YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

0(1(2(3(x0))))	→	2(3(3(x0)))
2(3(4(1(5(x0)))))	→	2(5(0(3(2(x0)))))
3(2(3(2(1(5(x0))))))	→	3(2(0(0(3(0(x0))))))
0(0(4(1(4(3(2(x0)))))))	→	5(5(3(3(0(1(x0))))))
5(1(2(1(0(0(3(2(x0))))))))	→	5(1(0(2(1(0(3(2(x0))))))))
4(3(2(4(0(2(0(5(2(x0)))))))))	→	0(5(1(1(2(2(1(2(x0))))))))
2(0(3(1(4(2(5(2(4(5(x0))))))))))	→	5(5(4(5(5(5(2(5(0(x0)))))))))
2(4(4(0(5(0(1(0(4(1(2(x0)))))))))))	→	2(4(1(3(4(0(2(0(2(5(2(x0)))))))))))
3(5(3(1(4(4(5(5(4(2(1(x0)))))))))))	→	3(3(5(2(3(4(5(4(3(0(1(x0)))))))))))
5(0(0(5(2(5(4(1(0(2(1(x0)))))))))))	→	5(4(5(4(5(1(1(1(3(2(x0))))))))))
4(1(4(3(3(2(3(0(1(3(5(1(x0))))))))))))	→	2(1(5(3(5(5(5(2(2(3(2(1(x0))))))))))))
5(4(0(4(0(4(2(2(5(5(4(5(x0))))))))))))	→	5(4(5(2(5(3(2(2(5(1(4(5(x0))))))))))))
5(4(2(5(0(3(1(4(3(0(1(4(1(x0)))))))))))))	→	5(4(4(2(5(0(2(5(5(3(2(2(1(x0)))))))))))))
3(4(4(1(0(2(3(3(1(4(5(5(5(3(x0))))))))))))))	→	1(3(4(5(5(3(0(2(2(1(3(2(3(3(x0))))))))))))))
5(2(5(1(5(0(4(3(2(2(2(3(0(4(0(x0)))))))))))))))	→	5(4(3(4(0(3(2(2(1(3(4(4(5(4(4(x0)))))))))))))))
0(5(2(1(1(1(3(4(1(0(4(5(5(4(2(5(x0))))))))))))))))	→	0(2(2(3(3(1(3(2(1(4(1(0(0(0(2(5(x0))))))))))))))))
5(2(4(5(2(1(5(2(4(1(0(3(3(0(0(2(x0))))))))))))))))	→	2(2(2(0(3(0(5(0(3(2(4(4(4(0(1(3(x0))))))))))))))))
0(1(0(2(3(5(3(4(0(2(4(1(1(2(5(1(3(5(x0))))))))))))))))))	→	0(1(3(5(2(0(5(1(2(3(5(1(2(3(3(1(4(x0)))))))))))))))))
1(0(3(4(2(4(5(2(2(4(3(3(3(3(3(2(3(5(x0))))))))))))))))))	→	1(0(0(2(5(3(5(2(3(4(2(0(0(3(2(3(2(4(1(x0)))))))))))))))))))
2(2(0(3(5(5(1(3(3(0(0(3(0(3(4(3(5(4(x0))))))))))))))))))	→	2(2(5(2(4(4(1(0(0(2(3(5(0(1(2(4(1(4(x0))))))))))))))))))
3(1(2(2(4(3(3(3(5(3(4(3(1(3(0(5(2(3(x0))))))))))))))))))	→	3(1(5(3(4(3(2(5(5(5(3(2(5(5(1(5(2(3(x0))))))))))))))))))
5(0(2(1(2(2(1(5(1(4(2(0(3(1(5(4(4(5(x0))))))))))))))))))	→	5(4(1(4(1(5(4(3(5(3(2(4(0(0(0(2(5(2(x0))))))))))))))))))
4(3(1(4(5(1(3(5(1(2(0(4(2(4(3(1(5(1(0(1(x0))))))))))))))))))))	→	5(1(3(5(3(4(4(2(2(5(1(0(0(2(4(4(2(3(0(0(1(x0)))))))))))))))))))))
1(1(2(4(5(1(4(4(1(3(1(3(1(4(4(4(3(3(4(1(2(x0)))))))))))))))))))))	→	0(4(2(2(2(2(5(1(2(1(4(4(5(1(1(0(4(5(2(3(4(x0)))))))))))))))))))))
1(4(0(2(0(0(5(1(4(4(0(3(4(2(1(4(1(5(5(1(5(x0)))))))))))))))))))))	→	1(1(3(3(2(2(2(0(5(3(4(5(3(2(1(0(1(2(4(3(4(x0)))))))))))))))))))))

