YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{351, 331, 317, 300, 282, 266, 251, 235, 220, 205, 190, 175, 162, 149, 137, 124, 113, 102, 91, 78, 68, 58, 51, 40, 32, 24, 17, 10, 5, 1}

transitions:

78 → 192

78 → 6

78 → 33

102 → 33

32 → 33

205 → 69

205 → 3

315 → 388

89 → 370

10 → 92

10 → 11

51 → 93

51 → 11

149 → 36

149 → 59

149 → 79

187 → 378

331 → 79

5 → 33

175 → 79

381 → 163

1 → 34

1 → 33

40 → 41

235 → 6

235 → 33

91 → 176

91 → 79

58 → 81

58 → 59

58 → 79

251 → 114

251 → 125

251 → 11

389 → 371

220 → 163

220 → 33

124 → 192

124 → 6

124 → 33

300 → 34

300 → 33

373 → 236

282 → 34

282 → 33

113 → 59

113 → 79

137 → 191

137 → 3

162 → 33

17 → 33

190 → 333

190 → 41

68 → 92

68 → 11

24 → 164

24 → 3

351 → 92

351 → 11

266 → 79

317 → 176

317 → 79

0₁(388) → 389

0₁(370) → 371

0₁(378) → 379

4₀(279) → 280

4₀(244) → 245

4₀(35) → 36

4₀(180) → 181

4₀(46) → 47

4₀(11) → 18

4₀(245) → 246

4₀(41) → 176

4₀(112) → 102

4₀(3) → 59

4₀(333) → 334

4₀(86) → 87

4₀(240) → 241

4₀(354) → 355

4₀(33) → 332

4₀(364) → 365

4₀(267) → 268

4₀(66) → 67

4₀(312) → 313

4₀(48) → 49

4₀(313) → 314

4₀(275) → 276

4₀(93) → 94

4₀(323) → 324

4₀(268) → 269

4₀(80) → 81

4₀(206) → 301

4₀(215) → 216

4₀(134) → 135

4₀(228) → 229

4₀(347) → 348

4₀(133) → 134

4₀(296) → 297

4₀(138) → 139

4₀(142) → 143

4₀(9) → 5

4₀(289) → 290

4₀(314) → 315

4₀(248) → 249

4₀(6) → 7

4₀(322) → 323

4₀(269) → 270

4₀(76) → 77

4₀(214) → 215

4₀(338) → 339

4₀(181) → 182

4₀(202) → 203

4₀(36) → 37

4₀(340) → 341

4₀(259) → 260

4₀(116) → 117

4₀(2) → 79

4₀(246) → 247

4₀(85) → 86

4₀(192) → 193

4₀(69) → 70

4₀(20) → 21

4₀(156) → 157

4₀(104) → 105

4₀(297) → 298

4₀(153) → 154

3₀(73) → 74

3₀(41) → 42

3₀(366) → 367

3₀(111) → 112

3₀(2) → 11

3₀(25) → 103

3₀(82) → 318

3₀(155) → 156

3₀(120) → 121

3₀(74) → 75

3₀(152) → 153

3₀(193) → 194

3₀(318) → 319

3₀(19) → 20

3₀(98) → 99

3₀(291) → 292

3₀(37) → 38

3₀(263) → 264

3₀(34) → 114

3₀(77) → 68

3₀(369) → 351

3₀(100) → 101

3₀(140) → 141

3₀(119) → 120

3₀(242) → 243

3₀(325) → 326

3₀(8) → 9

3₀(336) → 337

3₀(334) → 335

3₀(105) → 106

3₀(287) → 288

3₀(172) → 173

3₀(92) → 93

3₀(253) → 254

3₀(99) → 100

3₀(356) → 357

3₀(302) → 303

3₀(238) → 239

3₀(183) → 184

3₀(56) → 57

3₀(265) → 251

3₀(57) → 51

3₀(63) → 64

3₀(216) → 217

