YES(?,O(n^1)) 1114.49/297.08 YES(?,O(n^1)) 1114.49/297.08 1114.49/297.08 We are left with following problem, upon which TcT provides the 1114.49/297.08 certificate YES(?,O(n^1)). 1114.49/297.08 1114.49/297.08 Strict Trs: 1114.49/297.08 { 0(0(0(2(4(1(2(2(4(x1))))))))) -> 0(0(0(4(3(3(4(4(x1)))))))) 1114.49/297.08 , 0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) -> 1114.49/297.08 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) 1114.49/297.08 , 0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) -> 1114.49/297.08 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) 1114.49/297.08 , 0(1(2(3(x1)))) -> 1(4(3(x1))) 1114.49/297.08 , 0(1(4(3(2(3(2(3(5(3(x1)))))))))) -> 1(4(3(0(3(4(2(5(3(x1))))))))) 1114.49/297.08 , 0(1(4(5(0(5(x1)))))) -> 3(0(4(0(3(5(x1)))))) 1114.49/297.08 , 0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) -> 1114.49/297.08 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) 1114.49/297.08 , 0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) -> 1114.49/297.08 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) 1114.49/297.08 , 0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) -> 1114.49/297.08 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) 1114.49/297.08 , 0(2(5(2(1(5(x1)))))) -> 5(2(1(5(4(x1))))) 1114.49/297.08 , 0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) -> 1114.49/297.08 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) 1114.49/297.08 , 0(3(5(1(5(5(x1)))))) -> 0(5(1(5(4(x1))))) 1114.49/297.08 , 1(2(0(4(2(x1))))) -> 3(4(5(4(x1)))) 1114.49/297.08 , 1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) -> 1114.49/297.08 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) 1114.49/297.08 , 2(2(5(1(4(5(4(3(x1)))))))) -> 2(2(3(3(0(1(0(3(x1)))))))) 1114.49/297.08 , 2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) -> 1114.49/297.08 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) 1114.49/297.08 , 2(4(4(3(4(2(0(3(2(x1))))))))) -> 3(4(3(4(1(3(3(1(x1)))))))) 1114.49/297.08 , 3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) 1114.49/297.08 -> 1114.49/297.08 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) 1114.49/297.08 , 3(3(0(3(2(x1))))) -> 3(2(4(1(x1)))) 1114.49/297.08 , 3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) 1114.49/297.08 -> 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(x1))))))))))))))))))) 1114.49/297.08 , 4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) -> 1114.49/297.08 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) 1114.49/297.08 , 4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) -> 1114.49/297.08 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) 1114.49/297.08 , 5(2(1(0(4(x1))))) -> 5(5(4(5(x1)))) 1114.49/297.08 , 5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) -> 1114.49/297.08 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) 1114.49/297.08 , 5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) -> 1114.49/297.08 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) } 1114.49/297.08 Obligation: 1114.49/297.08 derivational complexity 1114.49/297.08 Answer: 1114.49/297.08 YES(?,O(n^1)) 1114.49/297.08 1114.49/297.08 The problem is match-bounded by 2. The enriched problem is 1114.49/297.08 compatible with the following automaton. 