YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{301, 293, 285, 276, 268, 260, 252, 244, 236, 227, 219, 211, 203, 194, 185, 175, 166, 157, 148, 139, 131, 122, 113, 103, 95, 86, 77, 67, 57, 48, 39, 31, 21, 12, 1}

transitions:

157 → 22

103 → 79

103 → 69

103 → 58

211 → 68

122 → 68

276 → 149

276 → 3

260 → 78

260 → 68

227 → 59

227 → 104

39 → 22

57 → 140

57 → 58

219 → 228

219 → 3

95 → 68

185 → 167

185 → 3

175 → 22

293 → 114

293 → 176

31 → 68

1 → 68

139 → 78

139 → 68

86 → 22

268 → 68

21 → 22

67 → 22

301 → 78

301 → 68

244 → 104

252 → 228

252 → 3

12 → 58

77 → 78

77 → 68

236 → 78

236 → 68

113 → 68

48 → 68

148 → 59

148 → 104

203 → 68

285 → 68

131 → 176

194 → 68

166 → 68

f6₀ → 2

4₀(59) → 302

4₀(87) → 294

4₀(189) → 190

4₀(155) → 156

4₀(130) → 122

4₀(92) → 93

4₀(295) → 296

4₀(22) → 23

4₀(243) → 236

4₀(237) → 238

4₀(214) → 215

4₀(213) → 214

4₀(308) → 301

4₀(71) → 72

4₀(117) → 118

4₀(151) → 152

4₀(2) → 68

4₀(163) → 164

4₀(3) → 78

4₀(26) → 27

4₀(221) → 222

4₀(255) → 256

4₀(129) → 130

4₀(28) → 29

4₀(287) → 288

4₀(264) → 265

4₀(101) → 102

4₀(134) → 135

4₀(187) → 188

4₀(158) → 159

4₀(223) → 224

4₀(195) → 196

4₀(209) → 210

4₀(257) → 258

3₀(114) → 115

3₀(182) → 183

3₀(65) → 66

3₀(126) → 127

3₀(225) → 226

3₀(150) → 151

3₀(239) → 240

3₀(245) → 246

3₀(41) → 42

3₀(78) → 79

3₀(279) → 280

3₀(30) → 21

3₀(183) → 184

3₀(159) → 160

3₀(144) → 145

3₀(147) → 139

3₀(160) → 161

3₀(37) → 38

3₀(199) → 200

3₀(58) → 87

3₀(207) → 208

3₀(51) → 52

3₀(136) → 137

3₀(84) → 85

3₀(112) → 103

3₀(143) → 144

3₀(6) → 7

3₀(277) → 278

3₀(247) → 248

3₀(110) → 111

3₀(120) → 121

3₀(294) → 295

3₀(55) → 56

3₀(109) → 110

3₀(56) → 48

3₀(197) → 198

3₀(36) → 37

3₀(29) → 30

3₀(222) → 223

3₀(87) → 88

3₀(238) → 239

3₀(3) → 186

3₀(249) → 250

3₀(172) → 173

3₀(97) → 98

3₀(104) → 277

3₀(154) → 155

3₀(116) → 117

3₀(9) → 10

3₀(196) → 197

3₀(96) → 97

3₀(146) → 147

3₀(83) → 84

3₀(127) → 128

3₀(253) → 254

3₀(115) → 116

3₀(297) → 298

3₀(133) → 134

3₀(5) → 6

3₀(246) → 247

3₀(10) → 11

3₀(291) → 292

3₀(2) → 58

3₀(188) → 189

3₀(68) → 69

3₀(198) → 199

3₀(66) → 57

3₀(22) → 140

3₀(186) → 187

3₀(52) → 53

5₀(74) → 75

5₀(16) → 17

5₀(190) → 191

5₀(35) → 36

5₀(292) → 285

5₀(229) → 230

5₀(141) → 142

5₀(278) → 279

5₀(234) → 235

5₀(210) → 203

5₀(105) → 106

5₀(3) → 13

5₀(7) → 8

5₀(271) → 272

5₀(186) → 261

5₀(303) → 304

5₀(33) → 34

5₀(58) → 167

5₀(273) → 274

5₀(121) → 113

5₀(123) → 124

5₀(135) → 136

5₀(167) → 212

5₀(170) → 171

5₀(108) → 109