3₀(221) → 222

3₀(274) → 275

3₀(206) → 352

3₀(33) → 125

3₀(349) → 350

3₀(3) → 92

3₀(75) → 76

3₀(171) → 172

3₀(343) → 344

0₀(114) → 115

0₀(326) → 327

0₀(219) → 205

0₀(148) → 137

0₀(225) → 226

0₀(315) → 316

0₀(165) → 166

0₀(260) → 261

0₀(327) → 328

0₀(42) → 43

0₀(272) → 273

0₀(41) → 191

0₀(159) → 160

0₀(108) → 109

0₀(199) → 200

0₀(166) → 167

0₀(118) → 119

0₀(368) → 369

0₀(178) → 179

0₀(207) → 208

0₀(310) → 311

0₀(217) → 218

0₀(132) → 133

0₀(34) → 35

0₀(344) → 345

0₀(335) → 336

0₀(11) → 69

0₀(358) → 359

0₀(95) → 96

0₀(38) → 39

0₀(203) → 204

0₀(257) → 258

0₀(247) → 248

0₀(43) → 44

0₀(79) → 80

0₀(187) → 188

0₀(158) → 159

0₀(258) → 259

0₀(176) → 177

0₀(55) → 56

0₀(209) → 210

0₀(361) → 362

0₀(109) → 110

0₀(249) → 250

0₀(139) → 140

0₀(164) → 165

0₀(286) → 287

0₀(324) → 325

0₀(255) → 256

0₀(163) → 164

0₀(184) → 185

0₀(236) → 237

0₀(96) → 97

0₀(101) → 91

0₀(261) → 262

0₀(208) → 209

0₀(94) → 95

0₀(224) → 225

0₀(305) → 306

0₀(367) → 368

0₀(348) → 349

0₀(27) → 28

0₀(273) → 274

0₀(53) → 54

0₀(31) → 24

0₀(62) → 63

0₀(2) → 3

0₀(256) → 257

0₀(44) → 45

0₀(16) → 10

0₀(89) → 90

5₀(301) → 302

5₀(25) → 206

5₀(201) → 202

5₀(135) → 136

5₀(278) → 279

5₀(362) → 363

5₀(211) → 212

5₀(230) → 231

5₀(117) → 118

5₀(26) → 27

5₀(169) → 170

5₀(11) → 12

5₀(60) → 61

5₀(226) → 227

5₀(241) → 242

5₀(146) → 147

5₀(4) → 52

5₀(295) → 296

5₀(7) → 8

5₀(360) → 361

5₀(339) → 340

5₀(280) → 281

5₀(92) → 252

5₀(167) → 168

5₀(15) → 16

5₀(357) → 358

5₀(194) → 195

5₀(182) → 183

5₀(52) → 53

5₀(290) → 291

5₀(271) → 272

5₀(3) → 283

5₀(206) → 267

5₀(308) → 309

5₀(65) → 66

5₀(311) → 312

5₀(150) → 151

5₀(345) → 346

5₀(110) → 111

5₀(250) → 235

5₀(144) → 145

5₀(79) → 138

5₀(210) → 211

5₀(262) → 263

5₀(126) → 127

5₀(328) → 329

5₀(233) → 234

5₀(12) → 150

5₀(127) → 128

5₀(231) → 232

5₀(337) → 338

5₀(71) → 72

5₀(2) → 25

5₀(243) → 244

2₀(303) → 304

2₀(64) → 65

2₀(284) → 285

2₀(179) → 180

2₀(131) → 132

2₀(59) → 60

2₀(147) → 148

2₀(121) → 122

2₀(293) → 294

2₀(87) → 88

2₀(189) → 175

2₀(185) → 186

2₀(79) → 163

2₀(352) → 353

2₀(128) → 129

2₀(21) → 22

2₀(97) → 98

2₀(157) → 158

2₀(34) → 236

2₀(270) → 271

2₀(350) → 331

2₀(130) → 131

2₀(125) → 126

2₀(341) → 342

2₀(54) → 55

2₀(61) → 62

2₀(22) → 23

2₀(173) → 174

2₀(222) → 223