Proof

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS

3(2(1(0(x0))))	→	3(3(2(x0)))
5(1(4(3(2(x0)))))	→	2(3(0(5(2(x0)))))
5(1(2(3(2(3(x0))))))	→	0(3(0(0(2(3(x0))))))
2(3(4(1(4(0(0(x0)))))))	→	1(0(3(3(5(5(x0))))))
2(3(0(0(1(2(1(5(x0))))))))	→	2(3(0(1(2(0(1(5(x0))))))))
2(5(0(2(0(4(2(3(4(x0)))))))))	→	2(1(2(2(1(1(5(0(x0))))))))
5(4(2(5(2(4(1(3(0(2(x0))))))))))	→	0(5(2(5(5(5(4(5(5(x0)))))))))
2(1(4(0(1(0(5(0(4(4(2(x0)))))))))))	→	2(5(2(0(2(0(4(3(1(4(2(x0)))))))))))
1(2(4(5(5(4(4(1(3(5(3(x0)))))))))))	→	1(0(3(4(5(4(3(2(5(3(3(x0)))))))))))
1(2(0(1(4(5(2(5(0(0(5(x0)))))))))))	→	2(3(1(1(1(5(4(5(4(5(x0))))))))))
1(5(3(1(0(3(2(3(3(4(1(4(x0))))))))))))	→	1(2(3(2(2(5(5(5(3(5(1(2(x0))))))))))))
5(4(5(5(2(2(4(0(4(0(4(5(x0))))))))))))	→	5(4(1(5(2(2(3(5(2(5(4(5(x0))))))))))))
1(4(1(0(3(4(1(3(0(5(2(4(5(x0)))))))))))))	→	1(2(2(3(5(5(2(0(5(2(4(4(5(x0)))))))))))))
3(5(5(5(4(1(3(3(2(0(1(4(4(3(x0))))))))))))))	→	3(3(2(3(1(2(2(0(3(5(5(4(3(1(x0))))))))))))))
0(4(0(3(2(2(2(3(4(0(5(1(5(2(5(x0)))))))))))))))	→	4(4(5(4(4(3(1(2(2(3(0(4(3(4(5(x0)))))))))))))))
5(2(4(5(5(4(0(1(4(3(1(1(1(2(5(0(x0))))))))))))))))	→	5(2(0(0(0(1(4(1(2(3(1(3(3(2(2(0(x0))))))))))))))))
2(0(0(3(3(0(1(4(2(5(1(2(5(4(2(5(x0))))))))))))))))	→	3(1(0(4(4(4(2(3(0(5(0(3(0(2(2(2(x0))))))))))))))))
5(3(1(5(2(1(1(4(2(0(4(3(5(3(2(0(1(0(x0))))))))))))))))))	→	4(1(3(3(2(1(5(3(2(1(5(0(2(5(3(1(0(x0)))))))))))))))))
5(3(2(3(3(3(3(3(4(2(2(5(4(2(4(3(0(1(x0))))))))))))))))))	→	1(4(2(3(2(3(0(0(2(4(3(2(5(3(5(2(0(0(1(x0)))))))))))))))))))
4(5(3(4(3(0(3(0(0(3(3(1(5(5(3(0(2(2(x0))))))))))))))))))	→	4(1(4(2(1(0(5(3(2(0(0(1(4(4(2(5(2(2(x0))))))))))))))))))
3(2(5(0(3(1(3(4(3(5(3(3(3(4(2(2(1(3(x0))))))))))))))))))	→	3(2(5(1(5(5(2(3(5(5(5(2(3(4(3(5(1(3(x0))))))))))))))))))
5(4(4(5(1(3(0(2(4(1(5(1(2(2(1(2(0(5(x0))))))))))))))))))	→	2(5(2(0(0(0(4(2(3(5(3(4(5(1(4(1(4(5(x0))))))))))))))))))
1(0(1(5(1(3(4(2(4(0(2(1(5(3(1(5(4(1(3(4(x0))))))))))))))))))))	→	1(0(0(3(2(4(4(2(0(0(1(5(2(2(4(4(3(5(3(1(5(x0)))))))))))))))))))))
2(1(4(3(3(4(4(4(1(3(1(3(1(4(4(1(5(4(2(1(1(x0)))))))))))))))))))))	→	4(3(2(5(4(0(1(1(5(4(4(1(2(1(5(2(2(2(2(4(0(x0)))))))))))))))))))))
5(1(5(5(1(4(1(2(4(3(0(4(4(1(5(0(0(2(0(4(1(x0)))))))))))))))))))))	→	4(3(4(2(1(0(1(2(3(5(4(3(5(0(2(2(2(3(3(1(1(x0)))))))))))))))))))))

