YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{298, 279, 262, 246, 228, 211, 194, 179, 164, 151, 137, 122, 108, 96, 85, 75, 65, 54, 46, 39, 34, 30, 25, 20, 17, 13, 10, 8, 5, 1}

transitions:

279 → 55

279 → 6

25 → 18

25 → 3

10 → 6

96 → 55

96 → 6

211 → 212

122 → 212

39 → 6

108 → 31

108 → 21

298 → 212

5 → 27

5 → 14

34 → 3

65 → 6

20 → 21

246 → 21

1 → 123

1 → 26

8 → 26

13 → 123

13 → 26

179 → 21

121 → 327

6 → 317

54 → 299

54 → 26

75 → 97

75 → 14

85 → 3

30 → 21

137 → 66

137 → 212

46 → 123

46 → 26

17 → 26

164 → 21

320 → 37

328 → 318

194 → 123

194 → 26

151 → 212

262 → 212

228 → 22

228 → 212

2₁(318) → 319

3₀(244) → 245

3₀(35) → 247

3₀(245) → 228

3₀(212) → 213

3₀(141) → 142

3₀(92) → 93

3₀(301) → 302

3₀(300) → 301

3₀(144) → 145

3₀(252) → 253

3₀(3) → 97

3₀(7) → 5

3₀(44) → 45

3₀(33) → 30

3₀(66) → 67

3₀(91) → 92

3₀(21) → 47

3₀(26) → 27

3₀(276) → 277

3₀(87) → 88

3₀(206) → 207

3₀(134) → 135

3₀(106) → 107

3₀(111) → 112

3₀(288) → 289

3₀(138) → 139

3₀(142) → 143

3₀(311) → 312

3₀(199) → 200

3₀(237) → 238

3₀(289) → 290

3₀(201) → 202

3₀(27) → 28

3₀(6) → 40

3₀(145) → 146

3₀(84) → 75

3₀(136) → 122

3₀(109) → 195

3₀(72) → 73

3₀(214) → 215

3₀(90) → 91

3₀(63) → 64

3₀(191) → 192

3₀(28) → 29

3₀(14) → 280

3₀(36) → 37

3₀(116) → 117

3₀(22) → 23

3₀(2) → 14

3₀(57) → 58

3₀(263) → 264

3₀(213) → 214

3₀(176) → 177

3₀(282) → 283

3₀(156) → 157

3₀(226) → 227

3₀(38) → 34

4₀(109) → 110

4₀(2) → 6

4₀(31) → 138

4₀(45) → 39

4₀(21) → 229

4₀(120) → 121

4₀(74) → 65

4₀(295) → 296

4₀(225) → 226

4₀(113) → 114

4₀(147) → 148

4₀(32) → 152

4₀(249) → 250

4₀(133) → 134

4₀(37) → 38

4₀(115) → 116

4₀(77) → 78

4₀(218) → 219

4₀(222) → 223

4₀(254) → 255

4₀(12) → 10

4₀(47) → 76

4₀(89) → 90

4₀(260) → 261

4₀(258) → 259

4₀(308) → 309

4₀(61) → 62

4₀(203) → 204

4₀(105) → 106

4₀(210) → 194

4₀(135) → 136

4₀(302) → 303

4₀(238) → 239

4₀(277) → 278

4₀(281) → 282

4₀(14) → 55

4₀(56) → 57

4₀(139) → 140

4₀(273) → 274

4₀(107) → 96

4₀(170) → 171

4₀(256) → 257

4₀(3) → 11

4₀(312) → 313

4₀(52) → 53

4₀(248) → 249

4₀(81) → 82

4₀(101) → 102

4₀(149) → 150

4₀(196) → 197

4₀(272) → 273

2₀(114) → 115

2₀(98) → 99

2₀(182) → 183

2₀(123) → 124

2₀(1) → 9

2₀(78) → 79

2₀(76) → 77

2₀(14) → 18

2₀(251) → 252

2₀(183) → 184

2₀(159) → 160

2₀(230) → 231

2₀(19) → 17

2₀(86) → 87

2₀(118) → 119

2₀(173) → 174

2₀(310) → 311

2₀(99) → 100

2₀(6) → 7

