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

1.1 Bounds

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

final states:

{328, 308, 290, 273, 256, 239, 222, 206, 188, 170, 155, 141, 128, 114, 103, 89, 78, 64, 53, 42, 32, 22, 14, 7, 1}

transitions:

78 → 257

78 → 8

239 → 65

32 → 90

89 → 23

128 → 66

128 → 3

103 → 90

273 → 94

273 → 43

273 → 8

1 → 90

222 → 189

222 → 23

170 → 257

170 → 8

141 → 3

308 → 129

308 → 8

22 → 274

22 → 23

53 → 171

188 → 65

114 → 43

114 → 8

14 → 90

7 → 309

7 → 8

290 → 8

42 → 129

42 → 8

64 → 9

64 → 3

256 → 274

256 → 23

206 → 65

328 → 3

155 → 24

155 → 23

1₀(65) → 329

1₀(166) → 167

1₀(278) → 279

1₀(316) → 317

1₀(162) → 163

1₀(146) → 147

1₀(157) → 158

1₀(174) → 175

1₀(193) → 194

1₀(3) → 15

1₀(251) → 252

1₀(303) → 304

1₀(44) → 45

1₀(48) → 49

1₀(24) → 25

1₀(121) → 122

1₀(52) → 42

1₀(228) → 229

1₀(133) → 134

1₀(111) → 112

1₀(138) → 139

1₀(18) → 19

1₀(99) → 100

1₀(179) → 180

1₀(336) → 337

1₀(131) → 132

1₀(94) → 95

1₀(247) → 248

1₀(299) → 300

1₀(344) → 345

1₀(320) → 321

1₀(148) → 149

1₀(258) → 259

1₀(76) → 77

1₀(10) → 11

1₀(220) → 221

1₀(88) → 78

1₀(4) → 5

1₀(117) → 118

1₀(191) → 192

1₀(343) → 344

1₀(283) → 284

1₀(330) → 331

1₀(2) → 65

1₀(23) → 223

1₀(185) → 186

1₀(242) → 243

1₀(164) → 165

1₀(34) → 35

1₀(168) → 169

1₀(54) → 55

1₀(12) → 13

1₀(255) → 239

1₀(153) → 154

1₀(232) → 233

0₀(331) → 332

0₀(109) → 110

0₀(2) → 3

0₀(25) → 156

0₀(45) → 46

0₀(160) → 161

0₀(95) → 96

0₀(340) → 341

0₀(275) → 276

0₀(58) → 59

0₀(51) → 52

0₀(19) → 20

0₀(110) → 111

0₀(28) → 29

0₀(266) → 267

0₀(4) → 54

0₀(136) → 137

0₀(144) → 145

0₀(140) → 128

0₀(243) → 244

0₀(267) → 268

0₀(150) → 151

0₀(47) → 48

0₀(8) → 9

0₀(123) → 124

0₀(207) → 208

0₀(332) → 333

0₀(61) → 62

0₀(203) → 204

0₀(126) → 127

0₀(108) → 109

0₀(92) → 93

0₀(298) → 299

0₀(277) → 278

0₀(346) → 328

0₀(212) → 213

0₀(154) → 141

0₀(217) → 218

0₀(134) → 135

0₀(137) → 138

0₀(97) → 98

0₀(244) → 245

0₀(67) → 68

0₀(282) → 283

0₀(130) → 131

0₀(240) → 241

0₀(86) → 87

0₀(3) → 4

0₀(248) → 249

0₀(81) → 82

0₀(104) → 105

0₀(101) → 102

0₀(40) → 41

0₀(65) → 66

3₀(326) → 327

3₀(98) → 99

3₀(106) → 107

3₀(124) → 125

3₀(177) → 178

3₀(23) → 115

3₀(100) → 101

3₀(70) → 71

3₀(315) → 316

3₀(165) → 166

3₀(63) → 53

3₀(250) → 251

3₀(30) → 31

3₀(37) → 38

3₀(230) → 231

3₀(142) → 143

3₀(293) → 294

3₀(281) → 282

3₀(125) → 126

3₀(11) → 12

3₀(43) → 44

3₀(213) → 214

3₀(152) → 153

3₀(149) → 150

3₀(294) → 295

3₀(323) → 324

3₀(312) → 313

3₀(90) → 91

3₀(268) → 269

3₀(29) → 30

3₀(82) → 83

3₀(3) → 33

3₀(175) → 176

3₀(286) → 287

3₀(69) → 70

3₀(313) → 314

3₀(264) → 265

3₀(345) → 346

3₀(116) → 117

3₀(9) → 10

3₀(235) → 236

3₀(311) → 312

3₀(285) → 286

3₀(96) → 97