2₀(365) → 366

2₀(191) → 192

2₀(237) → 238

2₀(206) → 207

2₀(252) → 253

2₀(212) → 213

2₀(84) → 85

2₀(306) → 307

2₀(14) → 15

2₀(307) → 308

2₀(151) → 152

2₀(82) → 83

2₀(83) → 84

2₀(281) → 266

2₀(2) → 33

2₀(3) → 6

2₀(107) → 108

2₀(304) → 305

2₀(168) → 169

2₀(143) → 144

2₀(298) → 299

2₀(28) → 29

2₀(264) → 265

2₀(292) → 293

2₀(29) → 30

2₀(319) → 320

2₀(161) → 149

2₀(276) → 277

2₀(346) → 347

2₀(115) → 116

2₀(33) → 34

2₀(13) → 14

2₀(47) → 48

2₀(136) → 124

2₀(106) → 107

2₀(39) → 32

2₀(254) → 255

2₀(223) → 224

2₀(81) → 82

2₀(195) → 196

2₀(283) → 284

2₀(309) → 310

2₀(320) → 321

2₀(160) → 161

f6₀ → 2

1₀(2) → 41

1₀(18) → 19

1₀(330) → 317

1₀(177) → 178

1₀(329) → 330

1₀(196) → 197

1₀(123) → 113

1₀(227) → 228

1₀(299) → 282

1₀(332) → 333

1₀(363) → 364

1₀(90) → 78

1₀(288) → 289

1₀(204) → 190

1₀(49) → 50

1₀(197) → 198

1₀(359) → 360

1₀(353) → 354

1₀(277) → 278

1₀(213) → 214

1₀(50) → 40

1₀(67) → 58

1₀(170) → 171

1₀(232) → 233

1₀(30) → 31

1₀(294) → 295

1₀(355) → 356

1₀(239) → 240

1₀(25) → 26

1₀(4) → 1

1₀(234) → 220

1₀(3) → 4

1₀(218) → 219

1₀(141) → 142

1₀(198) → 199

1₀(70) → 71

1₀(23) → 17

1₀(316) → 300

1₀(45) → 46

1₀(129) → 130

1₀(103) → 104

1₀(42) → 221

1₀(342) → 343

1₀(12) → 13

1₀(174) → 162

1₀(321) → 322

1₀(154) → 155

1₀(186) → 187

1₀(229) → 230

1₀(285) → 286

1₀(188) → 189

1₀(145) → 146

1₀(200) → 201

1₀(88) → 89

1₀(72) → 73

1₀(122) → 123

1₁(372) → 373

1₁(371) → 372

1₁(380) → 381

1₁(379) → 380

78	→	192
78	→	6
78	→	33
102	→	33
32	→	33
205	→	69
205	→	3
315	→	388
89	→	370
10	→	92
10	→	11
51	→	93
51	→	11
149	→	36
149	→	59
149	→	79
187	→	378
331	→	79
5	→	33
175	→	79
381	→	163
1	→	34
1	→	33
40	→	41
235	→	6
235	→	33
91	→	176
91	→	79
58	→	81
58	→	59
58	→	79
251	→	114
251	→	125
251	→	11
389	→	371
220	→	163
220	→	33
124	→	192
124	→	6
124	→	33
300	→	34
300	→	33
373	→	236
282	→	34
282	→	33
113	→	59
113	→	79
137	→	191
137	→	3
162	→	33
17	→	33
190	→	333
190	→	41
68	→	92
68	→	11
24	→	164
24	→	3
351	→	92
351	→	11
266	→	79
317	→	176
317	→	79
0₁(388)	→	389
0₁(370)	→	371
0₁(378)	→	379
4₀(279)	→	280
4₀(244)	→	245
4₀(35)	→	36
4₀(180)	→	181
4₀(46)	→	47
4₀(11)	→	18
4₀(245)	→	246
4₀(41)	→	176
4₀(112)	→	102
4₀(3)	→	59
4₀(333)	→	334
4₀(86)	→	87
4₀(240)	→	241
4₀(354)	→	355
4₀(33)	→	332
4₀(364)	→	365
4₀(267)	→	268
4₀(66)	→	67
4₀(312)	→	313
4₀(48)	→	49
4₀(313)	→	314
