YES(?,O(n^1)) 1112.89/297.06 YES(?,O(n^1)) 1112.89/297.06 1112.89/297.06 We are left with following problem, upon which TcT provides the 1112.89/297.06 certificate YES(?,O(n^1)). 1112.89/297.06 1112.89/297.06 Strict Trs: 1112.89/297.06 { 0(1(2(3(x1)))) -> 0(2(2(3(x1)))) 1112.89/297.06 , 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 1112.89/297.06 , 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 1112.89/297.06 , 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 1112.89/297.06 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 1112.89/297.06 , 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 1112.89/297.06 , 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 1112.89/297.06 , 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 1112.89/297.06 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 1112.89/297.06 , 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 1112.89/297.06 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 1112.89/297.06 , 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 1112.89/297.06 , 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 1112.89/297.06 , 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 1112.89/297.06 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 1112.89/297.06 , 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 1112.89/297.06 , 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 1112.89/297.06 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 1112.89/297.09 , 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 1112.89/297.09 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 1112.89/297.09 , 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 1112.89/297.09 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 1112.89/297.09 , 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 1112.89/297.09 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 1112.89/297.09 , 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 1112.89/297.09 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 1112.89/297.09 , 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 1112.89/297.09 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 1112.89/297.09 , 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 1112.89/297.09 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 1112.89/297.09 , 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 1112.89/297.09 , 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 1112.89/297.09 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 1112.89/297.09 , 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 1112.89/297.09 , 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) 1112.89/297.09 -> 1112.89/297.09 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) 