YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{294, 276, 257, 240, 224, 207, 194, 182, 170, 159, 148, 136, 125, 112, 103, 93, 83, 73, 64, 57, 50, 42, 34, 28, 20, 15, 10, 6, 5, 1}

transitions:

315 → 46

103 → 7

10 → 65

10 → 3

15 → 208

15 → 3

294 → 74

294 → 3

136 → 44

136 → 113

276 → 16

276 → 94

276 → 115

50 → 22

50 → 16

57 → 84

57 → 21

5 → 114

5 → 3

34 → 21

20 → 225

20 → 94

20 → 16

224 → 35

224 → 3

49 → 312

1 → 21

73 → 258

73 → 113

125 → 3

170 → 22

170 → 16

207 → 11

257 → 21

6 → 277

6 → 16

28 → 21

93 → 149

93 → 16

112 → 43

112 → 113

182 → 7

42 → 43

42 → 113

64 → 13

64 → 21

240 → 7

83 → 35

83 → 3

159 → 3

148 → 74

148 → 3

194 → 161

194 → 13

194 → 21

f6₀ → 2

5₀(303) → 304

5₀(138) → 139

5₀(121) → 122

5₀(236) → 237

5₀(77) → 78

5₀(96) → 97

5₀(297) → 298

5₀(137) → 138

5₀(155) → 156

5₀(18) → 19

5₀(200) → 201

5₀(128) → 129

5₀(193) → 182

5₀(227) → 228

5₀(166) → 167

5₀(21) → 137

5₀(118) → 119

5₀(94) → 104

5₀(120) → 121

5₀(54) → 55

5₀(211) → 212

5₀(46) → 47

5₀(190) → 191

5₀(242) → 243

5₀(199) → 200

5₀(109) → 110

5₀(62) → 63

5₀(167) → 168

5₀(306) → 307

5₀(76) → 77

5₀(117) → 118

5₀(74) → 75

5₀(256) → 240

5₀(218) → 219

5₀(111) → 103

5₀(177) → 178

5₀(2) → 7

5₀(228) → 229

5₀(142) → 143

5₀(304) → 305

5₀(168) → 169

5₀(264) → 265

5₀(210) → 211

5₀(8) → 241

5₀(78) → 79

5₀(47) → 48

5₀(158) → 148

5₀(219) → 220

5₀(104) → 105

5₀(141) → 142

3₀(106) → 107

3₀(126) → 127

3₀(225) → 226

3₀(239) → 224

3₀(298) → 299

3₀(26) → 27

3₀(216) → 217

3₀(252) → 253

3₀(14) → 10

3₀(30) → 31

3₀(37) → 38

3₀(86) → 87

3₀(178) → 179

3₀(8) → 9

3₀(174) → 175

3₀(45) → 46

3₀(84) → 85

3₀(132) → 133

3₀(267) → 268

3₀(11) → 208

3₀(60) → 61

3₀(134) → 135

3₀(247) → 248

3₀(43) → 51

3₀(79) → 80

3₀(149) → 150

3₀(258) → 259

3₀(176) → 177

3₀(92) → 83

3₀(202) → 203

3₀(185) → 186

3₀(90) → 91

3₀(268) → 269

3₀(3) → 35

3₀(266) → 267

3₀(175) → 176

3₀(40) → 41

3₀(259) → 260

3₀(113) → 114

3₀(288) → 289

3₀(145) → 146

3₀(94) → 95

3₀(61) → 62

3₀(127) → 128

3₀(273) → 274

3₀(21) → 65

3₀(71) → 72

3₀(48) → 49

3₀(296) → 297

3₀(2) → 3

3₀(233) → 234

3₀(39) → 40

3₀(16) → 74

1₀(189) → 190

1₀(221) → 222

1₀(244) → 245

1₀(35) → 225

1₀(65) → 126

1₀(180) → 181

1₀(245) → 246

1₀(234) → 235

1₀(300) → 301

1₀(270) → 271

1₀(144) → 145

1₀(3) → 94

1₀(7) → 149

1₀(129) → 130

1₀(21) → 22

1₀(143) → 144

1₀(150) → 151

1₀(275) → 257

1₀(215) → 216

1₀(272) → 273

1₀(114) → 115

1₀(56) → 50

1₀(68) → 69

1₀(237) → 238

1₀(289) → 290

1₀(70) → 71

1₀(201) → 202

1₀(27) → 20

1₀(262) → 263