2₀(220) → 221

2₀(231) → 232

2₀(155) → 156

2₀(283) → 284

2₀(294) → 295

2₀(202) → 203

2₀(129) → 130

2₀(18) → 19

2₀(82) → 83

2₀(3) → 4

2₀(299) → 300

2₀(271) → 272

2₀(40) → 41

2₀(284) → 285

2₀(264) → 265

2₀(221) → 222

2₀(285) → 286

2₀(261) → 246

2₀(83) → 84

2₀(215) → 216

2₀(223) → 224

2₀(49) → 50

2₀(297) → 279

2₀(48) → 49

2₀(103) → 104

2₀(2) → 3

2₀(171) → 172

2₀(16) → 13

2₀(240) → 241

0₀(125) → 126

0₀(286) → 287

0₀(29) → 25

0₀(296) → 297

0₀(287) → 288

0₀(192) → 193

0₀(255) → 256

0₀(88) → 89

0₀(94) → 95

0₀(117) → 118

0₀(124) → 125

0₀(169) → 170

0₀(11) → 12

0₀(60) → 61

0₀(242) → 243

0₀(157) → 158

0₀(198) → 199

0₀(128) → 129

0₀(7) → 263

0₀(6) → 31

0₀(234) → 235

0₀(305) → 306

0₀(22) → 180

0₀(15) → 16

0₀(314) → 315

0₀(154) → 155

0₀(14) → 15

0₀(165) → 166

0₀(31) → 32

0₀(70) → 71

0₀(224) → 225

0₀(274) → 275

0₀(216) → 217

0₀(229) → 230

0₀(195) → 196

0₀(32) → 33

0₀(95) → 85

0₀(110) → 111

0₀(121) → 108

0₀(131) → 132

0₀(247) → 248

0₀(79) → 80

0₀(24) → 20

0₀(51) → 52

0₀(130) → 131

0₀(313) → 314

0₀(23) → 24

0₀(233) → 234

0₀(315) → 316

0₀(188) → 189

0₀(253) → 254

0₀(178) → 164

0₀(71) → 72

0₀(2) → 21

5₀(184) → 185

5₀(132) → 133

5₀(180) → 181

5₀(236) → 237

5₀(93) → 94

5₀(189) → 190

5₀(265) → 266

5₀(197) → 198

5₀(200) → 201

5₀(68) → 69

5₀(227) → 211

5₀(172) → 173

5₀(278) → 262

5₀(21) → 22

5₀(232) → 233

5₀(175) → 176

5₀(268) → 269

5₀(97) → 98

5₀(190) → 191

5₀(243) → 244

5₀(181) → 182

5₀(217) → 218

5₀(50) → 51

5₀(69) → 70

5₀(6) → 66

5₀(269) → 270

5₀(186) → 187

5₀(167) → 168

5₀(241) → 242

5₀(80) → 81

5₀(14) → 109

5₀(239) → 240

5₀(307) → 308

5₀(162) → 163

5₀(43) → 44

5₀(177) → 178

5₀(174) → 175

5₀(2) → 212

5₀(163) → 151

5₀(3) → 86

5₀(316) → 298

5₀(304) → 305

5₀(168) → 169

5₀(143) → 144

5₀(292) → 293

5₀(161) → 162

5₀(259) → 260

5₀(158) → 159

5₀(67) → 68

5₀(153) → 154

5₀(150) → 137

5₀(104) → 105

5₀(209) → 210

f6₀ → 2

1₀(2) → 26

1₀(250) → 251

1₀(275) → 276

1₀(9) → 8

1₀(306) → 307

1₀(257) → 258

1₀(204) → 205

1₀(146) → 147

1₀(64) → 54

1₀(166) → 167

1₀(309) → 310

1₀(303) → 304

1₀(152) → 153

1₀(235) → 236

1₀(55) → 56

1₀(291) → 292

1₀(4) → 1

1₀(21) → 123

1₀(6) → 299

1₀(100) → 101

1₀(53) → 46

1₀(140) → 141

1₀(62) → 63

1₀(208) → 209

1₀(112) → 113

1₀(280) → 281

1₀(290) → 291

1₀(35) → 36

1₀(267) → 268

1₀(205) → 206

1₀(127) → 128

1₀(293) → 294

1₀(42) → 43

1₀(126) → 127

1₀(73) → 74

