4(1(0(x1))))))))) -> 2(4(2(1(1(2(5(5(x1)))))))) 1133.86/298.09 , 1(1(1(5(1(0(5(3(1(5(4(4(0(0(x1)))))))))))))) -> 1133.86/298.09 5(5(2(4(4(0(4(0(5(0(4(2(4(5(x1)))))))))))))) 1133.86/298.09 , 1(1(5(4(0(2(0(3(4(0(2(x1))))))))))) -> 1133.86/298.09 1(5(0(4(2(2(0(0(3(0(1(x1))))))))))) 1133.86/298.09 , 1(4(1(2(3(5(3(0(0(5(3(4(2(2(2(5(2(1(x1)))))))))))))))))) -> 1133.86/298.09 1(5(4(4(3(4(1(0(3(4(5(0(0(5(5(1(2(5(x1)))))))))))))))))) 1133.86/298.09 , 1(4(3(0(0(5(1(4(3(x1))))))))) -> 5(4(2(5(2(2(4(3(x1)))))))) 1133.86/298.09 , 2(0(1(2(0(3(x1)))))) -> 2(5(3(2(3(x1))))) 1133.86/298.09 , 2(1(5(4(3(5(0(1(2(1(4(5(0(1(2(2(3(4(x1)))))))))))))))))) -> 1133.86/298.09 0(0(0(0(4(5(2(0(2(0(1(2(5(1(5(2(1(4(x1)))))))))))))))))) 1133.86/298.09 , 2(5(2(3(4(0(0(4(4(3(x1)))))))))) -> 3(0(3(5(2(1(2(2(3(x1))))))))) 1133.86/298.09 , 3(3(1(4(4(2(2(1(1(3(4(x1))))))))))) -> 1133.86/298.09 3(3(3(5(5(5(4(1(2(3(x1)))))))))) 1133.86/298.09 , 4(0(0(5(2(4(3(4(3(4(4(0(0(3(x1)))))))))))))) -> 1133.86/298.09 3(0(3(4(0(1(2(4(0(5(2(5(3(x1))))))))))))) 1133.86/298.09 , 4(0(1(5(3(3(4(0(4(4(4(5(4(0(2(x1))))))))))))))) -> 1133.86/298.09 4(4(0(1(5(5(3(1(3(4(1(4(4(4(1(x1))))))))))))))) 1133.86/298.09 , 4(1(1(0(2(x1))))) -> 0(3(2(0(x1)))) 1133.86/298.09 , 4(1(5(0(3(4(0(3(2(5(5(0(4(0(0(3(x1)))))))))))))))) -> 1133.86/298.09 2(1(3(3(4(2(1(4(3(0(0(0(1(2(3(x1))))))))))))))) 1133.86/298.09 , 4(2(1(3(2(4(4(2(4(2(x1)))))))))) -> 1133.86/298.09 3(0(3(3(4(1(3(4(2(2(x1)))))))))) 1133.86/298.09 , 4(2(4(5(0(4(0(5(3(1(0(5(3(x1))))))))))))) -> 1133.86/298.09 4(0(4(5(5(0(3(0(5(5(5(4(x1)))))))))))) 1133.86/298.09 , 4(2(5(0(2(3(3(2(1(4(0(2(4(0(2(5(3(4(x1)))))))))))))))))) -> 1133.86/298.09 4(0(2(4(5(2(2(1(0(2(3(0(5(1(4(5(2(4(x1)))))))))))))))))) 1133.86/298.09 , 4(4(2(0(3(1(2(0(0(0(1(x1))))))))))) -> 1133.86/298.09 4(0(0(3(3(1(1(5(0(1(x1)))))))))) 1133.86/298.09 , 4(4(4(3(1(1(3(0(3(0(3(x1))))))))))) -> 1133.86/298.09 1(4(3(4(4(3(5(3(0(3(x1)))))))))) 1133.86/298.09 , 4(5(2(1(1(3(3(5(4(4(4(4(3(3(4(0(2(1(4(2(2(x1))))))))))))))))))))) 1133.86/298.09 -> 2(1(4(3(1(3(1(1(1(2(3(4(3(4(4(2(3(0(2(1(x1)))))))))))))))))))) 1133.86/298.09 , 4(5(3(4(5(x1))))) -> 2(3(1(5(x1)))) 1133.86/298.09 , 4(5(4(0(3(0(2(1(5(5(4(2(2(x1))))))))))))) -> 1133.86/298.09 2(1(0(0(1(2(0(0(4(0(1(2(3(3(x1)))))))))))))) 1133.86/298.09 , 5(2(5(0(1(1(3(0(4(4(2(4(3(2(x1)))))))))))))) -> 1133.86/298.09 5(3(2(0(1(2(5(1(2(2(5(1(3(x1))))))))))))) } 1133.86/298.09 Obligation: 1133.86/298.09 derivational complexity 1133.86/298.09 Answer: 1133.86/298.09 YES(?,O(n^1)) 1133.86/298.09 1133.86/298.09 The problem is match-bounded by 2. The enriched problem is 1133.86/298.09 compatible with the following automaton. 