1₀(284) → 285

1₀(161) → 162

1₀(171) → 172

1₀(281) → 282

1₀(107) → 108

1₀(220) → 221

1₀(4) → 5

1₀(265) → 266

1₀(43) → 277

1₀(2) → 16

1₀(246) → 247

1₀(213) → 214

1₀(277) → 278

1₀(154) → 155

1₀(241) → 295

1₀(282) → 283

1₀(255) → 256

1₀(235) → 236

1₁(314) → 315

0₀(2) → 113

0₀(25) → 26

0₀(95) → 96

0₀(261) → 262

0₀(295) → 296

0₀(124) → 112

0₀(152) → 153

0₀(58) → 59

0₀(51) → 52

0₀(44) → 45

0₀(88) → 89

0₀(291) → 292

0₀(87) → 88

0₀(4) → 160

0₀(115) → 116

0₀(292) → 293

0₀(165) → 166

0₀(286) → 287

0₀(243) → 244

0₀(85) → 86

0₀(280) → 281

0₀(198) → 199

0₀(8) → 171

0₀(187) → 188

0₀(214) → 215

0₀(230) → 231

0₀(105) → 106

0₀(11) → 12

0₀(108) → 109

0₀(135) → 125

0₀(9) → 6

0₀(302) → 303

0₀(251) → 252

0₀(212) → 213

0₀(139) → 140

0₀(97) → 98

0₀(17) → 18

0₀(156) → 157

0₀(131) → 132

0₀(66) → 67

0₀(67) → 68

0₀(184) → 185

0₀(204) → 205

0₀(241) → 242

0₀(38) → 39

0₀(206) → 194

0₀(3) → 258

0₀(52) → 53

0₀(29) → 30

0₀(43) → 44

0₀(301) → 302

0₀(101) → 102

0₀(153) → 154

0₀(7) → 43

4₀(2) → 11

4₀(157) → 158

4₀(163) → 164

4₀(250) → 251

4₀(196) → 197

4₀(123) → 124

4₀(263) → 264

4₀(65) → 66

4₀(197) → 198

4₀(260) → 261

4₀(191) → 192

4₀(308) → 309

4₀(4) → 1

4₀(8) → 195

4₀(21) → 29

4₀(222) → 223

4₀(151) → 152

4₀(254) → 255

4₀(223) → 207

4₀(3) → 4

4₀(164) → 165

4₀(249) → 250

4₀(100) → 101

4₀(53) → 54

4₀(203) → 204

4₀(140) → 141

4₀(94) → 183

4₀(32) → 33

4₀(81) → 82

4₀(173) → 174

4₀(269) → 270

4₀(208) → 209

4₀(305) → 306

4₀(307) → 308

4₀(205) → 206

4₀(172) → 173

4₀(75) → 76

4₀(226) → 227

4₀(186) → 187

4₀(209) → 210

4₀(162) → 163

4₀(278) → 279

4₀(41) → 34

4₀(16) → 17

4₀(285) → 286

4₀(188) → 189

4₀(31) → 32

4₀(231) → 232

4₀(287) → 288

4₀(179) → 180

4₀(72) → 64

4₀(116) → 117

4₀(102) → 93

4₁(313) → 314

3₁(312) → 313

2₀(19) → 15

2₀(299) → 300

2₀(238) → 239

2₀(283) → 284

2₀(160) → 161

2₀(99) → 100

2₀(82) → 73

2₀(293) → 276

2₀(279) → 280

2₀(192) → 193

2₀(122) → 123

2₀(98) → 99

2₀(63) → 57

2₀(69) → 70

2₀(59) → 60

2₀(169) → 159

2₀(11) → 84

2₀(36) → 37

2₀(146) → 147

2₀(1) → 58

2₀(7) → 8

2₀(13) → 14

2₀(22) → 23

2₀(147) → 136

2₀(248) → 249

2₀(181) → 170

2₀(89) → 90

2₀(232) → 233

2₀(49) → 42

2₀(290) → 291

2₀(271) → 272

2₀(119) → 120

2₀(35) → 36

2₀(80) → 81

2₀(217) → 218

2₀(133) → 134

2₀(311) → 294

2₀(274) → 275

2₀(229) → 230

2₀(195) → 196

2₀(310) → 311

2₀(110) → 111

2₀(183) → 184

2₀(24) → 25

2₀(33) → 28

2₀(130) → 131

2₀(23) → 24

2₀(91) → 92

2₀(12) → 13

2₀(253) → 254

2₀(55) → 56

2₀(2) → 21

2₀(309) → 310

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