YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

The given TRS is match-bounded by 0. This is shown by the following automaton.

final states:

{311, 293, 276, 257, 239, 222, 204, 187, 171, 154, 138, 123, 108, 93, 80, 69, 57, 45, 36, 29, 22, 17, 11, 6, 1}

transitions:

239 → 189

239 → 12

29 → 188

29 → 37

80 → 3

276 → 312

276 → 46

57 → 7

187 → 3

108 → 259

108 → 47

108 → 3

293 → 7

1 → 3

123 → 82

123 → 3

222 → 139

222 → 7

36 → 58

36 → 46

138 → 46

257 → 4

257 → 7

311 → 12

171 → 46

6 → 46

22 → 7

204 → 125

204 → 37

11 → 18

11 → 46

45 → 7

93 → 188

93 → 37

69 → 3

17 → 46

154 → 3

1₀(51) → 52

1₀(279) → 280

1₀(130) → 131

1₀(67) → 68

1₀(46) → 94

1₀(173) → 174

1₀(292) → 276

1₀(310) → 293

1₀(278) → 279

1₀(270) → 271

1₀(37) → 139

1₀(3) → 4

1₀(303) → 304

1₀(32) → 33

1₀(66) → 67

1₀(312) → 313

1₀(121) → 122

1₀(26) → 27

1₀(52) → 53

1₀(89) → 90

1₀(328) → 329

1₀(326) → 327

1₀(197) → 198

1₀(290) → 291

1₀(142) → 143

1₀(155) → 277

1₀(68) → 57

1₀(9) → 10

1₀(83) → 84

1₀(99) → 100

1₀(201) → 202

1₀(247) → 248

1₀(62) → 63

1₀(322) → 323

1₀(72) → 73

1₀(39) → 40

1₀(63) → 64

1₀(327) → 328

1₀(28) → 22

1₀(14) → 15

1₀(116) → 117

1₀(2) → 7

1₀(242) → 243

1₀(223) → 224

1₀(34) → 35

1₀(308) → 309

1₀(20) → 21

1₀(12) → 70

1₀(264) → 265

1₀(218) → 219

0₀(2) → 46

0₀(255) → 256

0₀(82) → 223

0₀(21) → 17

0₀(159) → 160

0₀(160) → 161

0₀(95) → 96

0₀(74) → 75

0₀(188) → 240

0₀(261) → 262

0₀(275) → 257

0₀(186) → 171

0₀(211) → 212

0₀(48) → 49

0₀(88) → 89

0₀(16) → 11

0₀(249) → 250

0₀(266) → 267

0₀(319) → 320

0₀(133) → 134

0₀(37) → 312

0₀(234) → 235

0₀(59) → 60

0₀(77) → 78

0₀(286) → 287

0₀(220) → 221

0₀(233) → 234

0₀(70) → 71

0₀(12) → 58

0₀(47) → 48

0₀(55) → 56

0₀(106) → 107

0₀(321) → 322

0₀(141) → 142

0₀(126) → 127

0₀(210) → 211

0₀(324) → 325

0₀(125) → 126

0₀(18) → 109

0₀(183) → 184

0₀(27) → 28

0₀(217) → 218

0₀(97) → 98

0₀(320) → 321

0₀(219) → 220

0₀(262) → 263

0₀(90) → 91

0₀(131) → 132

0₀(268) → 269

0₀(184) → 185

0₀(221) → 204

0₀(314) → 315

0₀(282) → 283

0₀(38) → 39

0₀(15) → 16

0₀(226) → 227

0₀(3) → 258

0₀(127) → 128

0₀(248) → 249

0₀(149) → 150

0₀(215) → 216

0₀(153) → 138

0₀(7) → 18

0₀(65) → 66

0₀(35) → 29

0₀(294) → 295

3₀(244) → 245

3₀(280) → 281

3₀(33) → 34

3₀(151) → 152

3₀(23) → 172

3₀(225) → 226

3₀(245) → 246

3₀(298) → 299

3₀(200) → 201

3₀(272) → 273

3₀(41) → 42

3₀(78) → 79

3₀(216) → 217

3₀(251) → 252

3₀(289) → 290

3₀(144) → 145

3₀(37) → 38

