YES(?,O(n^1)) 1111.37/298.50 YES(?,O(n^1)) 1111.37/298.50 1111.37/298.50 We are left with following problem, upon which TcT provides the 1111.37/298.50 certificate YES(?,O(n^1)). 1111.37/298.50 1111.37/298.50 Strict Trs: 1111.37/298.50 { 0(1(0(2(x1)))) -> 2(2(2(x1))) 1111.37/298.50 , 0(1(1(1(x1)))) -> 3(1(0(x1))) 1111.37/298.50 , 0(2(1(1(3(1(5(0(5(2(3(1(4(x1))))))))))))) -> 1111.37/298.50 3(0(1(5(1(4(4(5(0(5(1(1(4(x1))))))))))))) 1111.37/298.50 , 0(2(2(3(3(5(0(0(5(0(3(1(3(0(1(2(1(5(5(1(x1)))))))))))))))))))) -> 1111.37/298.50 0(0(3(2(5(2(5(2(3(2(1(2(5(4(3(4(5(0(4(x1))))))))))))))))))) 1111.37/298.50 , 1(0(3(3(2(5(0(0(3(0(3(2(4(1(4(0(2(4(2(x1))))))))))))))))))) -> 1111.37/298.50 4(3(4(2(1(4(2(4(3(3(2(2(2(1(1(1(5(3(2(x1))))))))))))))))))) 1111.37/298.50 , 1(0(4(2(3(3(5(4(3(5(0(2(0(4(5(0(2(0(2(4(x1)))))))))))))))))))) -> 1111.37/298.50 4(5(4(5(4(1(1(2(5(0(4(3(1(5(4(3(1(5(4(0(4(x1))))))))))))))))))))) 1111.37/298.50 , 1(1(2(4(2(2(2(1(1(3(4(1(2(x1))))))))))))) -> 1111.37/298.50 1(5(0(3(4(1(0(5(2(2(2(3(x1)))))))))))) 1111.37/298.50 , 1(2(0(4(1(x1))))) -> 2(5(2(2(x1)))) 1111.37/298.50 , 1(2(5(3(3(0(2(2(5(3(2(3(3(3(2(1(x1)))))))))))))))) -> 1111.37/298.50 1(1(0(0(4(1(2(1(0(5(0(0(3(5(0(4(1(x1))))))))))))))))) 1111.37/298.50 , 1(3(4(5(1(0(0(3(1(2(4(2(3(5(2(0(4(1(x1)))))))))))))))))) -> 1111.37/298.50 1(3(0(0(4(2(2(5(3(1(0(1(2(1(5(0(1(4(1(x1))))))))))))))))))) 1111.37/298.50 , 1(3(5(1(0(4(x1)))))) -> 4(0(0(0(1(4(x1)))))) 1111.37/298.50 , 1(4(0(0(2(4(0(3(3(2(0(3(1(x1))))))))))))) -> 1111.37/298.50 1(5(0(5(0(2(0(5(1(0(1(2(5(5(x1)))))))))))))) 1111.37/298.50 , 1(4(2(3(1(3(4(2(4(1(5(1(4(0(4(5(2(0(0(3(4(x1))))))))))))))))))))) 1111.37/298.50 -> 4(3(4(1(3(5(1(1(4(3(1(5(1(3(1(2(4(2(1(3(x1)))))))))))))))))))) 1111.37/298.50 , 1(5(1(0(3(x1))))) -> 5(5(0(3(x1)))) 1111.37/298.50 , 2(2(1(1(0(2(0(1(2(3(x1)))))))))) -> 5(4(4(5(2(5(5(2(3(x1))))))))) 1111.37/298.50 , 2(2(2(3(3(4(3(3(5(4(5(x1))))))))))) -> 1111.37/298.50 5(5(4(2(5(3(5(3(2(0(5(x1))))))))))) 1111.37/298.50 , 3(1(2(5(0(3(4(3(1(5(4(1(5(2(0(5(x1)))))))))))))))) -> 1111.37/298.50 3(1(0(4(2(0(5(2(4(4(2(2(1(1(1(5(x1)))))))))))))))) 1111.37/298.50 , 3(3(1(4(5(4(5(5(x1)))))))) -> 3(5(3(2(0(5(2(x1))))))) 1111.37/298.50 , 4(1(4(1(3(0(0(2(1(5(4(1(0(0(x1)))))))))))))) -> 1111.37/298.50 2(3(0(2(5(4(4(3(0(4(1(2(0(x1))))))))))))) 