1133.86/298.09 { 0_0(1) -> 1 1133.86/298.09 , 0_1(1) -> 168 1133.86/298.09 , 0_1(4) -> 3 1133.86/298.09 , 0_1(6) -> 2 1133.86/298.09 , 0_1(9) -> 8 1133.86/298.09 , 0_1(11) -> 10 1133.86/298.09 , 0_1(38) -> 168 1133.86/298.09 , 0_1(50) -> 49 1133.86/298.09 , 0_1(52) -> 51 1133.86/298.09 , 0_1(54) -> 53 1133.86/298.09 , 0_1(59) -> 58 1133.86/298.09 , 0_1(63) -> 62 1133.86/298.09 , 0_1(64) -> 63 1133.86/298.09 , 0_1(66) -> 65 1133.86/298.09 , 0_1(72) -> 71 1133.86/298.09 , 0_1(76) -> 75 1133.86/298.09 , 0_1(77) -> 76 1133.86/298.09 , 0_1(86) -> 229 1133.86/298.09 , 0_1(89) -> 1 1133.86/298.09 , 0_1(89) -> 5 1133.86/298.09 , 0_1(89) -> 29 1133.86/298.09 , 0_1(89) -> 166 1133.86/298.09 , 0_1(89) -> 245 1133.86/298.09 , 0_1(89) -> 266 1133.86/298.09 , 0_1(90) -> 89 1133.86/298.09 , 0_1(91) -> 90 1133.86/298.09 , 0_1(92) -> 91 1133.86/298.09 , 0_1(96) -> 95 1133.86/298.09 , 0_1(98) -> 97 1133.86/298.09 , 0_1(109) -> 178 1133.86/298.09 , 0_1(123) -> 178 1133.86/298.09 , 0_1(131) -> 130 1133.86/298.09 , 0_1(139) -> 138 1133.86/298.09 , 0_1(156) -> 155 1133.86/298.09 , 0_1(177) -> 176 1133.86/298.09 , 0_1(178) -> 177 1133.86/298.09 , 0_1(196) -> 154 1133.86/298.09 , 0_1(200) -> 199 1133.86/298.09 , 0_1(202) -> 201 1133.86/298.09 , 0_1(211) -> 210 1133.86/298.09 , 0_1(214) -> 213 1133.86/298.09 , 0_1(218) -> 196 1133.86/298.09 , 0_1(245) -> 244 1133.86/298.09 , 0_1(247) -> 169 1133.86/298.09 , 0_1(248) -> 247 1133.86/298.09 , 0_1(251) -> 250 1133.86/298.09 , 0_1(252) -> 251 1133.86/298.09 , 0_1(257) -> 256 1133.86/298.09 , 1_0(1) -> 1 1133.86/298.09 , 1_1(1) -> 66 1133.86/298.09 , 1_1(5) -> 109 1133.86/298.09 , 1_1(29) -> 104 1133.86/298.09 , 1_1(38) -> 66 1133.86/298.09 , 1_1(41) -> 40 1133.86/298.09 , 1_1(42) -> 41 1133.86/298.09 , 1_1(44) -> 246 1133.86/298.09 , 1_1(56) -> 215 1133.86/298.09 , 1_1(57) -> 1 1133.86/298.09 , 1_1(57) -> 29 1133.86/298.09 , 1_1(57) -> 66 1133.86/298.09 , 1_1(57) -> 104 1133.86/298.09 , 1_1(71) -> 70 1133.86/298.09 , 1_1(80) -> 79 1133.86/298.09 , 1_1(86) -> 264 1133.86/298.09 , 1_1(88) -> 123 1133.86/298.09 , 1_1(99) -> 98 1133.86/298.09 , 1_1(102) -> 101 1133.86/298.09 , 1_1(110) -> 109 1133.86/298.09 , 1_1(132) -> 131 1133.86/298.09 , 1_1(157) -> 156 1133.86/298.09 , 1_1(161) -> 160 1133.86/298.09 , 1_1(164) -> 