1114.49/297.08 { 0_0(1) -> 1 1114.49/297.08 , 0_1(1) -> 243 1114.49/297.08 , 0_1(2) -> 1 1114.49/297.08 , 0_1(2) -> 44 1114.49/297.08 , 0_1(2) -> 242 1114.49/297.08 , 0_1(2) -> 243 1114.49/297.08 , 0_1(3) -> 2 1114.49/297.08 , 0_1(4) -> 3 1114.49/297.08 , 0_1(12) -> 11 1114.49/297.08 , 0_1(18) -> 17 1114.49/297.08 , 0_1(23) -> 44 1114.49/297.08 , 0_1(27) -> 26 1114.49/297.08 , 0_1(32) -> 31 1114.49/297.08 , 0_1(36) -> 60 1114.49/297.08 , 0_1(37) -> 44 1114.49/297.08 , 0_1(38) -> 44 1114.49/297.08 , 0_1(43) -> 42 1114.49/297.08 , 0_1(44) -> 95 1114.49/297.08 , 0_1(45) -> 44 1114.49/297.08 , 0_1(48) -> 44 1114.49/297.08 , 0_1(52) -> 51 1114.49/297.08 , 0_1(54) -> 53 1114.49/297.08 , 0_1(58) -> 57 1114.49/297.08 , 0_1(61) -> 60 1114.49/297.08 , 0_1(72) -> 71 1114.49/297.08 , 0_1(74) -> 73 1114.49/297.08 , 0_1(80) -> 79 1114.49/297.08 , 0_1(82) -> 81 1114.49/297.08 , 0_1(83) -> 82 1114.49/297.08 , 0_1(87) -> 86 1114.49/297.08 , 0_1(90) -> 89 1114.49/297.08 , 0_1(93) -> 92 1114.49/297.08 , 0_1(96) -> 95 1114.49/297.08 , 0_1(97) -> 96 1114.49/297.08 , 0_1(98) -> 243 1114.49/297.08 , 0_1(102) -> 101 1114.49/297.08 , 0_1(126) -> 125 1114.49/297.08 , 0_1(139) -> 138 1114.49/297.08 , 0_1(220) -> 219 1114.49/297.08 , 0_1(231) -> 230 1114.49/297.08 , 0_1(232) -> 231 1114.49/297.08 , 0_1(233) -> 232 1114.49/297.08 , 0_1(243) -> 242 1114.49/297.08 , 0_1(248) -> 247 1114.49/297.08 , 0_2(263) -> 44 1114.49/297.08 , 1_0(1) -> 1 1114.49/297.08 , 1_1(1) -> 23 1114.49/297.08 , 1_1(8) -> 153 1114.49/297.08 , 1_1(10) -> 9 1114.49/297.08 , 1_1(11) -> 10 1114.49/297.08 , 1_1(28) -> 27 1114.49/297.08 , 1_1(36) -> 77 1114.49/297.08 , 1_1(37) -> 1 1114.49/297.08 , 1_1(37) -> 23 1114.49/297.08 , 1_1(37) -> 44 1114.49/297.08 , 1_1(37) -> 95 1114.49/297.08 , 1_1(37) -> 242 1114.49/297.08 , 1_1(37) -> 243 1114.49/297.08 , 1_1(44) -> 102 1114.49/297.08 , 1_1(45) -> 259 1114.49/297.08 , 1_1(50) -> 49 1114.49/297.08 , 1_1(53) -> 52 1114.49/297.08 , 1_1(55) -> 54 1114.49/297.08 , 1_1(60) -> 59 1114.49/297.08 , 1_1(70) -> 69 1114.49/297.08 , 1_1(73) -> 72 1114.49/297.08 , 1_1(79) -> 78 1114.49/297.08 , 1_1(86) -> 37 1114.49/297.08 , 1_1(98) -> 23 1114.49/297.08 , 1_1(105) -> 104 1114.49/297.08 , 1_1(106) -> 105 1114.49/297.08 , 1_1(107) -> 106 1114.49/297.08 , 1_1(112) -> 111 1114.49/297.08 , 1_1(115) -> 114 1114.49/297.08 , 1_1(153) -> 152 1114.49/297.08 , 1_1(177) -> 23 1114.49/297.08 , 1_1(223) -> 222 1114.49/297.08 , 1_1(237) -> 236 1114.49/297.08 , 1_1(240) -> 239 1114.49/297.08 , 1_1(241) -> 240 1114.49/297.08 , 1_1(245) -> 46 1114.49/297.08 , 1_1(253) -> 252 1114.49/297.08 , 1_1(255) -> 254 1114.49/297.08 , 1_2(260) -> 44 1114.49/297.08 , 1_2(265) -> 264 1114.49/297.08 , 2_0(1) -> 1 1114.49/297.08 , 2_1(1) -> 56 1114.49/297.08 , 2_1(7) -> 84 1114.49/297.08 , 2_1(13) -> 12 1114.49/297.08 , 2_1(19) -> 18 1114.49/297.08 , 2_1(21) -> 20 1114.49/297.08 , 2_1(25) -> 24 