YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{329, 321, 313, 304, 295, 287, 280, 272, 263, 254, 246, 238, 229, 221, 214, 206, 197, 190, 181, 173, 164, 155, 146, 137, 130, 121, 112, 103, 93, 84, 76, 69, 60, 52, 42, 32, 22, 12, 1}

transitions:

272 → 43

329 → 94

221 → 264

221 → 3

280 → 33

32 → 305

32 → 13

263 → 94

103 → 166

103 → 3

214 → 43

229 → 43

181 → 94

84 → 255

84 → 3

146 → 256

146 → 13

130 → 182

130 → 3

304 → 296

304 → 33

246 → 13

1 → 94

287 → 23

60 → 13

197 → 94

76 → 165

76 → 94

173 → 296

173 → 33

121 → 207

121 → 23

52 → 43

22 → 95

22 → 33

313 → 264

313 → 3

93 → 113

93 → 23

12 → 95

12 → 33

112 → 114

112 → 23

295 → 264

295 → 3

69 → 43

42 → 264

42 → 3

137 → 165

137 → 94

190 → 104

190 → 43

164 → 3

206 → 3

254 → 122

254 → 33

321 → 43

155 → 94

238 → 44

238 → 43

f6₀ → 2

5₀(303) → 295

5₀(274) → 275

5₀(284) → 285

5₀(123) → 124

5₀(261) → 262

5₀(335) → 336

5₀(233) → 234

5₀(72) → 73

5₀(317) → 318

5₀(55) → 56

5₀(118) → 119

5₀(157) → 158

5₀(34) → 77

5₀(98) → 99

5₀(120) → 112

5₀(188) → 189

5₀(54) → 55

5₀(61) → 222

5₀(242) → 243

5₀(114) → 115

5₀(222) → 223

5₀(140) → 141

5₀(62) → 63

5₀(85) → 207

5₀(241) → 242

5₀(4) → 5

5₀(14) → 15

5₀(239) → 240

5₀(113) → 114

5₀(2) → 23

5₀(228) → 221

5₀(3) → 4

5₀(26) → 27

5₀(45) → 46

5₀(316) → 317

5₀(170) → 171

5₀(27) → 28

5₀(129) → 121

5₀(336) → 337

5₀(149) → 150

5₀(161) → 162

5₀(110) → 111

5₀(33) → 113

5₀(13) → 330

5₀(102) → 93

5₀(294) → 287

5₀(106) → 107

5₀(178) → 179

5₀(187) → 188

5₀(219) → 220

5₀(51) → 42

5₀(160) → 161

5₀(203) → 204

5₀(257) → 258

3₀(244) → 245

3₀(33) → 34

3₀(124) → 125

3₀(70) → 71

3₀(306) → 307

3₀(279) → 272

3₀(63) → 64

3₀(251) → 252

3₀(289) → 290

3₀(59) → 52

3₀(159) → 160

3₀(37) → 38

3₀(230) → 231

3₀(108) → 109

3₀(85) → 86

3₀(156) → 157

3₀(278) → 279

3₀(205) → 197

3₀(309) → 310

3₀(125) → 126

3₀(95) → 96

3₀(265) → 266

3₀(167) → 168

3₀(231) → 232

3₀(307) → 308

3₀(134) → 135

3₀(43) → 138

3₀(107) → 108

3₀(79) → 80

3₀(77) → 78

3₀(194) → 195

3₀(92) → 84

3₀(209) → 210

3₀(185) → 186

3₀(46) → 47

3₀(268) → 269

3₀(29) → 30

3₀(28) → 29

3₀(3) → 122

3₀(249) → 250

3₀(47) → 48

3₀(276) → 277

3₀(64) → 65

3₀(324) → 325

3₀(104) → 105

3₀(113) → 247

3₀(57) → 58

3₀(235) → 236

3₀(285) → 286

3₀(191) → 192

3₀(96) → 191

3₀(128) → 129

3₀(94) → 95

3₀(180) → 173

3₀(300) → 301

3₀(305) → 306

3₀(189) → 181

3₀(127) → 128

3₀(328) → 321

3₀(337) → 329

3₀(49) → 50

3₀(20) → 21

3₀(13) → 296

3₀(21) → 12

3₀(31) → 22

3₀(133) → 134

3₀(296) → 297

3₀(122) → 123

3₀(10) → 11

3₀(2) → 33

3₀(290) → 291

3₀(153) → 154

3₀(237) → 229

3₀(44) → 45

3₀(138) → 322

3₀(198) → 239

3₀(89) → 90

3₀(333) → 334

2₀(211) → 212

2₀(53) → 54

2₀(169) → 170

2₀(212) → 213

2₀(162) → 163

2₀(234) → 235

2₀(301) → 302

2₀(30) → 31