163 1133.86/298.09 , 1_1(169) -> 38 1133.86/298.09 , 1_1(174) -> 173 1133.86/298.09 , 1_1(184) -> 183 1133.86/298.09 , 1_1(205) -> 66 1133.86/298.09 , 1_1(210) -> 209 1133.86/298.09 , 1_1(216) -> 215 1133.86/298.09 , 1_1(221) -> 220 1133.86/298.09 , 1_1(222) -> 221 1133.86/298.09 , 1_1(232) -> 231 1133.86/298.09 , 1_1(234) -> 233 1133.86/298.09 , 1_1(235) -> 234 1133.86/298.09 , 1_1(236) -> 235 1133.86/298.09 , 1_1(249) -> 248 1133.86/298.09 , 1_1(258) -> 257 1133.86/298.09 , 1_1(261) -> 260 1133.86/298.09 , 2_0(1) -> 1 1133.86/298.09 , 2_1(1) -> 5 1133.86/298.09 , 2_1(5) -> 110 1133.86/298.09 , 2_1(10) -> 9 1133.86/298.09 , 2_1(18) -> 17 1133.86/298.09 , 2_1(29) -> 84 1133.86/298.09 , 2_1(38) -> 1 1133.86/298.09 , 2_1(38) -> 5 1133.86/298.09 , 2_1(38) -> 29 1133.86/298.09 , 2_1(38) -> 56 1133.86/298.09 , 2_1(38) -> 166 1133.86/298.09 , 2_1(38) -> 167 1133.86/298.09 , 2_1(38) -> 168 1133.86/298.09 , 2_1(38) -> 266 1133.86/298.09 , 2_1(39) -> 110 1133.86/298.09 , 2_1(40) -> 39 1133.86/298.09 , 2_1(43) -> 42 1133.86/298.09 , 2_1(44) -> 80 1133.86/298.09 , 2_1(47) -> 46 1133.86/298.09 , 2_1(56) -> 55 1133.86/298.09 , 2_1(57) -> 84 1133.86/298.09 , 2_1(61) -> 60 1133.86/298.09 , 2_1(62) -> 61 1133.86/298.09 , 2_1(66) -> 245 1133.86/298.09 , 2_1(82) -> 81 1133.86/298.09 , 2_1(84) -> 83 1133.86/298.09 , 2_1(85) -> 84 1133.86/298.09 , 2_1(86) -> 88 1133.86/298.09 , 2_1(88) -> 110 1133.86/298.09 , 2_1(89) -> 5 1133.86/298.09 , 2_1(95) -> 94 1133.86/298.09 , 2_1(97) -> 96 1133.86/298.09 , 2_1(100) -> 99 1133.86/298.09 , 2_1(104) -> 103 1133.86/298.09 , 2_1(109) -> 108 1133.86/298.09 , 2_1(133) -> 132 1133.86/298.09 , 2_1(143) -> 142 1133.86/298.09 , 2_1(168) -> 167 1133.86/298.09 , 2_1(173) -> 172 1133.86/298.09 , 2_1(205) -> 196 1133.86/298.09 , 2_1(208) -> 207 1133.86/298.09 , 2_1(209) -> 208 1133.86/298.09 , 2_1(212) -> 211 1133.86/298.09 , 2_1(218) -> 5 1133.86/298.09 , 2_1(237) -> 236 1133.86/298.09 , 2_1(243) -> 242 1133.86/298.09 , 2_1(250) -> 249 1133.86/298.09 , 2_1(256) -> 255 1133.86/298.09 , 2_1(259) -> 258 1133.86/298.09 , 2_1(262) -> 261 1133.86/298.09 , 2_1(263) -> 262 1133.86/298.09 , 2_2(1) -> 266 1133.86/298.09 , 2_2(38) -> 266 1133.86/298.09 , 2_2(40) -> 266 1133.86/298.09 , 2_2(86) -> 266 1133.86/298.09 , 2_2(89) -> 266 1133.86/298.09 , 2_2(218) -> 266 1133.86/298.09 , 3_0(1) -> 1 1133.86/298.09 , 3_1(1) -> 86 1133.86/298.09 , 3_1(2) -> 1 1133.86/298.09 , 3_1(2) -> 5 1133.86/298.09 , 3_1(2) -> 29 