4₀(275)	→	276
4₀(93)	→	94
4₀(323)	→	324
4₀(268)	→	269
4₀(80)	→	81
4₀(206)	→	301
4₀(215)	→	216
4₀(134)	→	135
4₀(228)	→	229
4₀(347)	→	348
4₀(133)	→	134
4₀(296)	→	297
4₀(138)	→	139
4₀(142)	→	143
4₀(9)	→	5
4₀(289)	→	290
4₀(314)	→	315
4₀(248)	→	249
4₀(6)	→	7
4₀(322)	→	323
4₀(269)	→	270
4₀(76)	→	77
4₀(214)	→	215
4₀(338)	→	339
4₀(181)	→	182
4₀(202)	→	203
4₀(36)	→	37
4₀(340)	→	341
4₀(259)	→	260
4₀(116)	→	117
4₀(2)	→	79
4₀(246)	→	247
4₀(85)	→	86
4₀(192)	→	193
4₀(69)	→	70
4₀(20)	→	21
4₀(156)	→	157
4₀(104)	→	105
4₀(297)	→	298
4₀(153)	→	154
3₀(73)	→	74
3₀(41)	→	42
3₀(366)	→	367
3₀(111)	→	112
3₀(2)	→	11
3₀(25)	→	103
3₀(82)	→	318
3₀(155)	→	156
3₀(120)	→	121
3₀(74)	→	75
3₀(152)	→	153
3₀(193)	→	194
3₀(318)	→	319
3₀(19)	→	20
3₀(98)	→	99
3₀(291)	→	292
3₀(37)	→	38
3₀(263)	→	264
3₀(34)	→	114
3₀(77)	→	68
3₀(369)	→	351
3₀(100)	→	101
3₀(140)	→	141
3₀(119)	→	120
3₀(242)	→	243
3₀(325)	→	326
3₀(8)	→	9
3₀(336)	→	337
3₀(334)	→	335
3₀(105)	→	106
3₀(287)	→	288
3₀(172)	→	173
3₀(92)	→	93
3₀(253)	→	254
3₀(99)	→	100
3₀(356)	→	357
3₀(302)	→	303
3₀(238)	→	239
3₀(183)	→	184
3₀(56)	→	57
3₀(265)	→	251
3₀(57)	→	51
3₀(63)	→	64
3₀(216)	→	217
3₀(221)	→	222
3₀(274)	→	275
3₀(206)	→	352
3₀(33)	→	125
3₀(349)	→	350
3₀(3)	→	92
3₀(75)	→	76
3₀(171)	→	172
3₀(343)	→	344
0₀(114)	→	115
0₀(326)	→	327
0₀(219)	→	205
0₀(148)	→	137
0₀(225)	→	226
0₀(315)	→	316
0₀(165)	→	166
0₀(260)	→	261
0₀(327)	→	328
0₀(42)	→	43
0₀(272)	→	273
0₀(41)	→	191
0₀(159)	→	160
0₀(108)	→	109
0₀(199)	→	200
0₀(166)	→	167
0₀(118)	→	119
0₀(368)	→	369
0₀(178)	→	179
0₀(207)	→	208
0₀(310)	→	311
0₀(217)	→	218
0₀(132)	→	133
0₀(34)	→	35
0₀(344)	→	345
0₀(335)	→	336
0₀(11)	→	69
0₀(358)	→	359
0₀(95)	→	96
0₀(38)	→	39
0₀(203)	→	204
0₀(257)	→	258
0₀(247)	→	248
0₀(43)	→	44
0₀(79)	→	80
0₀(187)	→	188
0₀(158)	→	159
0₀(258)	→	259
0₀(176)	→	177
0₀(55)	→	56
0₀(209)	→	210
0₀(361)	→	362
0₀(109)	→	110
0₀(249)	→	250
0₀(139)	→	140
0₀(164)	→	165
0₀(286)	→	287
0₀(324)	→	325
0₀(255)	→	256
0₀(163)	→	164
0₀(184)	→	185
0₀(236)	→	237
0₀(96)	→	97
0₀(101)	→	91
0₀(261)	→	262
0₀(208)	→	209
0₀(94)	→	95
0₀(224)	→	225
0₀(305)	→	306
0₀(367)	→	368
0₀(348)	→	349
0₀(27)	→	28
0₀(273)	→	274
0₀(53)	→	54
0₀(31)	→	24
0₀(62)	→	63
0₀(2)	→	3
0₀(256)	→	257
0₀(44)	→	45
0₀(16)	→	10
0₀(89)	→	90
5₀(301)	→	302
5₀(25)	→	206
5₀(201)	→	202
5₀(135)	→	136
5₀(278)	→	279
5₀(362)	→	363
5₀(211)	→	212
5₀(230)	→	231
5₀(117)	→	118
5₀(26)	→	27
5₀(169)	→	170