5₀(304) → 305

5₀(68) → 228

5₀(59) → 204

5₀(118) → 119

5₀(145) → 146

5₀(274) → 275

5₀(177) → 178

5₀(72) → 73

5₀(15) → 16

5₀(258) → 259

5₀(149) → 150

5₀(205) → 206

5₀(281) → 282

5₀(220) → 221

5₀(63) → 64

5₀(261) → 262

5₀(191) → 192

5₀(181) → 182

5₀(124) → 125

5₀(202) → 194

5₀(265) → 266

5₀(22) → 149

5₀(2) → 3

5₀(242) → 243

5₀(305) → 306

5₀(176) → 177

5₀(17) → 18

5₀(69) → 245

5₀(306) → 307

5₀(152) → 153

5₀(226) → 219

5₀(153) → 154

0₀(111) → 112

0₀(2) → 22

0₀(231) → 232

0₀(82) → 83

0₀(45) → 46

0₀(269) → 270

0₀(161) → 162

0₀(58) → 195

0₀(201) → 202

0₀(44) → 45

0₀(162) → 163

0₀(42) → 43

0₀(4) → 5

0₀(59) → 60

0₀(289) → 290

0₀(174) → 166

0₀(76) → 67

0₀(100) → 101

0₀(254) → 255

0₀(165) → 157

0₀(286) → 287

0₀(119) → 120

0₀(267) → 260

0₀(70) → 71

0₀(47) → 39

0₀(91) → 92

0₀(270) → 271

0₀(106) → 107

0₀(105) → 269

0₀(296) → 297

0₀(298) → 299

0₀(290) → 291

0₀(27) → 28

0₀(54) → 55

0₀(137) → 138

0₀(169) → 170

0₀(299) → 300

0₀(216) → 217

0₀(138) → 131

0₀(184) → 175

0₀(69) → 70

0₀(307) → 308

0₀(38) → 31

0₀(53) → 54

0₀(94) → 86

0₀(104) → 158

0₀(171) → 172

0₀(208) → 209

0₀(22) → 40

2₀(2) → 104

2₀(250) → 251

2₀(275) → 268

2₀(263) → 264

2₀(128) → 129

2₀(204) → 205

2₀(230) → 231

2₀(49) → 50

2₀(99) → 100

2₀(79) → 80

2₀(215) → 216

2₀(235) → 227

2₀(24) → 25

2₀(107) → 108

2₀(25) → 26

2₀(217) → 218

2₀(43) → 44

2₀(8) → 9

2₀(61) → 62

2₀(164) → 165

2₀(11) → 1

2₀(218) → 211

2₀(87) → 286

2₀(23) → 24

2₀(132) → 133

2₀(125) → 126

2₀(262) → 263

2₀(251) → 244

2₀(93) → 94

2₀(240) → 241

2₀(302) → 303

2₀(22) → 49

2₀(40) → 41

2₀(212) → 213

2₀(34) → 35

2₀(266) → 267

2₀(58) → 59

2₀(179) → 180

2₀(13) → 14

2₀(200) → 201

2₀(88) → 89

2₀(68) → 123

2₀(158) → 237

2₀(102) → 95

1₀(19) → 20

1₀(140) → 141

1₀(283) → 284

1₀(142) → 143

1₀(192) → 193

1₀(46) → 47

1₀(98) → 99

1₀(50) → 51

1₀(282) → 283

1₀(60) → 61

1₀(241) → 242

1₀(4) → 253

1₀(90) → 91

1₀(13) → 96

1₀(284) → 276

1₀(288) → 289

1₀(280) → 281

1₀(22) → 114

1₀(20) → 12

1₀(167) → 168

1₀(248) → 249

1₀(89) → 90

1₀(156) → 148

1₀(232) → 233

1₀(149) → 220

1₀(193) → 185

1₀(14) → 15

1₀(40) → 132

1₀(256) → 257

1₀(3) → 4

1₀(80) → 81

1₀(206) → 207

1₀(62) → 63

1₀(224) → 225

1₀(81) → 82

1₀(32) → 33

1₀(173) → 174

1₀(18) → 19

1₀(85) → 77

1₀(180) → 181

1₀(64) → 65

1₀(300) → 293

1₀(228) → 229

1₀(23) → 32

1₀(259) → 252

1₀(233) → 234

1₀(104) → 105

1₀(75) → 76

1₀(178) → 179

1₀(2) → 176

1₀(272) → 273

1₀(73) → 74

1₀(168) → 169

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