3₀(86) → 87

3₀(118) → 119

3₀(7) → 8

3₀(178) → 179

3₀(136) → 137

3₀(205) → 206

3₀(132) → 133

3₀(105) → 106

3₀(265) → 266

3₀(79) → 69

3₀(152) → 153

3₀(158) → 159

3₀(202) → 203

3₀(274) → 275

3₀(238) → 222

3₀(18) → 19

3₀(3) → 124

3₀(284) → 285

3₀(164) → 165

3₀(64) → 65

3₀(140) → 141

3₀(288) → 289

3₀(285) → 286

3₀(232) → 233

3₀(12) → 13

3₀(128) → 129

3₀(162) → 163

3₀(180) → 181

3₀(300) → 301

3₀(49) → 50

3₀(273) → 274

3₀(325) → 326

3₀(135) → 136

3₀(53) → 54

3₀(71) → 72

3₀(31) → 32

3₀(318) → 319

3₀(122) → 108

3₀(291) → 292

3₀(2) → 81

3₀(4) → 5

3₀(24) → 25

3₀(254) → 255

3₀(240) → 241

5₀(301) → 302

5₀(25) → 26

5₀(246) → 247

5₀(296) → 297

5₀(61) → 62

5₀(263) → 264

5₀(50) → 51

5₀(94) → 95

5₀(124) → 125

5₀(169) → 170

5₀(260) → 261

5₀(196) → 197

5₀(295) → 296

5₀(7) → 188

5₀(56) → 45

5₀(13) → 14

5₀(147) → 148

5₀(166) → 167

5₀(316) → 317

5₀(161) → 162

5₀(181) → 182

5₀(139) → 140

5₀(155) → 156

5₀(235) → 236

5₀(182) → 183

5₀(267) → 268

5₀(119) → 120

5₀(103) → 104

5₀(3) → 30

5₀(165) → 166

5₀(30) → 31

5₀(206) → 207

5₀(306) → 307

5₀(150) → 151

5₀(163) → 164

5₀(175) → 176

5₀(185) → 186

5₀(85) → 86

5₀(114) → 115

5₀(313) → 314

5₀(23) → 24

5₀(174) → 175

5₀(115) → 116

5₀(315) → 316

5₀(104) → 105

5₀(12) → 23

5₀(2) → 37

5₀(243) → 244

5₀(317) → 318

4₀(146) → 147

4₀(176) → 177

4₀(302) → 303

4₀(236) → 237

4₀(330) → 311

4₀(60) → 61

4₀(156) → 157

4₀(96) → 97

4₀(230) → 231

4₀(297) → 298

4₀(193) → 194

4₀(227) → 228

4₀(12) → 205

4₀(40) → 41

4₀(19) → 20

4₀(120) → 121

4₀(188) → 189

4₀(73) → 74

4₀(250) → 251

4₀(91) → 92

4₀(277) → 278

4₀(237) → 238

4₀(199) → 200

4₀(214) → 215

4₀(42) → 43

4₀(109) → 110

4₀(213) → 214

4₀(252) → 253

4₀(212) → 213

4₀(84) → 85

4₀(117) → 118

4₀(241) → 242

4₀(307) → 308

4₀(256) → 239

4₀(82) → 83

4₀(43) → 44

4₀(177) → 178

4₀(113) → 114

4₀(2) → 12

4₀(299) → 300

4₀(228) → 229

4₀(107) → 93

4₀(231) → 232

4₀(271) → 272

4₀(304) → 305

4₀(124) → 294

4₀(287) → 288

4₀(101) → 102

4₀(259) → 260

4₀(134) → 135

4₀(207) → 208

4₀(100) → 101

4₀(195) → 196

4₀(283) → 284

4₀(309) → 310

4₀(209) → 210

4₀(112) → 113

f6₀ → 2

2₀(2) → 3

2₀(157) → 158

2₀(167) → 168

2₀(46) → 47

2₀(329) → 330

2₀(224) → 225

2₀(258) → 259

2₀(10) → 6

2₀(54) → 55

2₀(110) → 111

2₀(98) → 99

2₀(191) → 192

2₀(170) → 154

2₀(323) → 324

2₀(189) → 190

2₀(92) → 80

2₀(8) → 9

2₀(76) → 77

2₀(281) → 282

2₀(192) → 193

2₀(87) → 88

2₀(203) → 187

2₀(198) → 199

2₀(81) → 82