1114.49/297.08 , 2_1(26) -> 25 1114.49/297.08 , 2_1(33) -> 32 1114.49/297.08 , 2_1(34) -> 33 1114.49/297.08 , 2_1(35) -> 34 1114.49/297.08 , 2_1(37) -> 249 1114.49/297.08 , 2_1(38) -> 76 1114.49/297.08 , 2_1(41) -> 40 1114.49/297.08 , 2_1(46) -> 226 1114.49/297.08 , 2_1(67) -> 66 1114.49/297.08 , 2_1(77) -> 47 1114.49/297.08 , 2_1(84) -> 83 1114.49/297.08 , 2_1(92) -> 91 1114.49/297.08 , 2_1(95) -> 94 1114.49/297.08 , 2_1(98) -> 1 1114.49/297.08 , 2_1(98) -> 56 1114.49/297.08 , 2_1(98) -> 76 1114.49/297.08 , 2_1(99) -> 98 1114.49/297.08 , 2_1(125) -> 36 1114.49/297.08 , 2_1(132) -> 131 1114.49/297.08 , 2_1(133) -> 132 1114.49/297.08 , 2_1(134) -> 133 1114.49/297.08 , 2_1(152) -> 151 1114.49/297.08 , 2_1(177) -> 42 1114.49/297.08 , 2_1(178) -> 8 1114.49/297.08 , 2_1(197) -> 196 1114.49/297.08 , 2_1(227) -> 219 1114.49/297.08 , 2_1(228) -> 227 1114.49/297.08 , 2_1(230) -> 229 1114.49/297.08 , 2_1(238) -> 237 1114.49/297.08 , 2_1(239) -> 238 1114.49/297.08 , 2_1(247) -> 246 1114.49/297.08 , 3_0(1) -> 1 1114.49/297.08 , 3_1(1) -> 38 1114.49/297.08 , 3_1(2) -> 45 1114.49/297.08 , 3_1(6) -> 5 1114.49/297.08 , 3_1(7) -> 6 1114.49/297.08 , 3_1(14) -> 13 1114.49/297.08 , 3_1(17) -> 16 1114.49/297.08 , 3_1(22) -> 21 1114.49/297.08 , 3_1(23) -> 116 1114.49/297.08 , 3_1(38) -> 97 1114.49/297.08 , 3_1(39) -> 2 1114.49/297.08 , 3_1(42) -> 1 1114.49/297.08 , 3_1(42) -> 23 1114.49/297.08 , 3_1(42) -> 38 1114.49/297.08 , 3_1(42) -> 44 1114.49/297.08 , 3_1(42) -> 56 1114.49/297.08 , 3_1(42) -> 84 1114.49/297.08 , 3_1(42) -> 97 1114.49/297.08 , 3_1(42) -> 243 1114.49/297.08 , 3_1(46) -> 45 1114.49/297.08 , 3_1(49) -> 48 1114.49/297.08 , 3_1(55) -> 112 1114.49/297.08 , 3_1(65) -> 64 1114.49/297.08 , 3_1(69) -> 68 1114.49/297.08 , 3_1(75) -> 112 1114.49/297.08 , 3_1(91) -> 90 1114.49/297.08 , 3_1(100) -> 99 1114.49/297.08 , 3_1(101) -> 100 1114.49/297.08 , 3_1(103) -> 98 1114.49/297.08 , 3_1(104) -> 103 1114.49/297.08 , 3_1(109) -> 108 1114.49/297.08 , 3_1(110) -> 109 1114.49/297.08 , 3_1(116) -> 115 1114.49/297.08 , 3_1(135) -> 134 1114.49/297.08 , 3_1(136) -> 135 1114.49/297.08 , 3_1(137) -> 136 1114.49/297.08 , 3_1(151) -> 150 1114.49/297.08 , 3_1(180) -> 179 1114.49/297.08 , 3_1(182) -> 181 1114.49/297.08 , 3_1(190) -> 189 1114.49/297.08 , 3_1(222) -> 221 1114.49/297.08 , 3_1(235) -> 234 1114.49/297.08 , 3_1(250) -> 77 1114.49/297.08 , 3_1(254) -> 253 1114.49/297.08 , 3_2(100) -> 261 1114.49/297.08 , 3_2(103) -> 261 1114.49/297.08 , 4_0(1) -> 1 1114.49/297.08 , 4_1(1) -> 8 1114.49/297.08 , 4_1(2) -> 7 1114.49/297.08 , 4_1(5) -> 4 1114.49/297.08 , 4_1(7) -> 7 1114.49/297.08 , 4_1(8) -> 7 1114.49/297.08 , 4_1(16) -> 15 1114.49/297.08 , 4_1(23) -> 177 1114.49/297.08 , 4_1(24) -> 2 1114.49/297.08 , 4_1(25) -> 8 1114.49/297.08 , 4_1(30) -> 29 1114.49/297.08 , 4_1(31) -> 30 1114.49/297.08 , 4_1(36) -> 42 1114.49/297.08 , 4_1(37) -> 8 1114.49/297.08 , 4_1(38) -> 37 1114.49/297.08 , 4_1(40) -> 39 1114.49/297.08 , 4_1(42) -> 7 1114.49/297.08 , 4_1(44) -> 43 1114.49/297.08 , 4_1(46) -> 244 1114.49/297.08 , 4_1(47) -> 8 1114.49/297.08 , 4_1(48) -> 47 