1133.86/298.09 , 3_1(2) -> 80 1133.86/298.09 , 3_1(2) -> 168 1133.86/298.09 , 3_1(2) -> 266 1133.86/298.09 , 3_1(4) -> 1 1133.86/298.09 , 3_1(4) -> 65 1133.86/298.09 , 3_1(4) -> 168 1133.86/298.09 , 3_1(4) -> 178 1133.86/298.09 , 3_1(5) -> 4 1133.86/298.09 , 3_1(17) -> 16 1133.86/298.09 , 3_1(23) -> 22 1133.86/298.09 , 3_1(26) -> 25 1133.86/298.09 , 3_1(29) -> 28 1133.86/298.09 , 3_1(38) -> 1 1133.86/298.09 , 3_1(39) -> 86 1133.86/298.09 , 3_1(65) -> 64 1133.86/298.09 , 3_1(66) -> 38 1133.86/298.09 , 3_1(69) -> 68 1133.86/298.09 , 3_1(73) -> 72 1133.86/298.09 , 3_1(86) -> 86 1133.86/298.09 , 3_1(88) -> 87 1133.86/298.09 , 3_1(106) -> 6 1133.86/298.09 , 3_1(143) -> 226 1133.86/298.09 , 3_1(154) -> 86 1133.86/298.09 , 3_1(160) -> 159 1133.86/298.09 , 3_1(162) -> 161 1133.86/298.09 , 3_1(167) -> 89 1133.86/298.09 , 3_1(168) -> 228 1133.86/298.09 , 3_1(170) -> 169 1133.86/298.09 , 3_1(171) -> 170 1133.86/298.09 , 3_1(176) -> 175 1133.86/298.09 , 3_1(181) -> 106 1133.86/298.09 , 3_1(185) -> 184 1133.86/298.09 , 3_1(201) -> 200 1133.86/298.09 , 3_1(204) -> 226 1133.86/298.09 , 3_1(213) -> 212 1133.86/298.09 , 3_1(219) -> 218 1133.86/298.09 , 3_1(220) -> 219 1133.86/298.09 , 3_1(224) -> 223 1133.86/298.09 , 3_1(227) -> 226 1133.86/298.09 , 3_1(229) -> 228 1133.86/298.09 , 3_1(231) -> 230 1133.86/298.09 , 3_1(233) -> 232 1133.86/298.09 , 3_1(238) -> 237 1133.86/298.09 , 3_1(240) -> 239 1133.86/298.09 , 3_1(244) -> 243 1133.86/298.09 , 3_1(246) -> 38 1133.86/298.09 , 3_1(255) -> 45 1133.86/298.09 , 3_2(265) -> 178 1133.86/298.09 , 3_2(266) -> 265 1133.86/298.09 , 4_0(1) -> 1 1133.86/298.09 , 4_1(1) -> 29 1133.86/298.09 , 4_1(2) -> 29 1133.86/298.09 , 4_1(4) -> 29 1133.86/298.09 , 4_1(8) -> 6 1133.86/298.09 , 4_1(24) -> 23 1133.86/298.09 , 4_1(25) -> 24 1133.86/298.09 , 4_1(27) -> 26 1133.86/298.09 , 4_1(28) -> 27 1133.86/298.09 , 4_1(38) -> 29 1133.86/298.09 , 4_1(39) -> 38 1133.86/298.09 , 4_1(44) -> 56 1133.86/298.09 , 4_1(48) -> 47 1133.86/298.09 , 4_1(49) -> 48 1133.86/298.09 , 4_1(51) -> 50 1133.86/298.09 , 4_1(55) -> 54 1133.86/298.09 , 4_1(60) -> 59 1133.86/298.09 , 4_1(66) -> 166 1133.86/298.09 , 4_1(67) -> 58 1133.86/298.09 , 4_1(68) -> 67 1133.86/298.09 , 4_1(70) -> 69 1133.86/298.09 , 4_1(74) -> 73 1133.86/298.09 , 4_1(81) -> 45 1133.86/298.09 , 4_1(86) -> 85 1133.86/298.09 , 4_1(89) -> 29 1133.86/298.09 , 4_1(93) -> 92 1133.86/298.09 , 4_1(110) -> 185 1133.86/298.09 , 4_1(123) -> 122 1133.86/298.09 , 4_1(130) -> 106 