2₀(111) → 112

2₀(269) → 270

2₀(208) → 209

2₀(305) → 306

2₀(137) → 123

2₀(129) → 130

2₀(172) → 173

2₀(75) → 76

2₀(12) → 155

2₀(143) → 144

2₀(229) → 230

2₀(44) → 36

2₀(253) → 254

2₀(190) → 191

2₀(58) → 59

2₀(5) → 1

2₀(145) → 146

2₀(179) → 180

2₀(148) → 149

2₀(194) → 195

2₀(168) → 169

2₀(102) → 103

239	→	189
239	→	12
29	→	188
29	→	37
80	→	3
276	→	312
276	→	46
57	→	7
187	→	3
108	→	259
108	→	47
108	→	3
293	→	7
1	→	3
123	→	82
123	→	3
222	→	139
222	→	7
36	→	58
36	→	46
138	→	46
257	→	4
257	→	7
311	→	12
171	→	46
6	→	46
22	→	7
204	→	125
204	→	37
11	→	18
11	→	46
45	→	7
93	→	188
93	→	37
69	→	3
17	→	46
154	→	3
1₀(51)	→	52
1₀(279)	→	280
1₀(130)	→	131
1₀(67)	→	68
1₀(46)	→	94
1₀(173)	→	174
1₀(292)	→	276
1₀(310)	→	293
1₀(278)	→	279
1₀(270)	→	271
1₀(37)	→	139
1₀(3)	→	4
1₀(303)	→	304
1₀(32)	→	33
1₀(66)	→	67
1₀(312)	→	313
1₀(121)	→	122
1₀(26)	→	27
1₀(52)	→	53
1₀(89)	→	90
1₀(328)	→	329
1₀(326)	→	327
1₀(197)	→	198
1₀(290)	→	291
1₀(142)	→	143
1₀(155)	→	277
1₀(68)	→	57
1₀(9)	→	10
1₀(83)	→	84
1₀(99)	→	100
1₀(201)	→	202
1₀(247)	→	248
1₀(62)	→	63
1₀(322)	→	323
1₀(72)	→	73
1₀(39)	→	40
1₀(63)	→	64
1₀(327)	→	328
1₀(28)	→	22
1₀(14)	→	15
1₀(116)	→	117
1₀(2)	→	7
1₀(242)	→	243
1₀(223)	→	224
1₀(34)	→	35
1₀(308)	→	309
1₀(20)	→	21
1₀(12)	→	70
1₀(264)	→	265
1₀(218)	→	219
0₀(2)	→	46
0₀(255)	→	256
0₀(82)	→	223
0₀(21)	→	17
0₀(159)	→	160
0₀(160)	→	161
0₀(95)	→	96
0₀(74)	→	75
0₀(188)	→	240
0₀(261)	→	262
0₀(275)	→	257
0₀(186)	→	171
0₀(211)	→	212
0₀(48)	→	49
0₀(88)	→	89
0₀(16)	→	11
0₀(249)	→	250
0₀(266)	→	267
0₀(319)	→	320
0₀(133)	→	134
0₀(37)	→	312
0₀(234)	→	235
0₀(59)	→	60
0₀(77)	→	78
0₀(286)	→	287
0₀(220)	→	221
0₀(233)	→	234
0₀(70)	→	71
0₀(12)	→	58
0₀(47)	→	48
0₀(55)	→	56
0₀(106)	→	107
0₀(321)	→	322
0₀(141)	→	142
0₀(126)	→	127
0₀(210)	→	211
0₀(324)	→	325
0₀(125)	→	126
0₀(18)	→	109
0₀(183)	→	184
0₀(27)	→	28
0₀(217)	→	218
0₀(97)	→	98
0₀(320)	→	321
0₀(219)	→	220
0₀(262)	→	263
0₀(90)	→	91
0₀(131)	→	132
0₀(268)	→	269
0₀(184)	→	185
0₀(221)	→	204
0₀(314)	→	315
0₀(282)	→	283
0₀(38)	→	39
0₀(15)	→	16
0₀(226)	→	227
0₀(3)	→	258
0₀(127)	→	128
0₀(248)	→	249
0₀(149)	→	150
0₀(215)	→	216
0₀(153)	→	138
0₀(7)	→	18
0₀(65)	→	66
0₀(35)	→	29
0₀(294)	→	295
3₀(244)	→	245
3₀(280)	→	281
3₀(33)	→	34
3₀(151)	→	152
3₀(23)	→	172
3₀(225)	→	226
3₀(245)	→	246
3₀(298)	→	299
3₀(200)	→	201
3₀(272)	→	273
3₀(41)	→	42
3₀(78)	→	79
3₀(216)	→	217
3₀(251)	→	252
3₀(289)	→	290
3₀(144)	→	145
3₀(37)	→	38
3₀(86)	→	87
3₀(118)	→	119
3₀(7)	→	8
3₀(178)	→	179
3₀(136)	→	137
3₀(205)	→	206
3₀(132)	→	133
3₀(105)	→	106
3₀(265)	→	266