1₀(270) → 271

1₀(41) → 42

1₀(266) → 267

1₀(187) → 188

1₀(219) → 220

1₀(59) → 60

1₀(109) → 165

1₀(31) → 35

1₀(58) → 59

1₀(185) → 186

1₀(148) → 149

1₀(193) → 179

1₀(160) → 161

1₀(207) → 208

1₀(119) → 120

1₀(47) → 48

1₀(102) → 103

4₁(317) → 318

4₁(327) → 328

3₁(319) → 320

279	→	55
279	→	6
25	→	18
25	→	3
10	→	6
96	→	55
96	→	6
211	→	212
122	→	212
39	→	6
108	→	31
108	→	21
298	→	212
5	→	27
5	→	14
34	→	3
65	→	6
20	→	21
246	→	21
1	→	123
1	→	26
8	→	26
13	→	123
13	→	26
179	→	21
121	→	327
6	→	317
54	→	299
54	→	26
75	→	97
75	→	14
85	→	3
30	→	21
137	→	66
137	→	212
46	→	123
46	→	26
17	→	26
164	→	21
320	→	37
328	→	318
194	→	123
194	→	26
151	→	212
262	→	212
228	→	22
228	→	212
2₁(318)	→	319
3₀(244)	→	245
3₀(35)	→	247
3₀(245)	→	228
3₀(212)	→	213
3₀(141)	→	142
3₀(92)	→	93
3₀(301)	→	302
3₀(300)	→	301
3₀(144)	→	145
3₀(252)	→	253
3₀(3)	→	97
3₀(7)	→	5
3₀(44)	→	45
3₀(33)	→	30
3₀(66)	→	67
3₀(91)	→	92
3₀(21)	→	47
3₀(26)	→	27
3₀(276)	→	277
3₀(87)	→	88
3₀(206)	→	207
3₀(134)	→	135
3₀(106)	→	107
3₀(111)	→	112
3₀(288)	→	289
3₀(138)	→	139
3₀(142)	→	143
3₀(311)	→	312
3₀(199)	→	200
3₀(237)	→	238
3₀(289)	→	290
3₀(201)	→	202
3₀(27)	→	28
3₀(6)	→	40
3₀(145)	→	146
3₀(84)	→	75
3₀(136)	→	122
3₀(109)	→	195
3₀(72)	→	73
3₀(214)	→	215
3₀(90)	→	91
3₀(63)	→	64
3₀(191)	→	192
3₀(28)	→	29
3₀(14)	→	280
3₀(36)	→	37
3₀(116)	→	117
3₀(22)	→	23
3₀(2)	→	14
3₀(57)	→	58
3₀(263)	→	264
3₀(213)	→	214
3₀(176)	→	177
3₀(282)	→	283
3₀(156)	→	157
3₀(226)	→	227
3₀(38)	→	34
4₀(109)	→	110
4₀(2)	→	6
4₀(31)	→	138
4₀(45)	→	39
4₀(21)	→	229
4₀(120)	→	121
4₀(74)	→	65
4₀(295)	→	296
4₀(225)	→	226
4₀(113)	→	114
4₀(147)	→	148
4₀(32)	→	152
4₀(249)	→	250
4₀(133)	→	134
4₀(37)	→	38
4₀(115)	→	116
4₀(77)	→	78
4₀(218)	→	219
4₀(222)	→	223
4₀(254)	→	255
4₀(12)	→	10
4₀(47)	→	76
4₀(89)	→	90
4₀(260)	→	261
4₀(258)	→	259
4₀(308)	→	309
4₀(61)	→	62
4₀(203)	→	204
4₀(105)	→	106
4₀(210)	→	194
4₀(135)	→	136
4₀(302)	→	303
4₀(238)	→	239
4₀(277)	→	278
4₀(281)	→	282
4₀(14)	→	55
4₀(56)	→	57
4₀(139)	→	140
4₀(273)	→	274
4₀(107)	→	96
4₀(170)	→	171
4₀(256)	→	257
4₀(3)	→	11
4₀(312)	→	313
4₀(52)	→	53
4₀(248)	→	249
4₀(81)	→	82
4₀(101)	→	102
4₀(149)	→	150
4₀(196)	→	197
4₀(272)	→	273
2₀(114)	→	115
2₀(98)	→	99
2₀(182)	→	183
2₀(123)	→	124
2₀(1)	→	9
2₀(78)	→	79
2₀(76)	→	77
2₀(14)	→	18
2₀(251)	→	252
2₀(183)	→	184
2₀(159)	→	160
2₀(230)	→	231
2₀(19)	→	17
2₀(86)	→	87
2₀(118)	→	119
2₀(173)	→	174
2₀(310)	→	311
2₀(99)	→	100
2₀(6)	→	7
2₀(220)	→	221
2₀(231)	→	232
2₀(155)	→	156
2₀(283)	→	284
2₀(294)	→	295
2₀(202)	→	203
2₀(129)	→	130