1112.89/297.09 , 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 1112.89/297.09 , 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) } 1112.89/297.09 Obligation: 1112.89/297.09 derivational complexity 1112.89/297.09 Answer: 1112.89/297.09 YES(?,O(n^1)) 1112.89/297.09 1112.89/297.09 The problem is match-bounded by 2. The enriched problem is 1112.89/297.09 compatible with the following automaton. 1112.89/297.09 { 0_0(1) -> 1 1112.89/297.09 , 0_1(1) -> 25 1112.89/297.09 , 0_1(2) -> 1 1112.89/297.09 , 0_1(2) -> 25 1112.89/297.09 , 0_1(2) -> 108 1112.89/297.09 , 0_1(4) -> 59 1112.89/297.09 , 0_1(7) -> 6 1112.89/297.09 , 0_1(14) -> 25 1112.89/297.09 , 0_1(22) -> 21 1112.89/297.09 , 0_1(25) -> 24 1112.89/297.09 , 0_1(33) -> 32 1112.89/297.09 , 0_1(40) -> 39 1112.89/297.09 , 0_1(51) -> 286 1112.89/297.09 , 0_1(53) -> 15 1112.89/297.09 , 0_1(63) -> 62 1112.89/297.09 , 0_1(66) -> 65 1112.89/297.09 , 0_1(67) -> 66 1112.89/297.09 , 0_1(75) -> 74 1112.89/297.09 , 0_1(77) -> 76 1112.89/297.09 , 0_1(88) -> 108 1112.89/297.09 , 0_1(91) -> 90 1112.89/297.09 , 0_1(98) -> 97 1112.89/297.09 , 0_1(100) -> 99 1112.89/297.09 , 0_1(102) -> 101 1112.89/297.09 , 0_1(104) -> 103 1112.89/297.09 , 0_1(109) -> 108 1112.89/297.09 , 0_1(112) -> 111 1112.89/297.09 , 0_1(113) -> 112 1112.89/297.09 , 0_1(121) -> 120 1112.89/297.09 , 0_1(123) -> 122 1112.89/297.09 , 0_1(126) -> 125 1112.89/297.09 , 0_1(132) -> 131 1112.89/297.09 , 0_1(142) -> 141 1112.89/297.09 , 0_1(146) -> 1 1112.89/297.09 , 0_1(146) -> 25 1112.89/297.09 , 0_1(147) -> 185 1112.89/297.09 , 0_1(184) -> 183 1112.89/297.09 , 0_1(209) -> 208 1112.89/297.09 , 0_1(221) -> 220 1112.89/297.09 , 0_1(255) -> 254 1112.89/297.09 , 0_1(260) -> 259 1112.89/297.09 , 0_1(266) -> 29 1112.89/297.09 , 0_1(271) -> 270 1112.89/297.09 , 0_1(281) -> 280 1112.89/297.09 , 0_2(287) -> 108 1112.89/297.09 , 1_0(1) -> 1 1112.89/297.09 , 1_1(1) -> 55 1112.89/297.09 , 1_1(2) -> 23 1112.89/297.09 , 1_1(4) -> 23 1112.89/297.09 , 1_1(10) -> 102 1112.89/297.09 , 1_1(11) -> 35 1112.89/297.09 , 1_1(13) -> 15 1112.89/297.09 , 1_1(14) -> 102 1112.89/297.09 , 1_1(18) -> 17 1112.89/297.09 , 1_1(20) -> 19 1112.89/297.09 , 1_1(21) -> 20 1112.89/297.09 , 1_1(24) -> 15 1112.89/297.09 , 1_1(26) -> 88 1112.89/297.09 , 1_1(27) -> 55 1112.89/297.09 , 1_1(28) -> 15 1112.89/297.09 , 1_1(34) -> 33 1112.89/297.09 , 1_1(36) -> 55 1112.89/297.09 , 1_1(42) -> 41 1112.89/297.09 , 1_1(45) -> 44 1112.89/297.09 , 1_1(46) -> 45 1112.89/297.09 , 1_1(51) -> 50 1112.89/297.09 , 1_1(52) -> 88 1112.89/297.09 , 1_1(54) -> 53 1112.89/297.09 , 1_1(55) -> 54 1112.89/297.09 , 1_1(56) -> 265 1112.89/297.09 , 1_1(71) -> 70 1112.89/297.09 , 1_1(85) -> 84 1112.89/297.09 , 1_1(89) -> 56 1112.89/297.09 , 1_1(94) -> 93 1112.89/297.09 , 1_1(97) -> 96 1112.89/297.09 , 1_1(102) -> 262 1112.89/297.09 , 1_1(103) -> 26 1112.89/297.09 , 1_1(105) -> 104 1112.89/297.09 , 1_1(106) -> 105 1112.89/297.09 , 1_1(110) -> 109 1112.89/297.09 , 1_1(114) -> 113 1112.89/297.09 , 1_1(120) -> 119 1112.89/297.09 , 1_1(127) -> 126 1112.89/297.09 , 1_1(133) -> 132 1112.89/297.09 , 1_1(139) -> 138 1112.89/297.09 , 1_1(145) -> 102 1112.89/297.09 , 1_1(148) -> 265 1112.89/297.09 , 1_1(180) -> 179 1112.89/297.09 , 1_1(205) -> 27 1112.89/297.09 , 1_1(217) -> 216 1112.89/297.09 , 1_1(225) -> 70 1112.89/297.09 , 1_1(261) -> 260 1112.89/297.09 , 1_1(268) -> 267 1112.89/297.09 , 1_1(284) -> 283 1112.89/297.09 , 2_0(1) -> 1 1112.89/297.09 , 2_1(1) -> 52 1112.89/297.09 , 2_1(3) -> 2 1112.89/297.09 , 2_1(4) -> 3 1112.89/297.09 , 2_1(12) -> 11 1112.89/297.09 , 2_1(13) -> 12 1112.89/297.09 , 2_1(19) -> 18 1112.89/297.09 , 2_1(25) -> 285 1112.89/297.09 , 2_1(26) -> 52 1112.89/297.09 , 2_1(27) -> 26 1112.89/297.09 , 2_1(28) -> 52 1112.89/297.09 , 2_1(29) -> 52 1112.89/297.09 , 2_1(32) -> 31 1112.89/297.09 , 2_1(39) -> 38 1112.89/297.09 , 2_1(47) -> 46 1112.89/297.09 , 2_1(49) -> 48 1112.89/297.09 , 2_1(52) -> 146 1112.89/297.09 , 2_1(56) -> 1 1112.89/297.09 , 2_1(56) -> 52 1112.89/297.09 , 2_1(56) -> 146 1112.89/297.09 , 2_1(56) -> 147 1112.89/297.09 , 2_1(56) -> 224 1112.89/297.09 , 2_1(62) -> 61 1112.89/297.09 , 2_1(64) -> 63 1112.89/297.09 , 2_1(70) -> 69 1112.89/297.09 , 2_1(74) -> 15 1112.89/297.09 , 2_1(76) -> 75 1112.89/297.09 , 2_1(79) -> 78 1112.89/297.09 , 2_1(82) -> 81 1112.89/297.09 , 2_1(83) -> 82 1112.89/297.09 , 2_1(96) -> 95 1112.89/297.09 , 2_1(116) -> 115 1112.89/297.09 , 2_1(117) -> 116 1112.89/297.09 , 2_1(118) -> 117 1112.89/297.09 , 2_1(125) -> 27 1112.89/297.09 , 2_1(140) -> 139 1112.89/297.09 , 2_1(143) -> 142 1112.89/297.09 , 2_1(145) -> 144 1112.89/297.09 , 2_1(147) -> 146 1112.89/297.09 , 2_1(148) -> 147 1112.89/297.09 , 2_1(215) -> 214 1112.89/297.09 , 2_1(218) -> 217 1112.89/297.09 , 2_1(222) -> 12 1112.89/297.09 , 2_1(225) -> 224 1112.89/297.09 , 2_1(263) -> 103 1112.89/297.09 , 2_1(267) -> 266 1112.89/297.09 , 2_1(270) -> 269 1112.89/297.09 , 2_1(274) -> 273 1112.89/297.09 , 2_1(275) -> 274 1112.89/297.09 , 2_1(279) -> 278 1112.89/297.09 , 2_1(280) -> 279 1112.89/297.09 , 2_1(281) -> 1 1112.89/297.09 , 2_1(281) -> 52 1112.89/297.09 , 2_1(281) -> 146 1112.89/297.09 , 2_1(286) -> 285 1112.89/297.09 , 2_2(288) -> 287 1112.89/297.09 , 2_2(289) -> 288 1112.89/297.09 , 3_0(1) -> 1 1112.89/297.09 , 3_1(1) -> 4 1112.89/297.09 , 3_1(2) -> 4 1112.89/297.09 , 3_1(4) -> 124 1112.89/297.09 , 3_1(9) -> 8 1112.89/297.09 , 3_1(11) -> 2 1112.89/297.09 , 3_1(13) -> 221 1112.89/297.09 , 3_1(16) -> 15 1112.89/297.09 , 3_1(17) -> 16 1112.89/297.09 , 3_1(23) -> 22 1112.89/297.09 , 3_1(27) -> 1 1112.89/297.09 , 3_1(27) -> 3 1112.89/297.09 , 3_1(27) -> 4 1112.89/297.09 , 3_1(27) -> 8 1112.89/297.09 , 3_1(27) -> 52 1112.89/297.09 , 3_1(27) -> 124 1112.89/297.09 , 3_1(31) -> 30 1112.89/297.09 , 3_1(35) -> 34 1112.89/297.09 , 3_1(36) -> 1 1112.89/297.09 , 3_1(36) -> 3 1112.89/297.09 , 3_1(36) -> 52 1112.89/297.09 , 3_1(36) -> 55 1112.89/297.09 , 3_1(36) -> 102 1112.89/297.09 , 3_1(38) -> 8 1112.89/297.09 , 3_1(43) -> 42 1112.89/297.09 , 3_1(55) -> 73 1112.89/297.09 , 3_1(56) -> 4 1112.89/297.09 , 3_1(57) -> 56 1112.89/297.09 , 3_1(69) -> 68 1112.89/297.09 , 3_1(73) -> 72 1112.89/297.09 , 3_1(78) -> 77 1112.89/297.09 , 3_1(80) -> 79 1112.89/297.09 , 3_1(86) -> 85 1112.89/297.09 , 3_1(90) -> 89 1112.89/297.09 , 3_1(99) -> 98 1112.89/297.09 , 3_1(107) -> 106 1112.89/297.09 , 3_1(108) -> 107 1112.89/297.09 , 3_1(119) -> 118 1112.89/297.09 , 3_1(125) -> 4 1112.89/297.09 , 3_1(141) -> 140 1112.89/297.09 , 3_1(146) -> 2 1112.89/297.09 , 3_1(177) -> 27 1112.89/297.09 , 3_1(185) -> 184 1112.89/297.09 , 3_1(207) -> 205 1112.89/297.09 , 3_1(208) -> 207 1112.89/297.09 , 3_1(219) -> 218 1112.89/297.09 , 3_1(222) -> 221 1112.89/297.09 , 3_1(254) -> 103 1112.89/297.09 , 3_1(257) -> 256 1112.89/297.09 , 3_1(262) -> 261 1112.89/297.09 , 3_1(264) -> 263 1112.89/297.09 , 3_1(266) -> 2 1112.89/297.09 , 3_1(276) -> 275 1112.89/297.09 , 3_1(281) -> 4 1112.89/297.09 , 3_1(282) -> 281 1112.89/297.09 , 3_1(283) -> 29 1112.89/297.09 , 3_1(285) -> 284 1112.89/297.09 , 3_2(27) -> 289 1112.89/297.09 , 3_2(36) -> 289 1112.89/297.09 , 3_2(57) -> 289 1112.89/297.09 , 3_2(177) -> 289 1112.89/297.09 , 3_2(282) -> 289 1112.89/297.09 , 3_2(283) -> 289 1112.89/297.09 , 3_2(466) -> 3 1112.89/297.09 , 4_0(1) -> 1 1112.89/297.09 , 4_1(1) -> 148 1112.89/297.09 , 4_1(4) -> 225 1112.89/297.09 , 4_1(6) -> 5 1112.89/297.09 , 4_1(10) -> 28 1112.89/297.09 , 4_1(14) -> 13 1112.89/297.09 , 4_1(26) -> 1 1112.89/297.09 , 4_1(26) -> 12 1112.89/297.09 , 4_1(26) -> 13 1112.89/297.09 , 4_1(26) -> 28 1112.89/297.09 , 4_1(26) -> 49 1112.89/297.09 , 4_1(26) -> 52 1112.89/297.09 , 4_1(26) -> 55 1112.89/297.09 , 4_1(26) -> 56 1112.89/297.09 , 4_1(26) -> 88 1112.89/297.09 , 4_1(26) -> 110 1112.89/297.09 , 4_1(26) -> 147 1112.89/297.09 , 4_1(26) -> 148 1112.89/297.09 , 4_1(26) -> 225 1112.89/297.09 , 4_1(27) -> 56 1112.89/297.09 , 4_1(29) -> 26 1112.89/297.09 , 4_1(30) -> 29 1112.89/297.09 , 4_1(38) -> 37 1112.89/297.09 , 4_1(44) -> 43 1112.89/297.09 , 4_1(50) -> 49 1112.89/297.09 , 4_1(51) -> 13 1112.89/297.09 , 4_1(52) -> 110 1112.89/297.09 , 4_1(55) -> 49 1112.89/297.09 , 4_1(56) -> 148 1112.89/297.09 , 4_1(59) -> 58 1112.89/297.09 , 4_1(68) -> 67 1112.89/297.09 , 4_1(72) -> 71 1112.89/297.09 , 4_1(74) -> 148 1112.89/297.09 , 4_1(84) -> 83 1112.89/297.09 , 4_1(92) -> 91 1112.89/297.09 , 4_1(93) -> 92 1112.89/297.09 , 4_1(124) -> 123 1112.89/297.09 , 4_1(144) -> 143 1112.89/297.09 , 4_1(179) -> 177 1112.89/297.09 , 4_1(214) -> 213 1112.89/297.09 , 4_1(216) -> 215 1112.89/297.09 , 4_1(223) -> 222 1112.89/297.09 , 4_1(256) -> 103 1112.89/297.09 , 4_1(258) -> 257 1112.89/297.09 , 4_1(259) -> 258 1112.89/297.09 , 4_1(265) -> 264 1112.89/297.09 , 4_1(272) -> 271 1112.89/297.09 , 4_1(281) -> 56 1112.89/297.09 , 4_2(468) -> 467 1112.89/297.09 , 5_0(1) -> 1 1112.89/297.09 , 5_1(1) -> 14 1112.89/297.09 , 5_1(2) -> 10 1112.89/297.09 , 5_1(4) -> 10 1112.89/297.09 , 5_1(5) -> 2 1112.89/297.09 , 5_1(8) -> 7 1112.89/297.09 , 5_1(10) -> 9 1112.89/297.09 , 5_1(11) -> 145 1112.89/297.09 , 5_1(12) -> 14 1112.89/297.09 , 5_1(13) -> 27 1112.89/297.09 , 5_1(14) -> 38 1112.89/297.09 , 5_1(15) -> 1 1112.89/297.09 , 5_1(15) -> 2 1112.89/297.09 , 5_1(15) -> 3 1112.89/297.09 , 5_1(15) -> 14 1112.89/297.09 , 5_1(15) -> 15 1112.89/297.09 , 5_1(15) -> 50 1112.89/297.09 , 5_1(15) -> 52 1112.89/297.09 , 5_1(15) -> 54 1112.89/297.09 , 5_1(15) -> 55 1112.89/297.09 , 5_1(15) -> 102 1112.89/297.09 , 5_1(15) -> 146 1112.89/297.09 , 5_1(25) -> 255 1112.89/297.09 , 5_1(26) -> 1 1112.89/297.09 , 5_1(27) -> 10 1112.89/297.09 , 5_1(28) -> 27 1112.89/297.09 , 5_1(29) -> 1 1112.89/297.09 , 5_1(37) -> 36 1112.89/297.09 , 5_1(41) -> 40 1112.89/297.09 , 5_1(48) -> 47 1112.89/297.09 , 5_1(52) -> 51 1112.89/297.09 , 5_1(56) -> 14 1112.89/297.09 , 5_1(58) -> 57 1112.89/297.09 , 5_1(60) -> 15 1112.89/297.09 , 5_1(61) -> 60 1112.89/297.09 , 5_1(65) -> 64 1112.89/297.09 , 5_1(81) -> 80 1112.89/297.09 , 5_1(87) -> 86 1112.89/297.09 , 5_1(88) -> 87 1112.89/297.09 , 5_1(95) -> 94 1112.89/297.09 , 5_1(101) -> 100 1112.89/297.09 , 5_1(111) -> 89 1112.89/297.09 , 5_1(115) -> 114 1112.89/297.09 , 5_1(122) -> 121 1112.89/297.09 , 5_1(125) -> 14 1112.89/297.09 , 5_1(131) -> 127 1112.89/297.09 , 5_1(137) -> 133 1112.89/297.09 , 5_1(138) -> 137 1112.89/297.09 , 5_1(146) -> 145 1112.89/297.09 , 5_1(147) -> 223 1112.89/297.09 , 5_1(148) -> 282 1112.89/297.09 , 5_1(183) -> 180 1112.89/297.09 , 5_1(213) -> 209 1112.89/297.09 , 5_1(220) -> 219 1112.89/297.09 , 5_1(224) -> 223 1112.89/297.09 , 5_1(265) -> 1 1112.89/297.09 , 5_1(265) -> 14 1112.89/297.09 , 5_1(267) -> 14 1112.89/297.09 , 5_1(269) -> 268 1112.89/297.09 , 5_1(273) -> 272 1112.89/297.09 , 5_1(277) -> 276 1112.89/297.09 , 5_1(278) -> 277 1112.89/297.09 , 5_1(281) -> 14 1112.89/297.09 , 5_2(15) -> 469 1112.89/297.09 , 5_2(467) -> 466 1112.89/297.09 , 5_2(469) -> 468 } 1112.89/297.09 1112.89/297.09 Hurray, we answered YES(?,O(n^1)) 1113.53/297.58 EOF