1111.37/298.50 , 4(2(1(1(5(1(0(0(0(2(5(x1))))))))))) -> 1111.37/298.50 5(5(0(3(0(1(4(5(2(5(x1)))))))))) 1111.37/298.50 , 4(2(4(4(0(0(0(4(0(3(5(0(3(3(x1)))))))))))))) -> 1111.37/298.50 5(1(0(1(0(1(3(5(3(5(5(0(0(3(x1)))))))))))))) 1111.37/298.50 , 4(2(5(3(1(0(0(5(2(x1))))))))) -> 4(4(1(5(3(5(3(2(x1)))))))) 1111.37/298.50 , 4(5(1(4(x1)))) -> 1(5(4(4(x1)))) 1111.37/298.50 , 5(3(2(1(0(1(3(1(3(3(0(0(3(2(5(3(0(3(0(x1))))))))))))))))))) -> 1111.37/298.50 5(1(0(3(2(4(0(0(3(2(1(5(1(3(0(5(1(3(1(x1))))))))))))))))))) 1111.37/298.50 , 5(4(5(4(2(0(2(2(3(0(0(2(x1)))))))))))) -> 1111.37/298.50 5(3(4(5(0(3(2(1(1(2(2(x1))))))))))) } 1111.37/298.50 Obligation: 1111.37/298.50 derivational complexity 1111.37/298.50 Answer: 1111.37/298.50 YES(?,O(n^1)) 1111.37/298.50 1111.37/298.50 The problem is match-bounded by 2. The enriched problem is 1111.37/298.50 compatible with the following automaton. 1111.37/298.50 { 0_0(1) -> 1 1111.37/298.50 , 0_1(1) -> 5 1111.37/298.50 , 0_1(6) -> 4 1111.37/298.50 , 0_1(7) -> 109 1111.37/298.50 , 0_1(13) -> 12 1111.37/298.50 , 0_1(15) -> 109 1111.37/298.50 , 0_1(16) -> 33 1111.37/298.50 , 0_1(17) -> 1 1111.37/298.50 , 0_1(17) -> 5 1111.37/298.50 , 0_1(18) -> 17 1111.37/298.50 , 0_1(34) -> 161 1111.37/298.50 , 0_1(50) -> 136 1111.37/298.50 , 0_1(59) -> 58 1111.37/298.50 , 0_1(68) -> 5 1111.37/298.50 , 0_1(70) -> 69 1111.37/298.50 , 0_1(74) -> 73 1111.37/298.50 , 0_1(78) -> 5 1111.37/298.50 , 0_1(79) -> 78 1111.37/298.50 , 0_1(80) -> 79 1111.37/298.50 , 0_1(85) -> 84 1111.37/298.50 , 0_1(87) -> 86 1111.37/298.50 , 0_1(88) -> 87 1111.37/298.50 , 0_1(91) -> 90 1111.37/298.50 , 0_1(92) -> 109 1111.37/298.50 , 0_1(94) -> 93 1111.37/298.50 , 0_1(95) -> 94 1111.37/298.50 , 0_1(102) -> 101 1111.37/298.50 , 0_1(107) -> 106 1111.37/298.50 , 0_1(108) -> 34 1111.37/298.50 , 0_1(109) -> 108 1111.37/298.50 , 0_1(111) -> 110 1111.37/298.50 , 0_1(113) -> 112 1111.37/298.50 , 0_1(116) -> 115 1111.37/298.50 , 0_1(119) -> 161 1111.37/298.50 , 0_1(136) -> 303 1111.37/298.50 , 0_1(145) -> 250 1111.37/298.50 , 0_1(218) -> 152 1111.37/298.50 , 0_1(252) -> 251 1111.37/298.50 , 0_1(258) -> 257 1111.37/298.50 , 0_1(287) -> 286 1111.37/298.50 , 0_1(291) -> 290 1111.37/298.50 , 0_1(316) -> 315 1111.37/298.50 , 0_1(317) -> 316 1111.37/298.50 , 0_1(330) -> 329 1111.37/298.50 , 