3₀(192) → 193

3₀(189) → 240

3₀(15) → 16

3₀(223) → 224

3₀(325) → 326

3₀(181) → 182

3₀(297) → 298

3₀(5) → 6

3₀(17) → 18

3₀(122) → 123

3₀(321) → 322

3₀(2) → 171

3₀(24) → 104

3₀(171) → 172

3₀(66) → 67

3₀(16) → 17

2₀(143) → 144

2₀(341) → 342

2₀(21) → 14

2₀(186) → 187

2₀(218) → 219

2₀(287) → 288

2₀(120) → 121

2₀(279) → 280

2₀(151) → 152

2₀(172) → 173

2₀(208) → 209

2₀(335) → 336

2₀(237) → 238

2₀(257) → 258

2₀(211) → 212

2₀(260) → 261

2₀(4) → 291

2₀(295) → 296

2₀(270) → 271

2₀(13) → 7

2₀(41) → 32

2₀(167) → 168

2₀(161) → 162

2₀(107) → 108

2₀(276) → 277

2₀(15) → 142

2₀(334) → 335

2₀(194) → 195

2₀(307) → 290

2₀(189) → 190

2₀(74) → 75

2₀(62) → 63

2₀(224) → 225

2₀(195) → 196

2₀(219) → 220

2₀(302) → 303

2₀(310) → 311

2₀(79) → 80

2₀(38) → 39

2₀(33) → 34

2₀(199) → 200

2₀(91) → 92

2₀(233) → 234

2₀(115) → 207

2₀(231) → 232

2₀(322) → 323

2₀(253) → 254

2₀(55) → 56

2₀(187) → 170

2₀(337) → 338

2₀(105) → 106

2₀(2) → 90

2₀(73) → 74

2₀(309) → 310

5₀(90) → 129

5₀(262) → 263

5₀(59) → 60

5₀(132) → 133

5₀(333) → 334

5₀(180) → 181

5₀(263) → 264

5₀(236) → 237

5₀(93) → 94

5₀(156) → 157

5₀(229) → 230

5₀(305) → 306

5₀(20) → 21

5₀(72) → 73

5₀(317) → 318

5₀(200) → 201

5₀(198) → 199

5₀(227) → 228

5₀(342) → 343

5₀(205) → 188

5₀(23) → 309

5₀(50) → 51

5₀(215) → 216

5₀(269) → 270

5₀(145) → 146

5₀(280) → 281

5₀(119) → 120

5₀(324) → 325

5₀(306) → 307

5₀(182) → 183

5₀(314) → 315

5₀(80) → 81

5₀(216) → 217

5₀(49) → 50

5₀(318) → 319

5₀(83) → 84

5₀(2) → 8

5₀(3) → 43

5₀(36) → 37

5₀(304) → 305

5₀(27) → 28

5₀(291) → 292

5₀(129) → 130

5₀(292) → 293

5₀(319) → 320

5₀(210) → 211

5₀(8) → 257

5₀(288) → 289

5₀(259) → 260

5₀(115) → 116

5₀(196) → 197

5₀(234) → 235

5₀(39) → 40

5₀(178) → 179

5₀(289) → 273

5₀(158) → 159

5₀(25) → 26

5₀(204) → 205

5₀(301) → 302

5₀(159) → 160

5₀(246) → 247

5₀(249) → 250

5₀(112) → 113

f6₀ → 2

4₀(2) → 23

4₀(163) → 164

4₀(274) → 275

4₀(46) → 47

4₀(329) → 330

4₀(56) → 57

4₀(300) → 301

4₀(184) → 185

4₀(271) → 272

4₀(197) → 198

4₀(202) → 203

4₀(225) → 226

4₀(252) → 253

4₀(113) → 103

4₀(71) → 72

4₀(8) → 189

4₀(26) → 27

4₀(254) → 255

4₀(272) → 256

4₀(3) → 274

4₀(214) → 215

4₀(284) → 285

4₀(84) → 85

4₀(147) → 148

4₀(135) → 136

4₀(6) → 1

4₀(87) → 88

4₀(176) → 177

4₀(245) → 246

4₀(118) → 119

4₀(238) → 222

4₀(23) → 24

4₀(221) → 206

4₀(241) → 242

4₀(173) → 174

4₀(139) → 140

4₀(15) → 79

4₀(35) → 36

4₀(127) → 114

4₀(75) → 76

4₀(85) → 86

4₀(183) → 184

4₀(201) → 202

4₀(57) → 58

4₀(226) → 227

4₀(338) → 339

4₀(60) → 61

4₀(209) → 210

4₀(261) → 262

4₀(190) → 191

4₀(31) → 22

4₀(327) → 308

4₀(77) → 64

4₀(296) → 297

4₀(169) → 155

4₀(68) → 69

4₀(339) → 340

4₀(265) → 266

4₀(102) → 89

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