2₀(210) → 211

2₀(158) → 159

2₀(144) → 145

2₀(105) → 215

2₀(3) → 61

2₀(86) → 87

2₀(33) → 255

2₀(58) → 59

2₀(312) → 304

2₀(48) → 49

2₀(184) → 185

2₀(150) → 151

2₀(323) → 324

2₀(215) → 216

2₀(165) → 166

2₀(111) → 103

2₀(288) → 289

2₀(311) → 312

2₀(18) → 19

2₀(199) → 200

2₀(332) → 333

2₀(9) → 10

2₀(208) → 209

2₀(198) → 314

2₀(179) → 180

2₀(302) → 303

2₀(71) → 72

2₀(320) → 313

2₀(148) → 149

2₀(171) → 172

2₀(13) → 264

2₀(88) → 89

2₀(318) → 319

2₀(5) → 70

2₀(4) → 53

2₀(327) → 328

2₀(225) → 226

2₀(202) → 203

2₀(250) → 251

2₀(43) → 182

2₀(182) → 183

2₀(40) → 41

2₀(139) → 140

2₀(2) → 3

2₀(23) → 198

2₀(213) → 206

2₀(147) → 148

2₀(223) → 224

2₀(176) → 177

2₀(266) → 267

2₀(172) → 164

2₀(216) → 217

2₀(152) → 153

2₀(331) → 332

0₀(2) → 43

0₀(132) → 133

0₀(82) → 83

0₀(269) → 270

0₀(177) → 178

0₀(74) → 75

0₀(326) → 327

0₀(227) → 228

0₀(193) → 194

0₀(19) → 20

0₀(293) → 294

0₀(291) → 292

0₀(192) → 193

0₀(136) → 130

0₀(292) → 293

0₀(100) → 101

0₀(218) → 219

0₀(165) → 174

0₀(286) → 280

0₀(245) → 238

0₀(220) → 214

0₀(325) → 326

0₀(8) → 9

0₀(91) → 92

0₀(207) → 208

0₀(270) → 271

0₀(36) → 37

0₀(277) → 278

0₀(183) → 184

0₀(281) → 282

0₀(56) → 57

0₀(273) → 274

0₀(17) → 18

0₀(236) → 237

0₀(262) → 254

0₀(131) → 132

0₀(299) → 300

0₀(314) → 315

0₀(166) → 167

0₀(3) → 85

0₀(252) → 253

0₀(264) → 265

0₀(75) → 69

0₀(43) → 44

0₀(248) → 249

0₀(94) → 104

0₀(196) → 190

4₀(2) → 13

4₀(330) → 331

4₀(275) → 276

4₀(117) → 118

4₀(50) → 51

4₀(260) → 261

4₀(232) → 233

4₀(255) → 256

4₀(25) → 26

4₀(43) → 156

4₀(4) → 288

4₀(61) → 62

4₀(334) → 335

4₀(11) → 1

4₀(256) → 257

4₀(198) → 199

4₀(23) → 147

4₀(94) → 305

4₀(81) → 82

4₀(240) → 241

4₀(39) → 40

4₀(201) → 202

4₀(319) → 320

4₀(73) → 74

4₀(154) → 146

4₀(226) → 227

4₀(41) → 32

4₀(16) → 17

4₀(253) → 246

4₀(109) → 110

4₀(283) → 284

4₀(77) → 281

4₀(13) → 14

4₀(200) → 201

4₀(68) → 60

4₀(116) → 117

4₀(119) → 120

1₀(87) → 88

1₀(143) → 144

1₀(101) → 102

1₀(186) → 187

1₀(142) → 143

1₀(97) → 98

1₀(135) → 136

1₀(78) → 79

1₀(99) → 100

1₀(151) → 152

1₀(5) → 6

1₀(122) → 273

1₀(141) → 142

1₀(282) → 283

1₀(297) → 298

1₀(66) → 67

1₀(96) → 97

1₀(7) → 8

1₀(43) → 165

1₀(6) → 7

1₀(90) → 91

1₀(67) → 68

1₀(15) → 16

1₀(83) → 76

1₀(271) → 263

1₀(267) → 268

1₀(145) → 137

1₀(298) → 299

1₀(35) → 36

1₀(80) → 81

1₀(217) → 218

1₀(308) → 309

1₀(224) → 225

1₀(65) → 66

1₀(34) → 35

1₀(195) → 196

1₀(310) → 311

1₀(163) → 155

1₀(138) → 139

1₀(175) → 176

1₀(247) → 248

1₀(24) → 25

1₀(126) → 127

1₀(77) → 131

1₀(38) → 39

1₀(33) → 230

1₀(23) → 24

1₀(174) → 175

1₀(259) → 260

1₀(115) → 116

1₀(315) → 316

1₀(204) → 205

1₀(322) → 323

1₀(105) → 106

1₀(2) → 94

1₀(258) → 259

1₀(243) → 244

1₀(168) → 169

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