YES(?,O(n^1)) 1128.63/297.06 YES(?,O(n^1)) 1128.63/297.06 1128.63/297.06 We are left with following problem, upon which TcT provides the 1128.63/297.06 certificate YES(?,O(n^1)). 1128.63/297.06 1128.63/297.06 Strict Trs: 1128.63/297.06 { 0(1(2(1(x1)))) -> 3(1(1(x1))) 1128.63/297.06 , 0(1(3(3(4(3(3(x1))))))) -> 0(3(2(0(3(x1))))) 1128.63/297.06 , 0(2(4(5(0(x1))))) -> 0(5(2(0(x1)))) 1128.63/297.06 , 0(3(1(1(2(2(3(5(1(5(5(4(0(x1))))))))))))) -> 1128.63/297.06 0(3(2(5(0(1(5(0(1(1(5(3(0(x1))))))))))))) 1128.63/297.06 , 0(4(3(5(5(x1))))) -> 0(3(5(5(x1)))) 1128.63/297.06 , 0(5(3(5(5(1(0(3(4(3(1(1(5(5(1(4(3(5(5(1(x1)))))))))))))))))))) -> 1128.63/297.06 0(0(5(1(2(1(1(4(4(4(2(3(1(5(5(5(1(4(2(x1))))))))))))))))))) 1128.63/297.06 , 1(0(4(3(0(3(5(5(0(4(3(5(5(2(4(4(4(1(4(x1))))))))))))))))))) -> 1128.63/297.06 1(1(3(5(1(1(0(5(0(0(3(3(1(5(4(4(4(1(x1)))))))))))))))))) 1128.63/297.06 , 1(1(4(4(3(x1))))) -> 1(2(2(4(4(x1))))) 1128.63/297.06 , 1(2(0(0(3(5(0(0(x1)))))))) -> 5(1(0(4(0(5(3(2(x1)))))))) 1128.63/297.06 , 1(2(5(0(2(3(2(4(1(3(4(3(2(4(x1)))))))))))))) -> 1128.63/297.06 2(3(1(2(3(0(2(0(2(2(0(0(2(x1))))))))))))) 1128.63/297.06 , 1(3(3(5(2(5(2(4(5(3(0(2(4(x1))))))))))))) -> 1128.63/297.06 4(5(1(4(3(2(1(5(5(5(5(x1))))))))))) 1128.63/297.06 , 1(5(2(3(5(2(3(0(5(5(0(1(0(3(1(5(0(x1))))))))))))))))) -> 1128.63/297.06 0(2(2(0(4(1(3(4(0(5(4(2(0(4(1(5(1(0(x1)))))))))))))))))) 1128.63/297.06 , 2(0(2(4(0(0(3(1(2(x1))))))))) -> 2(3(0(1(2(4(1(3(3(x1))))))))) 1128.63/297.06 , 2(1(4(5(4(3(2(5(2(2(2(4(1(2(5(4(x1)))))))))))))))) -> 1128.63/297.06 2(3(0(0(1(1(2(4(1(4(5(5(0(3(x1)))))))))))))) 1128.63/297.06 , 2(5(1(2(3(2(2(x1))))))) -> 4(1(1(1(1(4(1(x1))))))) 1128.63/297.06 , 3(0(0(4(0(1(1(0(5(3(x1)))))))))) -> 0(1(0(0(4(3(2(4(3(x1))))))))) 1128.63/297.06 , 3(1(4(0(3(1(0(3(0(2(4(4(x1)))))))))))) -> 1128.63/297.06 3(2(3(0(0(0(2(5(5(1(2(4(x1)))))))))))) 1128.63/297.06 , 3(3(1(1(3(2(0(2(4(2(1(2(1(1(4(4(1(x1))))))))))))))))) -> 1128.63/297.06 1(2(2(2(3(3(0(2(4(5(3(4(0(4(1(4(1(x1))))))))))))))))) 1128.63/297.06 , 3(4(3(0(4(2(1(1(4(3(x1)))))))))) -> 3(2(5(1(3(1(1(1(1(x1))))))))) 1128.63/297.06 , 3(5(1(2(0(4(1(1(x1)))))))) -> 3(5(4(0(3(4(1(x1))))))) 1128.63/297.06 , 4(0(2(0(3(4(3(0(3(0(4(x1))))))))))) -> 1128.63/297.06 4(4(5(2(0(3(2(4(1(5(4(x1))))))))))) 1128.63/297.06 , 4(1(0(2(5(4(5(2(4(4(5(x1))))))))))) -> 1128.63/297.06 2(0(2(0(1(2(5(1(4(5(x1)))))))))) 