3₀(79)	→	69
3₀(152)	→	153
3₀(158)	→	159
3₀(202)	→	203
3₀(274)	→	275
3₀(238)	→	222
3₀(18)	→	19
3₀(3)	→	124
3₀(284)	→	285
3₀(164)	→	165
3₀(64)	→	65
3₀(140)	→	141
3₀(288)	→	289
3₀(285)	→	286
3₀(232)	→	233
3₀(12)	→	13
3₀(128)	→	129
3₀(162)	→	163
3₀(180)	→	181
3₀(300)	→	301
3₀(49)	→	50
3₀(273)	→	274
3₀(325)	→	326
3₀(135)	→	136
3₀(53)	→	54
3₀(71)	→	72
3₀(31)	→	32
3₀(318)	→	319
3₀(122)	→	108
3₀(291)	→	292
3₀(2)	→	81
3₀(4)	→	5
3₀(24)	→	25
3₀(254)	→	255
3₀(240)	→	241
5₀(301)	→	302
5₀(25)	→	26
5₀(246)	→	247
5₀(296)	→	297
5₀(61)	→	62
5₀(263)	→	264
5₀(50)	→	51
5₀(94)	→	95
5₀(124)	→	125
5₀(169)	→	170
5₀(260)	→	261
5₀(196)	→	197
5₀(295)	→	296
5₀(7)	→	188
5₀(56)	→	45
5₀(13)	→	14
5₀(147)	→	148
5₀(166)	→	167
5₀(316)	→	317
5₀(161)	→	162
5₀(181)	→	182
5₀(139)	→	140
5₀(155)	→	156
5₀(235)	→	236
5₀(182)	→	183
5₀(267)	→	268
5₀(119)	→	120
5₀(103)	→	104
5₀(3)	→	30
5₀(165)	→	166
5₀(30)	→	31
5₀(206)	→	207
5₀(306)	→	307
5₀(150)	→	151
5₀(163)	→	164
5₀(175)	→	176
5₀(185)	→	186
5₀(85)	→	86
5₀(114)	→	115
5₀(313)	→	314
5₀(23)	→	24
5₀(174)	→	175
5₀(115)	→	116
5₀(315)	→	316
5₀(104)	→	105
5₀(12)	→	23
5₀(2)	→	37
5₀(243)	→	244
5₀(317)	→	318
4₀(146)	→	147
4₀(176)	→	177
4₀(302)	→	303
4₀(236)	→	237
4₀(330)	→	311
4₀(60)	→	61
4₀(156)	→	157
4₀(96)	→	97
4₀(230)	→	231
4₀(297)	→	298
4₀(193)	→	194
4₀(227)	→	228
4₀(12)	→	205
4₀(40)	→	41
4₀(19)	→	20
4₀(120)	→	121
4₀(188)	→	189
4₀(73)	→	74
4₀(250)	→	251
4₀(91)	→	92
4₀(277)	→	278
4₀(237)	→	238
4₀(199)	→	200
4₀(214)	→	215
4₀(42)	→	43
4₀(109)	→	110
4₀(213)	→	214
4₀(252)	→	253
4₀(212)	→	213
4₀(84)	→	85
4₀(117)	→	118
4₀(241)	→	242
4₀(307)	→	308
4₀(256)	→	239
4₀(82)	→	83
4₀(43)	→	44
4₀(177)	→	178
4₀(113)	→	114
4₀(2)	→	12
4₀(299)	→	300
4₀(228)	→	229
4₀(107)	→	93
4₀(231)	→	232
4₀(271)	→	272
4₀(304)	→	305
4₀(124)	→	294
4₀(287)	→	288
4₀(101)	→	102
4₀(259)	→	260
4₀(134)	→	135
4₀(207)	→	208
4₀(100)	→	101
4₀(195)	→	196
4₀(283)	→	284
4₀(309)	→	310
4₀(209)	→	210
4₀(112)	→	113
f6₀	→	2
2₀(2)	→	3
2₀(157)	→	158
2₀(167)	→	168
2₀(46)	→	47
2₀(329)	→	330
2₀(224)	→	225
2₀(258)	→	259
2₀(10)	→	6
2₀(54)	→	55
2₀(110)	→	111
2₀(98)	→	99
2₀(191)	→	192
2₀(170)	→	154
2₀(323)	→	324
2₀(189)	→	190
2₀(92)	→	80
2₀(8)	→	9
2₀(76)	→	77
2₀(281)	→	282
2₀(192)	→	193
2₀(87)	→	88
2₀(203)	→	187
2₀(198)	→	199
2₀(81)	→	82
2₀(111)	→	112
2₀(269)	→	270
2₀(208)	→	209
2₀(305)	→	306
2₀(137)	→	123
2₀(129)	→	130
2₀(172)	→	173
2₀(75)	→	76
2₀(12)	→	155
2₀(143)	→	144
2₀(229)	→	230
2₀(44)	→	36
2₀(253)	→	254
2₀(190)	→	191
2₀(58)	→	59
2₀(5)	→	1
2₀(145)	→	146
2₀(179)	→	180
2₀(148)	→	149
2₀(194)	→	195
2₀(168)	→	169
2₀(102)	→	103