0_1(378) -> 377 1111.37/298.50 , 0_2(68) -> 394 1111.37/298.50 , 0_2(78) -> 396 1111.37/298.50 , 0_2(399) -> 398 1111.37/298.50 , 1_0(1) -> 1 1111.37/298.50 , 1_1(1) -> 92 1111.37/298.50 , 1_1(2) -> 381 1111.37/298.50 , 1_1(3) -> 259 1111.37/298.50 , 1_1(5) -> 4 1111.37/298.50 , 1_1(6) -> 92 1111.37/298.50 , 1_1(7) -> 6 1111.37/298.50 , 1_1(9) -> 8 1111.37/298.50 , 1_1(15) -> 14 1111.37/298.50 , 1_1(16) -> 15 1111.37/298.50 , 1_1(17) -> 92 1111.37/298.50 , 1_1(27) -> 26 1111.37/298.50 , 1_1(38) -> 37 1111.37/298.50 , 1_1(47) -> 46 1111.37/298.50 , 1_1(48) -> 47 1111.37/298.50 , 1_1(49) -> 48 1111.37/298.50 , 1_1(50) -> 134 1111.37/298.50 , 1_1(55) -> 54 1111.37/298.50 , 1_1(56) -> 55 1111.37/298.50 , 1_1(62) -> 61 1111.37/298.50 , 1_1(66) -> 65 1111.37/298.50 , 1_1(68) -> 1 1111.37/298.50 , 1_1(68) -> 7 1111.37/298.50 , 1_1(68) -> 15 1111.37/298.50 , 1_1(68) -> 16 1111.37/298.50 , 1_1(68) -> 92 1111.37/298.50 , 1_1(68) -> 134 1111.37/298.50 , 1_1(68) -> 228 1111.37/298.50 , 1_1(68) -> 259 1111.37/298.50 , 1_1(68) -> 380 1111.37/298.50 , 1_1(73) -> 72 1111.37/298.50 , 1_1(78) -> 68 1111.37/298.50 , 1_1(82) -> 81 1111.37/298.50 , 1_1(84) -> 83 1111.37/298.50 , 1_1(91) -> 107 1111.37/298.50 , 1_1(92) -> 228 1111.37/298.50 , 1_1(101) -> 100 1111.37/298.50 , 1_1(103) -> 102 1111.37/298.50 , 1_1(105) -> 104 1111.37/298.50 , 1_1(115) -> 114 1111.37/298.50 , 1_1(117) -> 116 1111.37/298.50 , 1_1(119) -> 229 1111.37/298.50 , 1_1(120) -> 36 1111.37/298.50 , 1_1(123) -> 122 1111.37/298.50 , 1_1(124) -> 123 1111.37/298.50 , 1_1(127) -> 126 1111.37/298.50 , 1_1(129) -> 128 1111.37/298.50 , 1_1(131) -> 130 1111.37/298.50 , 1_1(228) -> 227 1111.37/298.50 , 1_1(229) -> 228 1111.37/298.50 , 1_1(259) -> 380 1111.37/298.50 , 1_1(286) -> 119 1111.37/298.50 , 1_1(290) -> 287 1111.37/298.50 , 1_1(294) -> 291 1111.37/298.50 , 1_1(307) -> 306 1111.37/298.50 , 1_1(320) -> 319 1111.37/298.50 , 1_1(328) -> 327 1111.37/298.50 , 1_1(336) -> 335 1111.37/298.50 , 1_1(381) -> 380 1111.37/298.50 , 1_2(394) -> 393 1111.37/298.50 , 1_2(396) -> 395 1111.37/298.50 , 1_2(452) -> 119 1111.37/298.50 , 2_0(1) -> 1 1111.37/298.50 , 2_1(1) -> 3 1111.37/298.50 , 2_1(2) -> 1 1111.37/298.50 , 2_1(2) -> 5 1111.37/298.50 , 2_1(2) -> 16 1111.37/298.50 , 2_1(2) -> 91 1111.37/298.50 , 2_1(2) -> 92 1111.37/298.50 , 2_1(2) -> 109 1111.37/298.50 , 2_1(2) -> 259 1111.37/298.50 , 2_1(3) -> 2 1111.37/298.50 , 2_1(5) -> 3 1111.37/298.50 , 2_1(17) -> 3 1111.37/298.50 , 2_1(20) -> 19 1111.37/298.50 , 2_1(22) -> 21 1111.37/298.50 , 2_1(24) -> 23 1111.37/298.50 , 2_1(26) -> 25 1111.37/298.50 , 2_1(28) -> 27 1111.37/298.50 , 2_1(37) -> 36 1111.37/298.50 , 2_1(40) -> 39 1111.37/298.50 , 2_1(44) -> 43 1111.37/298.50 , 2_1(45) -> 44 1111.37/298.50 , 2_1(46) -> 45 1111.37/298.50 , 2_1(50) -> 77 1111.37/298.50 , 2_1(57) -> 56 1111.37/298.50 , 2_1(68) -> 3 1111.37/298.50 , 2_1(76) -> 75 1111.37/298.50 , 2_1(77) -> 76 1111.37/298.50 , 2_1(83) -> 82 1111.37/298.50 , 2_1(97) -> 96 1111.37/298.50 , 2_1(98) -> 97 1111.37/298.50 , 2_1(104) -> 103 1111.37/298.50 , 2_1(109) -> 160 1111.37/298.50 , 2_1(112) -> 111 1111.37/298.50 , 2_1(118) -> 117 1111.37/298.50 , 2_1(119) -> 3 1111.37/298.50 , 2_1(132) -> 131 1111.37/298.50 , 2_1(134) -> 133 1111.37/298.50 , 2_1(135) -> 3 1111.37/298.50 , 2_1(136) -> 3 1111.37/298.50 , 2_1(142) -> 141 1111.37/298.50 , 2_1(152) -> 34 1111.37/298.50 , 2_1(159) -> 77 1111.37/298.50 , 2_1(160) -> 1 1111.37/298.50 , 2_1(160) -> 5 1111.37/298.50 , 2_1(160) -> 109 1111.37/298.50 , 2_1(161) -> 160 1111.37/298.50 , 2_1(223) -> 222 1111.37/298.50 , 2_1(226) -> 225 1111.37/298.50 , 2_1(227) -> 226 1111.37/298.50 , 2_1(250) -> 249 1111.37/298.50 , 2_1(253) -> 252 1111.37/298.50 , 2_1(286) -> 3 1111.37/298.50 , 2_1(312) -> 311 1111.37/298.50 , 2_1(319) -> 318 1111.37/298.50 , 2_1(380) -> 379 1111.37/298.50 , 3_0(1) -> 1 1111.37/298.50 , 3_1(1) -> 50 1111.37/298.50 , 3_1(2) -> 50 1111.37/298.50 , 3_1(3) -> 50 1111.37/298.50 , 3_1(4) -> 1 1111.37/298.50 , 3_1(4) -> 5 1111.37/298.50 , 3_1(4) -> 50 1111.37/298.50 , 3_1(4) -> 109 1111.37/298.50 , 3_1(4) -> 336 1111.37/298.50 , 3_1(19) -> 18 1111.37/298.50 , 3_1(25) -> 24 1111.37/298.50 , 3_1(31) -> 30 1111.37/298.50 , 3_1(32) -> 88 1111.37/298.50 , 3_1(34) -> 50 1111.37/298.50 , 3_1(35) -> 34 1111.37/298.50 , 3_1(42) -> 41 1111.37/298.50 , 3_1(43) -> 42 1111.37/298.50 , 3_1(49) -> 308 1111.37/298.50 , 3_1(61) -> 60 1111.37/298.50 , 3_1(65) -> 64 1111.37/298.50 , 3_1(71) -> 70 1111.37/298.50 , 3_1(89) -> 88 1111.37/298.50 , 3_1(92) -> 336 1111.37/298.50 , 3_1(93) -> 68 1111.37/298.50 , 3_1(100) -> 99 1111.37/298.50 , 