5₀(11)	→	12
5₀(60)	→	61
5₀(226)	→	227
5₀(241)	→	242
5₀(146)	→	147
5₀(4)	→	52
5₀(295)	→	296
5₀(7)	→	8
5₀(360)	→	361
5₀(339)	→	340
5₀(280)	→	281
5₀(92)	→	252
5₀(167)	→	168
5₀(15)	→	16
5₀(357)	→	358
5₀(194)	→	195
5₀(182)	→	183
5₀(52)	→	53
5₀(290)	→	291
5₀(271)	→	272
5₀(3)	→	283
5₀(206)	→	267
5₀(308)	→	309
5₀(65)	→	66
5₀(311)	→	312
5₀(150)	→	151
5₀(345)	→	346
5₀(110)	→	111
5₀(250)	→	235
5₀(144)	→	145
5₀(79)	→	138
5₀(210)	→	211
5₀(262)	→	263
5₀(126)	→	127
5₀(328)	→	329
5₀(233)	→	234
5₀(12)	→	150
5₀(127)	→	128
5₀(231)	→	232
5₀(337)	→	338
5₀(71)	→	72
5₀(2)	→	25
5₀(243)	→	244
2₀(303)	→	304
2₀(64)	→	65
2₀(284)	→	285
2₀(179)	→	180
2₀(131)	→	132
2₀(59)	→	60
2₀(147)	→	148
2₀(121)	→	122
2₀(293)	→	294
2₀(87)	→	88
2₀(189)	→	175
2₀(185)	→	186
2₀(79)	→	163
2₀(352)	→	353
2₀(128)	→	129
2₀(21)	→	22
2₀(97)	→	98
2₀(157)	→	158
2₀(34)	→	236
2₀(270)	→	271
2₀(350)	→	331
2₀(130)	→	131
2₀(125)	→	126
2₀(341)	→	342
2₀(54)	→	55
2₀(61)	→	62
2₀(22)	→	23
2₀(173)	→	174
2₀(222)	→	223
2₀(365)	→	366
2₀(191)	→	192
2₀(237)	→	238
2₀(206)	→	207
2₀(252)	→	253
2₀(212)	→	213
2₀(84)	→	85
2₀(306)	→	307
2₀(14)	→	15
2₀(307)	→	308
2₀(151)	→	152
2₀(82)	→	83
2₀(83)	→	84
2₀(281)	→	266
2₀(2)	→	33
2₀(3)	→	6
2₀(107)	→	108
2₀(304)	→	305
2₀(168)	→	169
2₀(143)	→	144
2₀(298)	→	299
2₀(28)	→	29
2₀(264)	→	265
2₀(292)	→	293
2₀(29)	→	30
2₀(319)	→	320
2₀(161)	→	149
2₀(276)	→	277
2₀(346)	→	347
2₀(115)	→	116
2₀(33)	→	34
2₀(13)	→	14
2₀(47)	→	48
2₀(136)	→	124
2₀(106)	→	107
2₀(39)	→	32
2₀(254)	→	255
2₀(223)	→	224
2₀(81)	→	82
2₀(195)	→	196
2₀(283)	→	284
2₀(309)	→	310
2₀(320)	→	321
2₀(160)	→	161
f6₀	→	2
1₀(2)	→	41
1₀(18)	→	19
1₀(330)	→	317
1₀(177)	→	178
1₀(329)	→	330
1₀(196)	→	197
1₀(123)	→	113
1₀(227)	→	228
1₀(299)	→	282
1₀(332)	→	333
1₀(363)	→	364
1₀(90)	→	78
1₀(288)	→	289
1₀(204)	→	190
1₀(49)	→	50
1₀(197)	→	198
1₀(359)	→	360
1₀(353)	→	354
1₀(277)	→	278
1₀(213)	→	214
1₀(50)	→	40
1₀(67)	→	58
1₀(170)	→	171
1₀(232)	→	233
1₀(30)	→	31
1₀(294)	→	295
1₀(355)	→	356
1₀(239)	→	240
1₀(25)	→	26
1₀(4)	→	1
1₀(234)	→	220
1₀(3)	→	4
1₀(218)	→	219
1₀(141)	→	142
1₀(198)	→	199
1₀(70)	→	71
1₀(23)	→	17
1₀(316)	→	300
1₀(45)	→	46
1₀(129)	→	130
1₀(103)	→	104
1₀(42)	→	221
1₀(342)	→	343
1₀(12)	→	13
1₀(174)	→	162
1₀(321)	→	322
1₀(154)	→	155
1₀(186)	→	187
1₀(229)	→	230
1₀(285)	→	286
1₀(188)	→	189
1₀(145)	→	146
1₀(200)	→	201
1₀(88)	→	89
1₀(72)	→	73
1₀(122)	→	123
1₁(372)	→	373
1₁(371)	→	372
1₁(380)	→	381
1₁(379)	→	380