1128.63/297.06 , 5(1(2(0(0(2(1(4(1(5(3(0(1(4(4(5(1(x1))))))))))))))))) -> 1128.63/297.06 5(5(2(5(4(5(4(2(5(2(5(1(0(2(3(1(x1)))))))))))))))) 1128.63/297.06 , 5(1(5(5(5(4(x1)))))) -> 5(2(4(1(1(4(x1)))))) 1128.63/297.06 , 5(4(3(5(0(3(0(3(1(0(1(1(1(2(x1)))))))))))))) -> 1128.63/297.06 5(2(3(1(4(1(5(5(1(4(2(0(x1)))))))))))) } 1128.63/297.06 Obligation: 1128.63/297.06 derivational complexity 1128.63/297.06 Answer: 1128.63/297.06 YES(?,O(n^1)) 1128.63/297.06 1128.63/297.06 The problem is match-bounded by 2. The enriched problem is 1128.63/297.06 compatible with the following automaton. 1128.63/297.06 { 0_0(1) -> 1 1128.63/297.06 , 0_1(1) -> 6 1128.63/297.06 , 0_1(4) -> 1 1128.63/297.06 , 0_1(4) -> 3 1128.63/297.06 , 0_1(4) -> 6 1128.63/297.06 , 0_1(4) -> 7 1128.63/297.06 , 0_1(4) -> 15 1128.63/297.06 , 0_1(4) -> 69 1128.63/297.06 , 0_1(4) -> 146 1128.63/297.06 , 0_1(7) -> 6 1128.63/297.06 , 0_1(9) -> 8 1128.63/297.06 , 0_1(12) -> 11 1128.63/297.06 , 0_1(17) -> 4 1128.63/297.06 , 0_1(33) -> 69 1128.63/297.06 , 0_1(40) -> 39 1128.63/297.06 , 0_1(42) -> 41 1128.63/297.06 , 0_1(43) -> 42 1128.63/297.06 , 0_1(50) -> 6 1128.63/297.06 , 0_1(52) -> 146 1128.63/297.06 , 0_1(55) -> 54 1128.63/297.06 , 0_1(57) -> 56 1128.63/297.06 , 0_1(59) -> 6 1128.63/297.06 , 0_1(64) -> 63 1128.63/297.06 , 0_1(66) -> 65 1128.63/297.06 , 0_1(69) -> 68 1128.63/297.06 , 0_1(79) -> 78 1128.63/297.06 , 0_1(84) -> 83 1128.63/297.06 , 0_1(88) -> 87 1128.63/297.06 , 0_1(92) -> 60 1128.63/297.06 , 0_1(97) -> 92 1128.63/297.06 , 0_1(109) -> 108 1128.63/297.06 , 0_1(110) -> 109 1128.63/297.06 , 0_1(117) -> 116 1128.63/297.06 , 0_1(118) -> 117 1128.63/297.06 , 0_1(119) -> 118 1128.63/297.06 , 0_1(141) -> 140 1128.63/297.06 , 0_1(147) -> 146 1128.63/297.06 , 0_1(173) -> 172 1128.63/297.06 , 0_1(185) -> 184 1128.63/297.06 , 0_1(190) -> 59 1128.63/297.06 , 0_1(192) -> 191 1128.63/297.06 , 0_1(208) -> 207 1128.63/297.06 , 0_1(209) -> 1 1128.63/297.06 , 0_1(209) -> 146 1128.63/297.06 , 1_0(1) -> 1 1128.63/297.06 , 1_1(1) -> 3 1128.63/297.06 , 1_1(2) -> 152 1128.63/297.06 , 1_1(3) -> 2 1128.63/297.06 , 1_1(4) -> 3 1128.63/297.06 , 1_1(6) -> 91 1128.63/297.06 , 1_1(10) -> 9 1128.63/297.06 , 1_1(13) -> 12 1128.63/297.06 , 1_1(14) -> 13 1128.63/297.06 , 1_1(19) -> 18 1128.63/297.06 , 1_1(21) -> 20 1128.63/297.06 , 1_1(22) -> 21 1128.63/297.06 , 1_1(28) -> 27 1128.63/297.06 , 1_1(32) -> 31 1128.63/297.06 , 1_1(33) -> 127 1128.63/297.06 , 1_1(34) -> 1 1128.63/297.06 , 1_1(34) -> 2 1128.63/297.06 , 1_1(34) -> 3 1128.63/297.06 , 1_1(34) -> 7 1128.63/297.06 , 1_1(34) -> 15 1128.63/297.06 , 1_1(34) -> 91 1128.63/297.06 , 1_1(34) -> 96 1128.63/297.06 , 1_1(34) -> 211 1128.63/297.06 , 1_1(35) -> 34 1128.63/297.06 , 1_1(38) -> 37 1128.63/297.06 , 1_1(39) -> 38 1128.63/297.06 , 1_1(46) -> 45 1128.63/297.06 , 1_1(49) -> 107 1128.63/297.06 , 1_1(52) -> 212 1128.63/297.06 , 1_1(54) -> 53 1128.63/297.06 , 1_1(59) -> 3 1128.63/297.06 , 1_1(61) -> 60 1128.63/297.06 , 1_1(70) -> 3 1128.63/297.06 , 1_1(72) -> 71 1128.63/297.06 , 1_1(76) -> 75 1128.63/297.06 , 1_1(81) -> 80 1128.63/297.06 , 1_1(90) -> 89 1128.63/297.06 , 1_1(93) -> 92 1128.63/297.06 , 1_1(96) -> 95 1128.63/297.06 , 1_1(98) -> 97 1128.63/297.06 , 1_1(99) -> 98 1128.63/297.06 , 1_1(102) -> 101 1128.63/297.06 , 1_1(105) -> 70 1128.63/297.06 , 1_1(106) -> 105 1128.63/297.06 , 1_1(107) -> 106 1128.63/297.06 , 1_1(108) -> 4 1128.63/297.06 , 1_1(112) -> 127 1128.63/297.06 , 1_1(126) -> 89 1128.63/297.06 , 1_1(150) -> 149 1128.63/297.06 , 1_1(151) -> 152 1128.63/297.06 , 1_1(152) -> 151 1128.63/297.06 , 1_1(189) -> 188 1128.63/297.06 , 1_1(193) -> 192 1128.63/297.06 , 1_1(196) -> 195 1128.63/297.06 , 1_1(207) -> 206 1128.63/297.06 , 1_1(212) -> 211 1128.63/297.06 , 1_1(214) -> 213 1128.63/297.06 , 1_1(216) -> 215 1128.63/297.06 , 1_1(219) -> 218 1128.63/297.06 , 1_2(290) -> 289 1128.63/297.06 , 1_2(291) -> 290 1128.63/297.06 , 2_0(1) -> 1 1128.63/297.06 , 2_1(1) -> 33 1128.63/297.06 , 2_1(4) -> 33 1128.63/297.06 , 2_1(6) -> 5 1128.63/297.06 , 2_1(17) -> 33 1128.63/297.06 , 2_1(20) -> 19 1128.63/297.06 , 2_1(26) -> 25 1128.63/297.06 , 2_1(34) -> 33 1128.63/297.06 , 2_1(50) -> 34 1128.63/297.06 , 2_1(51) -> 50 1128.63/297.06 , 2_1(52) -> 112 1128.63/297.06 , 2_1(54) -> 33 1128.63/297.06 , 2_1(59) -> 1 1128.63/297.06 , 2_1(59) -> 3 1128.63/297.06 , 2_1(59) -> 5 1128.63/297.06 , 2_1(59) -> 33 1128.63/297.06 , 2_1(59) -> 49 1128.63/297.06 , 2_1(59) -> 52 1128.63/297.06 , 2_1(59) -> 127 1128.63/297.06 , 2_1(62) -> 61 1128.63/297.06 , 2_1(65) -> 64 1128.63/297.06 , 2_1(67) -> 66 1128.63/297.06 , 2_1(68) -> 67 1128.63/297.06 , 2_1(70) -> 4 1128.63/297.06 , 2_1(75) -> 74 1128.63/297.06 , 2_1(77) -> 4 1128.63/297.06 , 2_1(78) -> 77 1128.63/297.06 , 2_1(87) -> 