3_1(121) -> 120 1111.37/298.50 , 3_1(126) -> 125 1111.37/298.50 , 3_1(130) -> 129 1111.37/298.50 , 3_1(158) -> 157 1111.37/298.50 , 3_1(160) -> 159 1111.37/298.50 , 3_1(249) -> 248 1111.37/298.50 , 3_1(251) -> 2 1111.37/298.50 , 3_1(257) -> 256 1111.37/298.50 , 3_1(296) -> 294 1111.37/298.50 , 3_1(299) -> 298 1111.37/298.50 , 3_1(311) -> 287 1111.37/298.50 , 3_1(318) -> 317 1111.37/298.50 , 3_1(329) -> 328 1111.37/298.50 , 3_1(373) -> 119 1111.37/298.50 , 3_1(379) -> 378 1111.37/298.50 , 3_1(395) -> 50 1111.37/298.50 , 3_2(311) -> 399 1111.37/298.50 , 3_2(393) -> 109 1111.37/298.50 , 3_2(395) -> 4 1111.37/298.50 , 3_2(395) -> 109 1111.37/298.50 , 4_0(1) -> 1 1111.37/298.50 , 4_1(1) -> 16 1111.37/298.50 , 4_1(5) -> 67 1111.37/298.50 , 4_1(7) -> 119 1111.37/298.50 , 4_1(10) -> 9 1111.37/298.50 , 4_1(11) -> 10 1111.37/298.50 , 4_1(16) -> 69 1111.37/298.50 , 4_1(30) -> 29 1111.37/298.50 , 4_1(32) -> 31 1111.37/298.50 , 4_1(33) -> 67 1111.37/298.50 , 4_1(34) -> 1 1111.37/298.50 , 4_1(34) -> 4 1111.37/298.50 , 4_1(34) -> 15 1111.37/298.50 , 4_1(34) -> 16 1111.37/298.50 , 4_1(34) -> 92 1111.37/298.50 , 4_1(34) -> 134 1111.37/298.50 , 4_1(36) -> 35 1111.37/298.50 , 4_1(39) -> 38 1111.37/298.50 , 4_1(41) -> 40 1111.37/298.50 , 4_1(52) -> 51 1111.37/298.50 , 4_1(54) -> 53 1111.37/298.50 , 4_1(60) -> 59 1111.37/298.50 , 4_1(64) -> 63 1111.37/298.50 , 4_1(68) -> 16 1111.37/298.50 , 4_1(72) -> 71 1111.37/298.50 , 4_1(78) -> 16 1111.37/298.50 , 4_1(81) -> 80 1111.37/298.50 , 4_1(92) -> 91 1111.37/298.50 , 4_1(96) -> 95 1111.37/298.50 , 4_1(119) -> 7 1111.37/298.50 , 4_1(125) -> 124 1111.37/298.50 , 4_1(133) -> 132 1111.37/298.50 , 4_1(137) -> 119 1111.37/298.50 , 4_1(139) -> 137 1111.37/298.50 , 4_1(145) -> 7 1111.37/298.50 , 4_1(224) -> 223 1111.37/298.50 , 4_1(225) -> 224 1111.37/298.50 , 4_1(255) -> 254 1111.37/298.50 , 4_1(256) -> 255 1111.37/298.50 , 4_1(259) -> 258 1111.37/298.50 , 4_1(286) -> 16 1111.37/298.50 , 4_1(306) -> 34 1111.37/298.50 , 4_1(315) -> 312 1111.37/298.50 , 4_1(375) -> 373 1111.37/298.50 , 4_1(452) -> 16 1111.37/298.50 , 4_2(10) -> 454 1111.37/298.50 , 4_2(454) -> 453 1111.37/298.50 , 5_0(1) -> 1 1111.37/298.50 , 5_1(1) -> 119 1111.37/298.50 , 5_1(2) -> 2 1111.37/298.50 , 5_1(3) -> 145 1111.37/298.50 , 5_1(5) -> 119 1111.37/298.50 , 5_1(8) -> 7 