1114.49/297.08 , 4_1(51) -> 50 1114.49/297.08 , 4_1(56) -> 63 1114.49/297.08 , 4_1(57) -> 3 1114.49/297.08 , 4_1(63) -> 62 1114.49/297.08 , 4_1(64) -> 42 1114.49/297.08 , 4_1(78) -> 57 1114.49/297.08 , 4_1(81) -> 80 1114.49/297.08 , 4_1(88) -> 87 1114.49/297.08 , 4_1(98) -> 37 1114.49/297.08 , 4_1(100) -> 37 1114.49/297.08 , 4_1(103) -> 37 1114.49/297.08 , 4_1(114) -> 65 1114.49/297.08 , 4_1(129) -> 126 1114.49/297.08 , 4_1(179) -> 178 1114.49/297.08 , 4_1(181) -> 180 1114.49/297.08 , 4_1(191) -> 190 1114.49/297.08 , 4_1(196) -> 195 1114.49/297.08 , 4_1(218) -> 1 1114.49/297.08 , 4_1(218) -> 7 1114.49/297.08 , 4_1(218) -> 8 1114.49/297.08 , 4_1(218) -> 42 1114.49/297.08 , 4_1(218) -> 244 1114.49/297.08 , 4_1(219) -> 218 1114.49/297.08 , 4_1(221) -> 220 1114.49/297.08 , 4_1(236) -> 235 1114.49/297.08 , 4_1(244) -> 7 1114.49/297.08 , 4_1(252) -> 251 1114.49/297.08 , 4_1(256) -> 255 1114.49/297.08 , 4_1(257) -> 256 1114.49/297.08 , 4_1(258) -> 257 1114.49/297.08 , 4_1(259) -> 258 1114.49/297.08 , 4_2(244) -> 266 1114.49/297.08 , 4_2(261) -> 260 1114.49/297.08 , 4_2(279) -> 278 1114.49/297.08 , 5_0(1) -> 1 1114.49/297.08 , 5_1(1) -> 46 1114.49/297.08 , 5_1(7) -> 36 1114.49/297.08 , 5_1(8) -> 36 1114.49/297.08 , 5_1(9) -> 2 1114.49/297.08 , 5_1(15) -> 14 1114.49/297.08 , 5_1(20) -> 19 1114.49/297.08 , 5_1(23) -> 22 1114.49/297.08 , 5_1(24) -> 46 1114.49/297.08 , 5_1(29) -> 28 1114.49/297.08 , 5_1(36) -> 35 1114.49/297.08 , 5_1(37) -> 36 1114.49/297.08 , 5_1(38) -> 41 1114.49/297.08 , 5_1(42) -> 36 1114.49/297.08 , 5_1(47) -> 1 1114.49/297.08 , 5_1(47) -> 36 1114.49/297.08 , 5_1(47) -> 41 1114.49/297.08 , 5_1(47) -> 46 1114.49/297.08 , 5_1(47) -> 55 1114.49/297.08 , 5_1(47) -> 243 1114.49/297.08 , 5_1(55) -> 74 1114.49/297.08 , 5_1(56) -> 55 1114.49/297.08 , 5_1(59) -> 58 1114.49/297.08 , 5_1(62) -> 61 1114.49/297.08 , 5_1(66) -> 65 1114.49/297.08 , 5_1(68) -> 67 1114.49/297.08 , 5_1(71) -> 70 1114.49/297.08 , 5_1(74) -> 223 1114.49/297.08 , 5_1(75) -> 74 1114.49/297.08 , 5_1(76) -> 75 1114.49/297.08 , 5_1(77) -> 2 1114.49/297.08 , 5_1(89) -> 88 1114.49/297.08 , 5_1(94) -> 93 1114.49/297.08 , 5_1(98) -> 55 1114.49/297.08 , 5_1(102) -> 201 1114.49/297.08 , 5_1(108) -> 107 1114.49/297.08 , 5_1(111) -> 110 1114.49/297.08 , 5_1(131) -> 129 1114.49/297.08 , 5_1(138) -> 137 1114.49/297.08 , 5_1(149) -> 139 1114.49/297.08 , 5_1(150) -> 149 1114.49/297.08 , 5_1(189) -> 182 1114.49/297.08 , 5_1(195) -> 191 1114.49/297.08 , 5_1(201) -> 197 1114.49/297.08 , 5_1(218) -> 46 1114.49/297.08 , 5_1(224) -> 223 1114.49/297.08 , 5_1(225) -> 224 1114.49/297.08 , 5_1(226) -> 225 1114.49/297.08 , 5_1(229) -> 228 1114.49/297.08 , 5_1(234) -> 233 1114.49/297.08 , 5_1(242) -> 241 1114.49/297.08 , 5_1(244) -> 47 1114.49/297.08 , 5_1(246) -> 245 1114.49/297.08 , 5_1(249) -> 248 1114.49/297.08 , 5_1(251) -> 250 1114.49/297.08 , 5_2(88) -> 279 1114.49/297.08 , 5_2(264) -> 263 1114.49/297.08 , 5_2(266) -> 265 1114.49/297.08 , 5_2(277) -> 248 1114.49/297.08 , 5_2(278) -> 277 } 1114.49/297.08 1114.49/297.08 Hurray, we answered YES(?,O(n^1)) 1115.18/297.56 EOF