1.1 Bounds

The given TRS is match-bounded by 1. This is shown by the following automaton.

final states:

{282, 262, 243, 227, 210, 194, 176, 160, 145, 130, 117, 103, 92, 83, 72, 63, 53, 43, 36, 28, 21, 15, 9, 5, 1}

transitions:

279 → 308

176 → 16

103 → 18

103 → 10

15 → 11

15 → 3

145 → 131

145 → 3

227 → 16

9 → 74

9 → 16

5 → 16

243 → 161

243 → 104

130 → 6

130 → 16

1 → 4

1 → 10

36 → 16

21 → 11

21 → 3

72 → 22

72 → 104

53 → 73

53 → 104

117 → 29

313 → 74

28 → 3

63 → 73

63 → 104

282 → 16

83 → 38

83 → 65

83 → 16

160 → 245

160 → 16

92 → 104

43 → 3

210 → 4

210 → 10

194 → 64

262 → 3

3₁(311) → 312

5₁(309) → 310

0₀(260) → 261

0₀(239) → 240

0₀(19) → 20

0₀(11) → 12

0₀(141) → 142

0₀(200) → 201

0₀(157) → 158

0₀(49) → 50

0₀(252) → 253

0₀(95) → 96

0₀(25) → 26

0₀(186) → 187

0₀(253) → 254

0₀(61) → 62

0₀(276) → 277

0₀(140) → 141

0₀(288) → 289

0₀(238) → 239

0₀(296) → 297

0₀(142) → 143

0₀(199) → 200

0₀(237) → 238

0₀(151) → 152

0₀(6) → 7

0₀(119) → 120

0₀(109) → 110

0₀(187) → 188

0₀(204) → 205

0₀(177) → 178

0₀(42) → 36

0₀(149) → 150

0₀(14) → 9

0₀(259) → 260

0₀(47) → 48

0₀(22) → 23

0₀(2) → 29

0₀(147) → 148

0₀(164) → 165

0₀(104) → 177

0₀(12) → 13

5₀(73) → 74

5₀(41) → 42

5₀(2) → 16

5₀(179) → 180

5₀(58) → 59

5₀(51) → 52

5₀(211) → 212

5₀(88) → 89

5₀(16) → 17

5₀(162) → 163

5₀(98) → 99

5₀(37) → 38

5₀(144) → 130

5₀(292) → 293

5₀(289) → 290

5₀(77) → 78

5₀(224) → 225

5₀(76) → 77

5₀(218) → 219

5₀(222) → 223

5₀(165) → 166

5₀(233) → 234

5₀(267) → 268

5₀(150) → 151

5₀(91) → 83

5₀(203) → 204

5₀(230) → 231

5₀(106) → 107

5₀(181) → 182

5₀(217) → 218

5₀(54) → 55

5₀(64) → 65

5₀(273) → 274

5₀(97) → 98

5₀(169) → 170

5₀(250) → 251

5₀(107) → 108

5₀(244) → 245

5₀(216) → 217

5₀(84) → 85

5₀(66) → 67

5₀(221) → 222

5₀(39) → 40

5₀(241) → 242

5₀(38) → 39

5₀(146) → 195