1133.86/298.09 , 4_1(138) -> 133 1133.86/298.09 , 4_1(154) -> 1 1133.86/298.09 , 4_1(154) -> 29 1133.86/298.09 , 4_1(154) -> 54 1133.86/298.09 , 4_1(155) -> 154 1133.86/298.09 , 4_1(163) -> 162 1133.86/298.09 , 4_1(165) -> 164 1133.86/298.09 , 4_1(166) -> 165 1133.86/298.09 , 4_1(172) -> 171 1133.86/298.09 , 4_1(175) -> 174 1133.86/298.09 , 4_1(178) -> 252 1133.86/298.09 , 4_1(183) -> 181 1133.86/298.09 , 4_1(197) -> 196 1133.86/298.09 , 4_1(206) -> 205 1133.86/298.09 , 4_1(217) -> 216 1133.86/298.09 , 4_1(223) -> 57 1133.86/298.09 , 4_1(225) -> 224 1133.86/298.09 , 4_1(226) -> 225 1133.86/298.09 , 4_1(230) -> 169 1133.86/298.09 , 4_1(239) -> 238 1133.86/298.09 , 4_1(241) -> 240 1133.86/298.09 , 4_1(242) -> 241 1133.86/298.09 , 4_1(247) -> 29 1133.86/298.09 , 4_1(255) -> 29 1133.86/298.09 , 5_0(1) -> 1 1133.86/298.09 , 5_1(1) -> 44 1133.86/298.09 , 5_1(3) -> 2 1133.86/298.09 , 5_1(4) -> 38 1133.86/298.09 , 5_1(16) -> 11 1133.86/298.09 , 5_1(22) -> 18 1133.86/298.09 , 5_1(29) -> 204 1133.86/298.09 , 5_1(44) -> 43 1133.86/298.09 , 5_1(45) -> 1 1133.86/298.09 , 5_1(45) -> 44 1133.86/298.09 , 5_1(45) -> 66 1133.86/298.09 , 5_1(45) -> 104 1133.86/298.09 , 5_1(45) -> 139 1133.86/298.09 , 5_1(46) -> 45 1133.86/298.09 , 5_1(53) -> 52 1133.86/298.09 , 5_1(57) -> 44 1133.86/298.09 , 5_1(58) -> 57 1133.86/298.09 , 5_1(65) -> 222 1133.86/298.09 , 5_1(66) -> 263 1133.86/298.09 , 5_1(75) -> 74 1133.86/298.09 , 5_1(78) -> 77 1133.86/298.09 , 5_1(79) -> 78 1133.86/298.09 , 5_1(80) -> 139 1133.86/298.09 , 5_1(83) -> 82 1133.86/298.09 , 5_1(84) -> 217 1133.86/298.09 , 5_1(86) -> 143 1133.86/298.09 , 5_1(87) -> 38 1133.86/298.09 , 5_1(89) -> 44 1133.86/298.09 , 5_1(90) -> 44 1133.86/298.09 , 5_1(94) -> 93 1133.86/298.09 , 5_1(101) -> 100 1133.86/298.09 , 5_1(103) -> 102 1133.86/298.09 , 5_1(108) -> 106 1133.86/298.09 , 5_1(121) -> 3 1133.86/298.09 , 5_1(122) -> 121 1133.86/298.09 , 5_1(142) -> 139 1133.86/298.09 , 5_1(158) -> 157 1133.86/298.09 , 5_1(159) -> 158 1133.86/298.09 , 5_1(169) -> 44 1133.86/298.09 , 5_1(198) -> 197 1133.86/298.09 , 5_1(199) -> 198 1133.86/298.09 , 5_1(203) -> 202 1133.86/298.09 , 5_1(204) -> 203 1133.86/298.09 , 5_1(207) -> 206 1133.86/298.09 , 5_1(215) -> 214 1133.86/298.09 , 5_1(218) -> 44 1133.86/298.09 , 5_1(228) -> 227 1133.86/298.09 , 5_1(245) -> 102 1133.86/298.09 , 5_1(260) -> 259 1133.86/298.09 , 5_1(264) -> 263 } 1133.86/298.09 1133.86/298.09 Hurray, we answered YES(?,O(n^1)) 1134.61/298.57 EOF