86 1128.63/297.06 , 2_1(94) -> 93 1128.63/297.06 , 2_1(100) -> 99 1128.63/297.06 , 2_1(113) -> 112 1128.63/297.06 , 2_1(114) -> 2 1128.63/297.06 , 2_1(120) -> 119 1128.63/297.06 , 2_1(126) -> 193 1128.63/297.06 , 2_1(138) -> 51 1128.63/297.06 , 2_1(142) -> 141 1128.63/297.06 , 2_1(184) -> 183 1128.63/297.06 , 2_1(187) -> 186 1128.63/297.06 , 2_1(191) -> 190 1128.63/297.06 , 2_1(194) -> 193 1128.63/297.06 , 2_1(198) -> 197 1128.63/297.06 , 2_1(203) -> 202 1128.63/297.06 , 2_1(205) -> 204 1128.63/297.06 , 2_1(209) -> 208 1128.63/297.06 , 2_1(210) -> 53 1128.63/297.06 , 2_2(288) -> 287 1128.63/297.06 , 3_0(1) -> 1 1128.63/297.06 , 3_1(1) -> 7 1128.63/297.06 , 3_1(2) -> 1 1128.63/297.06 , 3_1(2) -> 6 1128.63/297.06 , 3_1(2) -> 7 1128.63/297.06 , 3_1(2) -> 209 1128.63/297.06 , 3_1(3) -> 209 1128.63/297.06 , 3_1(5) -> 4 1128.63/297.06 , 3_1(6) -> 15 1128.63/297.06 , 3_1(7) -> 96 1128.63/297.06 , 3_1(27) -> 26 1128.63/297.06 , 3_1(33) -> 58 1128.63/297.06 , 3_1(36) -> 35 1128.63/297.06 , 3_1(44) -> 43 1128.63/297.06 , 3_1(45) -> 44 1128.63/297.06 , 3_1(49) -> 173 1128.63/297.06 , 3_1(50) -> 7 1128.63/297.06 , 3_1(53) -> 209 1128.63/297.06 , 3_1(59) -> 7 1128.63/297.06 , 3_1(60) -> 59 1128.63/297.06 , 3_1(63) -> 62 1128.63/297.06 , 3_1(70) -> 1 1128.63/297.06 , 3_1(70) -> 7 1128.63/297.06 , 3_1(71) -> 209 1128.63/297.06 , 3_1(74) -> 73 1128.63/297.06 , 3_1(77) -> 7 1128.63/297.06 , 3_1(82) -> 81 1128.63/297.06 , 3_1(112) -> 111 1128.63/297.06 , 3_1(116) -> 114 1128.63/297.06 , 3_1(139) -> 138 1128.63/297.06 , 3_1(140) -> 139 1128.63/297.06 , 3_1(145) -> 144 1128.63/297.06 , 3_1(151) -> 150 1128.63/297.06 , 3_1(186) -> 185 1128.63/297.06 , 3_1(208) -> 58 1128.63/297.06 , 3_1(213) -> 210 1128.63/297.06 , 4_0(1) -> 1 1128.63/297.06 , 4_1(1) -> 52 1128.63/297.06 , 4_1(2) -> 52 1128.63/297.06 , 4_1(3) -> 49 1128.63/297.06 , 4_1(5) -> 219 1128.63/297.06 , 4_1(7) -> 113 1128.63/297.06 , 4_1(16) -> 196 1128.63/297.06 , 4_1(23) -> 22 1128.63/297.06 , 4_1(24) -> 23 1128.63/297.06 , 4_1(25) -> 24 1128.63/297.06 , 4_1(33) -> 32 1128.63/297.06 , 4_1(34) -> 49 1128.63/297.06 , 4_1(48) -> 47 1128.63/297.06 , 4_1(49) -> 48 1128.63/297.06 , 4_1(52) -> 51 1128.63/297.06 , 4_1(56) -> 55 1128.63/297.06 , 4_1(70) -> 1 1128.63/297.06 , 4_1(70) -> 3 1128.63/297.06 , 4_1(70) -> 33 1128.63/297.06 , 4_1(70) -> 52 1128.63/297.06 , 4_1(70) -> 95 1128.63/297.06 , 4_1(70) -> 193 1128.63/297.06 , 4_1(73) -> 72 1128.63/297.06 , 4_1(80) -> 79 1128.63/297.06 , 4_1(83) -> 82 1128.63/297.06 , 4_1(86) -> 85 1128.63/297.06 , 4_1(89) -> 88 1128.63/297.06 , 4_1(95) -> 94 1128.63/297.06 , 4_1(101) -> 100 1128.63/297.06 , 4_1(103) -> 102 1128.63/297.06 , 4_1(105) -> 49 1128.63/297.06 , 4_1(107) -> 147 1128.63/297.06 , 4_1(111) -> 110 1128.63/297.06 , 4_1(143) -> 142 1128.63/297.06 , 4_1(146) -> 145 1128.63/297.06 , 4_1(172) -> 71 1128.63/297.06 , 4_1(182) -> 70 1128.63/297.06 , 4_1(188) -> 187 1128.63/297.06 , 4_1(200) -> 199 1128.63/297.06 , 4_1(202) -> 201 1128.63/297.06 , 4_1(211) -> 210 1128.63/297.06 , 4_1(215) -> 214 1128.63/297.06 , 4_2(70) -> 291 1128.63/297.06 , 4_2(182) -> 291 1128.63/297.06 , 4_2(289) -> 288 1128.63/297.06 , 5_0(1) -> 1 1128.63/297.06 , 5_1(1) -> 16 1128.63/297.06 , 5_1(3) -> 126 1128.63/297.06 , 5_1(4) -> 76 1128.63/297.06 , 5_1(5) -> 4 1128.63/297.06 , 5_1(6) -> 104 1128.63/297.06 , 5_1(7) -> 14 1128.63/297.06 , 5_1(8) -> 6 1128.63/297.06 , 5_1(11) -> 10 1128.63/297.06 , 5_1(15) -> 14 1128.63/297.06 , 5_1(16) -> 5 1128.63/297.06 , 5_1(18) -> 17 1128.63/297.06 , 5_1(29) -> 28 1128.63/297.06 , 5_1(30) -> 29 1128.63/297.06 , 5_1(31) -> 30 1128.63/297.06 , 5_1(33) -> 4 1128.63/297.06 , 5_1(37) -> 36 1128.63/297.06 , 5_1(41) -> 40 1128.63/297.06 , 5_1(47) -> 46 1128.63/297.06 , 5_1(52) -> 189 1128.63/297.06 , 5_1(53) -> 1 1128.63/297.06 , 5_1(53) -> 3 1128.63/297.06 , 5_1(53) -> 16 1128.63/297.06 , 5_1(53) -> 126 1128.63/297.06 , 5_1(53) -> 127 1128.63/297.06 , 5_1(53) -> 189 1128.63/297.06 , 5_1(58) -> 57 1128.63/297.06 , 5_1(70) -> 16 1128.63/297.06 , 5_1(71) -> 70 1128.63/297.06 , 5_1(85) -> 84 1128.63/297.06 , 5_1(91) -> 90 1128.63/297.06 , 5_1(104) -> 103 1128.63/297.06 , 5_1(107) -> 194 1128.63/297.06 , 5_1(126) -> 120 1128.63/297.06 , 5_1(127) -> 126 1128.63/297.06 , 5_1(144) -> 143 1128.63/297.06 , 5_1(149) -> 114 1128.63/297.06 , 5_1(182) -> 16 1128.63/297.06 , 5_1(183) -> 182 1128.63/297.06 , 5_1(195) -> 194 1128.63/297.06 , 5_1(197) -> 53 1128.63/297.06 , 5_1(199) -> 198 1128.63/297.06 , 5_1(201) -> 200 1128.63/297.06 , 5_1(204) -> 203 1128.63/297.06 , 5_1(206) -> 205 1128.63/297.06 , 5_1(217) -> 216 1128.63/297.06 , 5_1(218) -> 217 1128.63/297.06 , 5_2(287) -> 126 } 1128.63/297.06 1128.63/297.06 Hurray, we answered YES(?,O(n^1)) 1129.46/297.70 EOF