5₀(3) → 6

5₀(29) → 30

5₀(75) → 76

5₀(127) → 128

5₀(94) → 95

5₀(278) → 279

2₀(114) → 115

2₀(182) → 183

2₀(65) → 84

2₀(33) → 34

2₀(23) → 24

2₀(100) → 101

2₀(225) → 226

2₀(206) → 207

2₀(298) → 299

2₀(81) → 82

2₀(78) → 79

2₀(279) → 280

2₀(86) → 87

2₀(178) → 179

2₀(136) → 137

2₀(35) → 28

2₀(8) → 5

2₀(143) → 144

2₀(32) → 33

2₀(265) → 266

2₀(167) → 168

2₀(220) → 221

2₀(257) → 258

2₀(79) → 80

2₀(110) → 111

2₀(242) → 227

2₀(201) → 202

2₀(294) → 295

2₀(55) → 56

2₀(131) → 132

2₀(185) → 186

2₀(263) → 264

2₀(29) → 131

2₀(195) → 196

2₀(87) → 88

2₀(3) → 146

2₀(266) → 267

2₀(249) → 250

2₀(40) → 41

2₀(286) → 287

2₀(121) → 122

2₀(264) → 265

2₀(111) → 112

2₀(163) → 164

2₀(235) → 236

2₀(285) → 286

2₀(191) → 192

2₀(96) → 97

2₀(101) → 102

2₀(248) → 249

2₀(50) → 51

2₀(146) → 147

2₀(189) → 190

2₀(215) → 216

2₀(27) → 21

2₀(287) → 288

2₀(71) → 63

2₀(48) → 49

2₀(122) → 123

2₀(10) → 11

2₀(93) → 94

2₀(2) → 3

2₀(269) → 270

2₀(153) → 154

2₀(254) → 255

2₀(171) → 172

2₀(240) → 241

2₀(52) → 43

1₀(170) → 171

1₀(29) → 161

1₀(112) → 113

1₀(82) → 72

1₀(223) → 224

1₀(123) → 124

1₀(208) → 209

1₀(44) → 45

1₀(297) → 298

1₀(69) → 70

1₀(198) → 199

1₀(295) → 296

1₀(270) → 271

1₀(275) → 276

1₀(10) → 211

1₀(20) → 15

1₀(166) → 167

1₀(67) → 68

1₀(139) → 140

1₀(89) → 90

1₀(251) → 252

1₀(193) → 176

1₀(16) → 22

1₀(3) → 73

1₀(31) → 32

1₀(30) → 31

1₀(102) → 92

1₀(261) → 243

1₀(62) → 53

1₀(137) → 138

1₀(274) → 275

1₀(158) → 159

1₀(34) → 35

1₀(229) → 230

1₀(24) → 25

1₀(134) → 135

1₀(64) → 228

1₀(205) → 206

1₀(174) → 175

1₀(68) → 69

1₀(268) → 269

1₀(104) → 283

1₀(2) → 104

4₀(64) → 93

4₀(184) → 185

4₀(90) → 91

4₀(138) → 139

4₀(59) → 60

4₀(236) → 237

4₀(16) → 64

4₀(156) → 157

4₀(105) → 106

4₀(65) → 66

4₀(197) → 198

4₀(155) → 156

4₀(247) → 248

4₀(128) → 129

4₀(175) → 160