2₀(18)	→	19
2₀(82)	→	83
2₀(3)	→	4
2₀(299)	→	300
2₀(271)	→	272
2₀(40)	→	41
2₀(284)	→	285
2₀(264)	→	265
2₀(221)	→	222
2₀(285)	→	286
2₀(261)	→	246
2₀(83)	→	84
2₀(215)	→	216
2₀(223)	→	224
2₀(49)	→	50
2₀(297)	→	279
2₀(48)	→	49
2₀(103)	→	104
2₀(2)	→	3
2₀(171)	→	172
2₀(16)	→	13
2₀(240)	→	241
0₀(125)	→	126
0₀(286)	→	287
0₀(29)	→	25
0₀(296)	→	297
0₀(287)	→	288
0₀(192)	→	193
0₀(255)	→	256
0₀(88)	→	89
0₀(94)	→	95
0₀(117)	→	118
0₀(124)	→	125
0₀(169)	→	170
0₀(11)	→	12
0₀(60)	→	61
0₀(242)	→	243
0₀(157)	→	158
0₀(198)	→	199
0₀(128)	→	129
0₀(7)	→	263
0₀(6)	→	31
0₀(234)	→	235
0₀(305)	→	306
0₀(22)	→	180
0₀(15)	→	16
0₀(314)	→	315
0₀(154)	→	155
0₀(14)	→	15
0₀(165)	→	166
0₀(31)	→	32
0₀(70)	→	71
0₀(224)	→	225
0₀(274)	→	275
0₀(216)	→	217
0₀(229)	→	230
0₀(195)	→	196
0₀(32)	→	33
0₀(95)	→	85
0₀(110)	→	111
0₀(121)	→	108
0₀(131)	→	132
0₀(247)	→	248
0₀(79)	→	80
0₀(24)	→	20
0₀(51)	→	52
0₀(130)	→	131
0₀(313)	→	314
0₀(23)	→	24
0₀(233)	→	234
0₀(315)	→	316
0₀(188)	→	189
0₀(253)	→	254
0₀(178)	→	164
0₀(71)	→	72
0₀(2)	→	21
5₀(184)	→	185
5₀(132)	→	133
5₀(180)	→	181
5₀(236)	→	237
5₀(93)	→	94
5₀(189)	→	190
5₀(265)	→	266
5₀(197)	→	198
5₀(200)	→	201
5₀(68)	→	69
5₀(227)	→	211
5₀(172)	→	173
5₀(278)	→	262
5₀(21)	→	22
5₀(232)	→	233
5₀(175)	→	176
5₀(268)	→	269
5₀(97)	→	98
5₀(190)	→	191
5₀(243)	→	244
5₀(181)	→	182
5₀(217)	→	218
5₀(50)	→	51
5₀(69)	→	70
5₀(6)	→	66
5₀(269)	→	270
5₀(186)	→	187
5₀(167)	→	168
5₀(241)	→	242
5₀(80)	→	81
5₀(14)	→	109
5₀(239)	→	240
5₀(307)	→	308
5₀(162)	→	163
5₀(43)	→	44
5₀(177)	→	178
5₀(174)	→	175
5₀(2)	→	212
5₀(163)	→	151
5₀(3)	→	86
5₀(316)	→	298
5₀(304)	→	305
5₀(168)	→	169
5₀(143)	→	144
5₀(292)	→	293
5₀(161)	→	162
5₀(259)	→	260
5₀(158)	→	159
5₀(67)	→	68
5₀(153)	→	154
5₀(150)	→	137
5₀(104)	→	105
5₀(209)	→	210
f6₀	→	2
1₀(2)	→	26
1₀(250)	→	251
1₀(275)	→	276
1₀(9)	→	8
1₀(306)	→	307
1₀(257)	→	258
1₀(204)	→	205
1₀(146)	→	147
1₀(64)	→	54
1₀(166)	→	167
1₀(309)	→	310
1₀(303)	→	304
1₀(152)	→	153
1₀(235)	→	236
1₀(55)	→	56
1₀(291)	→	292
1₀(4)	→	1
1₀(21)	→	123
1₀(6)	→	299
1₀(100)	→	101
1₀(53)	→	46
1₀(140)	→	141
1₀(62)	→	63
1₀(208)	→	209
1₀(112)	→	113
1₀(280)	→	281
1₀(290)	→	291
1₀(35)	→	36
1₀(267)	→	268
1₀(205)	→	206
1₀(127)	→	128
1₀(293)	→	294
1₀(42)	→	43
1₀(126)	→	127
1₀(73)	→	74
1₀(270)	→	271
1₀(41)	→	42
1₀(266)	→	267
1₀(187)	→	188
1₀(219)	→	220
1₀(59)	→	60
1₀(109)	→	165
1₀(31)	→	35
1₀(58)	→	59
1₀(185)	→	186
1₀(148)	→	149
1₀(193)	→	179
1₀(160)	→	161
1₀(207)	→	208
1₀(119)	→	120
1₀(47)	→	48
1₀(102)	→	103
4₁(317)	→	318
4₁(327)	→	328
3₁(319)	→	320