1111.37/298.50 , 5_1(12) -> 11 1111.37/298.50 , 5_1(14) -> 13 1111.37/298.50 , 5_1(21) -> 20 1111.37/298.50 , 5_1(23) -> 22 1111.37/298.50 , 5_1(29) -> 28 1111.37/298.50 , 5_1(33) -> 32 1111.37/298.50 , 5_1(50) -> 49 1111.37/298.50 , 5_1(51) -> 34 1111.37/298.50 , 5_1(53) -> 52 1111.37/298.50 , 5_1(58) -> 57 1111.37/298.50 , 5_1(63) -> 62 1111.37/298.50 , 5_1(67) -> 66 1111.37/298.50 , 5_1(68) -> 119 1111.37/298.50 , 5_1(69) -> 68 1111.37/298.50 , 5_1(75) -> 74 1111.37/298.50 , 5_1(77) -> 145 1111.37/298.50 , 5_1(86) -> 85 1111.37/298.50 , 5_1(90) -> 89 1111.37/298.50 , 5_1(99) -> 98 1111.37/298.50 , 5_1(106) -> 105 1111.37/298.50 , 5_1(110) -> 70 1111.37/298.50 , 5_1(114) -> 113 1111.37/298.50 , 5_1(119) -> 1 1111.37/298.50 , 5_1(119) -> 2 1111.37/298.50 , 5_1(119) -> 3 1111.37/298.50 , 5_1(119) -> 5 1111.37/298.50 , 5_1(119) -> 16 1111.37/298.50 , 5_1(119) -> 49 1111.37/298.50 , 5_1(119) -> 75 1111.37/298.50 , 5_1(119) -> 91 1111.37/298.50 , 5_1(119) -> 92 1111.37/298.50 , 5_1(119) -> 109 1111.37/298.50 , 5_1(119) -> 118 1111.37/298.50 , 5_1(119) -> 119 1111.37/298.50 , 5_1(119) -> 259 1111.37/298.50 , 5_1(122) -> 121 1111.37/298.50 , 5_1(128) -> 127 1111.37/298.50 , 5_1(135) -> 1 1111.37/298.50 , 5_1(135) -> 16 1111.37/298.50 , 5_1(135) -> 92 1111.37/298.50 , 5_1(135) -> 229 1111.37/298.50 , 5_1(136) -> 135 1111.37/298.50 , 5_1(141) -> 139 1111.37/298.50 , 5_1(145) -> 142 1111.37/298.50 , 5_1(157) -> 152 1111.37/298.50 , 5_1(159) -> 158 1111.37/298.50 , 5_1(222) -> 218 1111.37/298.50 , 5_1(248) -> 4 1111.37/298.50 , 5_1(254) -> 253 1111.37/298.50 , 5_1(286) -> 119 1111.37/298.50 , 5_1(298) -> 296 1111.37/298.50 , 5_1(302) -> 299 1111.37/298.50 , 5_1(303) -> 302 1111.37/298.50 , 5_1(308) -> 307 1111.37/298.50 , 5_1(327) -> 320 1111.37/298.50 , 5_1(335) -> 330 1111.37/298.50 , 5_1(377) -> 375 1111.37/298.50 , 5_2(397) -> 4 1111.37/298.50 , 5_2(397) -> 15 1111.37/298.50 , 5_2(397) -> 48 1111.37/298.50 , 5_2(397) -> 92 1111.37/298.50 , 5_2(397) -> 107 1111.37/298.50 , 5_2(397) -> 228 1111.37/298.50 , 5_2(397) -> 229 1111.37/298.50 , 5_2(397) -> 259 1111.37/298.50 , 5_2(397) -> 380 1111.37/298.50 , 5_2(397) -> 381 1111.37/298.50 , 5_2(398) -> 397 1111.37/298.50 , 5_2(453) -> 452 } 1111.37/298.50 1111.37/298.50 Hurray, we answered YES(?,O(n^1)) 1111.88/299.01 EOF