4₀(118) → 119

4₀(125) → 126

4₀(46) → 47

4₀(277) → 278

4₀(126) → 127

4₀(213) → 214

4₀(192) → 193

4₀(256) → 257

4₀(281) → 262

4₀(299) → 300

4₀(228) → 229

4₀(3) → 44

4₀(231) → 232

4₀(271) → 272

4₀(291) → 292

4₀(255) → 256

4₀(129) → 117

4₀(29) → 263

4₀(272) → 273

4₀(196) → 197

4₀(17) → 37

4₀(207) → 208

4₀(154) → 155

4₀(301) → 282

4₀(57) → 58

4₀(246) → 247

4₀(209) → 194

f6₀ → 2

3₀(2) → 10

3₀(18) → 19

3₀(56) → 57

3₀(133) → 134

3₀(258) → 259

3₀(10) → 54

3₀(300) → 301

3₀(202) → 203

3₀(64) → 118

3₀(99) → 100

3₀(80) → 81

3₀(232) → 233

3₀(113) → 114

3₀(152) → 153

3₀(4) → 1

3₀(159) → 145

3₀(124) → 125

3₀(26) → 27

3₀(234) → 235

3₀(104) → 105

3₀(74) → 75

3₀(3) → 4

3₀(214) → 215

3₀(17) → 18

3₀(284) → 285

3₀(135) → 136

3₀(245) → 246

3₀(70) → 71

3₀(132) → 133

3₀(173) → 174

3₀(161) → 162

3₀(280) → 281

3₀(7) → 8

3₀(290) → 291

3₀(180) → 181

3₀(45) → 46

3₀(22) → 244

3₀(172) → 173

3₀(293) → 294

3₀(85) → 86

3₀(183) → 184

3₀(120) → 121

3₀(226) → 210

3₀(60) → 61

3₀(212) → 213

3₀(108) → 109

3₀(219) → 220

3₀(188) → 189

3₀(190) → 191

3₀(283) → 284

3₀(13) → 14

3₀(148) → 149

3₀(115) → 116

3₀(116) → 103

3₀(168) → 169

0₁(310) → 311

2₁(308) → 309

2₁(312) → 313

279	→	308
176	→	16
103	→	18
103	→	10
15	→	11
15	→	3
145	→	131
145	→	3
227	→	16
9	→	74
9	→	16
5	→	16
243	→	161
243	→	104
130	→	6
130	→	16
1	→	4
1	→	10
36	→	16
21	→	11
21	→	3
72	→	22
72	→	104
53	→	73
53	→	104
117	→	29
313	→	74
28	→	3
63	→	73
63	→	104
282	→	16
83	→	38
83	→	65
83	→	16
160	→	245
160	→	16
92	→	104
43	→	3
210	→	4
210	→	10
194	→	64
262	→	3
3₁(311)	→	312
5₁(309)	→	310
0₀(260)	→	261
0₀(239)	→	240
0₀(19)	→	20
0₀(11)	→	12
0₀(141)	→	142
0₀(200)	→	201
0₀(157)	→	158
0₀(49)	→	50
0₀(252)	→	253
0₀(95)	→	96
0₀(25)	→	26
0₀(186)	→	187
0₀(253)	→	254
0₀(61)	→	62
0₀(276)	→	277
0₀(140)	→	141
0₀(288)	→	289
0₀(238)	→	239
0₀(296)	→	297
0₀(142)	→	143
0₀(199)	→	200
0₀(237)	→	238
0₀(151)	→	152
0₀(6)	→	7
0₀(119)	→	120
0₀(109)	→	110
0₀(187)	→	188
0₀(204)	→	205
0₀(177)	→	178
0₀(42)	→	36
0₀(149)	→	150
0₀(14)	→	9
0₀(259)	→	260
0₀(47)	→	48
0₀(22)	→	23
0₀(2)	→	29
0₀(147)	→	148
0₀(164)	→	165
0₀(104)	→	177
0₀(12)	→	13
5₀(73)	→	74
5₀(41)	→	42
5₀(2)	→	16
5₀(179)	→	180
5₀(58)	→	59
5₀(51)	→	52
5₀(211)	→	212
5₀(88)	→	89
5₀(16)	→	17
5₀(162)	→	163
5₀(98)	→	99
5₀(37)	→	38
5₀(144)	→	130
5₀(292)	→	293
5₀(289)	→	290
5₀(77)	→	78
5₀(224)	→	225
5₀(76)	→	77
5₀(218)	→	219
5₀(222)	→	223
5₀(165)	→	166
5₀(233)	→	234
5₀(267)	→	268
5₀(150)	→	151
5₀(91)	→	83
5₀(203)	→	204
5₀(230)	→	231
5₀(106)	→	107
5₀(181)	→	182
5₀(217)	→	218
5₀(54)	→	55
5₀(64)	→	65
5₀(273)	→	274
5₀(97)	→	98
5₀(169)	→	170
5₀(250)	→	251
5₀(107)	→	108
5₀(244)	→	245
5₀(216)	→	217
5₀(84)	→	85
5₀(66)	→	67
5₀(221)	→	222
5₀(39)	→	40
5₀(241)	→	242
5₀(38)	→	39
5₀(146)	→	195
5₀(3)	→	6
5₀(29)	→	30
5₀(75)	→	76
5₀(127)	→	128
5₀(94)	→	95
5₀(278)	→	279
2₀(114)	→	115
2₀(182)	→	183
2₀(65)	→	84
2₀(33)	→	34
2₀(23)	→	24
2₀(100)	→	101
2₀(225)	→	226
2₀(206)	→	207
2₀(298)	→	299
2₀(81)	→	82
2₀(78)	→	79
2₀(279)	→	280
2₀(86)	→	87
2₀(178)	→	179
2₀(136)	→	137
2₀(35)	→	28
2₀(8)	→	5
2₀(143)	→	144
2₀(32)	→	33
2₀(265)	→	266
2₀(167)	→	168
2₀(220)	→	221
2₀(257)	→	258
2₀(79)	→	80
2₀(110)	→	111
2₀(242)	→	227
2₀(201)	→	202
2₀(294)	→	295
2₀(55)	→	56
2₀(131)	→	132
2₀(185)	→	186
2₀(263)	→	264
2₀(29)	→	131
2₀(195)	→	196
2₀(87)	→	88
2₀(3)	→	146
2₀(266)	→	267
2₀(249)	→	250
2₀(40)	→	41
2₀(286)	→	287
2₀(121)	→	122
2₀(264)	→	265
2₀(111)	→	112
2₀(163)	→	164
2₀(235)	→	236
2₀(285)	→	286
2₀(191)	→	192
2₀(96)	→	97
2₀(101)	→	102
2₀(248)	→	249
2₀(50)	→	51
2₀(146)	→	147
2₀(189)	→	190
2₀(215)	→	216
2₀(27)	→	21
2₀(287)	→	288
2₀(71)	→	63
2₀(48)	→	49
2₀(122)	→	123
2₀(10)	→	11
2₀(93)	→	94
2₀(2)	→	3
2₀(269)	→	270
2₀(153)	→	154
2₀(254)	→	255
2₀(171)	→	172
2₀(240)	→	241
2₀(52)	→	43
1₀(170)	→	171
1₀(29)	→	161
1₀(112)	→	113
1₀(82)	→	72
1₀(223)	→	224
1₀(123)	→	124
1₀(208)	→	209
1₀(44)	→	45
1₀(297)	→	298
1₀(69)	→	70
1₀(198)	→	199
1₀(295)	→	296
1₀(270)	→	271
1₀(275)	→	276
1₀(10)	→	211
1₀(20)	→	15
1₀(166)	→	167
1₀(67)	→	68
1₀(139)	→	140
1₀(89)	→	90
1₀(251)	→	252
1₀(193)	→	176
1₀(16)	→	22
1₀(3)	→	73
1₀(31)	→	32
1₀(30)	→	31
1₀(102)	→	92
1₀(261)	→	243
1₀(62)	→	53
1₀(137)	→	138
1₀(274)	→	275
1₀(158)	→	159
1₀(34)	→	35
1₀(229)	→	230
1₀(24)	→	25
1₀(134)	→	135
1₀(64)	→	228
1₀(205)	→	206
1₀(174)	→	175
1₀(68)	→	69
1₀(268)	→	269
1₀(104)	→	283
1₀(2)	→	104
4₀(64)	→	93
4₀(184)	→	185
4₀(90)	→	91
4₀(138)	→	139
4₀(59)	→	60
4₀(236)	→	237
4₀(16)	→	64
4₀(156)	→	157
4₀(105)	→	106
4₀(65)	→	66
4₀(197)	→	198
4₀(155)	→	156
4₀(247)	→	248
4₀(128)	→	129
4₀(175)	→	160
4₀(118)	→	119
4₀(125)	→	126
4₀(46)	→	47
4₀(277)	→	278
4₀(126)	→	127
4₀(213)	→	214
4₀(192)	→	193
4₀(256)	→	257
4₀(281)	→	262
4₀(299)	→	300
4₀(228)	→	229
4₀(3)	→	44
4₀(231)	→	232
4₀(271)	→	272
4₀(291)	→	292
4₀(255)	→	256
4₀(129)	→	117
4₀(29)	→	263
4₀(272)	→	273
4₀(196)	→	197
4₀(17)	→	37
4₀(207)	→	208
4₀(154)	→	155
4₀(301)	→	282
4₀(57)	→	58
4₀(246)	→	247
4₀(209)	→	194
f6₀	→	2
3₀(2)	→	10
3₀(18)	→	19
3₀(56)	→	57
3₀(133)	→	134
3₀(258)	→	259
3₀(10)	→	54
3₀(300)	→	301
3₀(202)	→	203
3₀(64)	→	118
3₀(99)	→	100
3₀(80)	→	81
3₀(232)	→	233
3₀(113)	→	114
3₀(152)	→	153
3₀(4)	→	1
3₀(159)	→	145
3₀(124)	→	125
3₀(26)	→	27
3₀(234)	→	235
3₀(104)	→	105
3₀(74)	→	75
3₀(3)	→	4
3₀(214)	→	215
3₀(17)	→	18
3₀(284)	→	285
3₀(135)	→	136
3₀(245)	→	246
3₀(70)	→	71
3₀(132)	→	133
3₀(173)	→	174
3₀(161)	→	162
3₀(280)	→	281
3₀(7)	→	8
3₀(290)	→	291
3₀(180)	→	181
3₀(45)	→	46
3₀(22)	→	244
3₀(172)	→	173
3₀(293)	→	294
3₀(85)	→	86
3₀(183)	→	184
3₀(120)	→	121
3₀(226)	→	210
3₀(60)	→	61
3₀(212)	→	213
3₀(108)	→	109
3₀(219)	→	220
3₀(188)	→	189
3₀(190)	→	191
3₀(283)	→	284
3₀(13)	→	14
3₀(148)	→	149
3₀(115)	→	116
3₀(116)	→	103
3₀(168)	→	169
0₁(310)	→	311
2₁(308)	→	309
2₁(312)	→	313