YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

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

Proof

1 String Reversal

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

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

1.1 Bounds

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

final states:

{277, 257, 238, 221, 204, 187, 173, 156, 142, 128, 118, 105, 95, 84, 74, 64, 55, 45, 36, 30, 26, 19, 14, 8, 1}

transitions:

221 → 20

128 → 9

84 → 10

84 → 20

187 → 38

187 → 20

95 → 56

95 → 9

55 → 20

1 → 56

1 → 9

8 → 3

26 → 3

36 → 46

257 → 3

173 → 143

173 → 31

277 → 205

277 → 46

105 → 31

204 → 47

204 → 46

118 → 47

118 → 46

45 → 9

14 → 75

14 → 20

30 → 31

64 → 258

64 → 31

142 → 31

74 → 38

74 → 20

19 → 65

19 → 9

156 → 21

156 → 46

238 → 38

238 → 20

3₀(189) → 190

3₀(51) → 52

3₀(254) → 255

3₀(260) → 261

3₀(67) → 68

3₀(46) → 47

3₀(166) → 167

3₀(183) → 184

3₀(292) → 293

3₀(78) → 119

3₀(127) → 118

3₀(212) → 213

3₀(141) → 128

3₀(200) → 201

3₀(234) → 235

3₀(210) → 211

3₀(3) → 4

3₀(44) → 36

3₀(32) → 33

3₀(253) → 254

3₀(231) → 232

3₀(273) → 274

3₀(21) → 22

3₀(150) → 151

3₀(50) → 51

3₀(135) → 136

3₀(106) → 107

3₀(290) → 291

3₀(108) → 109

3₀(272) → 273

3₀(114) → 115

3₀(9) → 205

3₀(198) → 199

3₀(179) → 180

3₀(131) → 132

3₀(119) → 120

3₀(110) → 111

3₀(62) → 63

3₀(101) → 102

3₀(39) → 40

3₀(126) → 127

3₀(171) → 172

3₀(220) → 204

3₀(88) → 89

3₀(5) → 6

3₀(47) → 278

3₀(116) → 117

3₀(2) → 46

3₀(178) → 179

3₀(263) → 264

3₀(223) → 224

3₀(176) → 177

3₀(266) → 267

3₀(69) → 70

3₀(20) → 21

3₀(194) → 195

3₀(152) → 153

4₀(109) → 110

4₀(2) → 37

4₀(31) → 32

4₀(155) → 142

4₀(261) → 262

4₀(113) → 114

4₀(167) → 168

4₀(201) → 202

4₀(293) → 294

4₀(103) → 104

4₀(209) → 210

4₀(87) → 88

4₀(133) → 134

4₀(4) → 5

4₀(59) → 60

4₀(46) → 157

4₀(112) → 113

4₀(83) → 74

4₀(218) → 219

4₀(165) → 166

4₀(243) → 244

4₀(85) → 96

4₀(280) → 281

4₀(61) → 62

4₀(203) → 187

4₀(181) → 182

4₀(163) → 164

4₀(57) → 58

4₀(138) → 139

4₀(66) → 67

4₀(285) → 286

4₀(268) → 269

4₀(206) → 207

4₀(226) → 227

4₀(264) → 265

4₀(96) → 97

4₀(215) → 216

4₀(65) → 66

4₀(151) → 152

4₀(35) → 30

4₀(294) → 295

5₀(70) → 71

5₀(239) → 240

5₀(78) → 79

5₀(251) → 252

5₀(37) → 38

5₀(85) → 86

5₀(130) → 131

5₀(207) → 208

5₀(281) → 282

5₀(132) → 133

5₀(34) → 35

5₀(11) → 12

5₀(168) → 169

5₀(265) → 266

5₀(38) → 174

5₀(6) → 7

5₀(134) → 135

5₀(242) → 243

5₀(158) → 159

5₀(56) → 57

5₀(46) → 75

5₀(195) → 196

5₀(274) → 275

5₀(82) → 83

5₀(271) → 272

5₀(40) → 41

5₀(286) → 287

5₀(255) → 256

5₀(154) → 155

5₀(111) → 112

5₀(9) → 10

5₀(288) → 289

5₀(235) → 236

5₀(191) → 192

5₀(12) → 13

5₀(275) → 276

5₀(287) → 288

5₀(20) → 85

5₀(115) → 116

5₀(71) → 72

5₀(48) → 49

5₀(246) → 247

5₀(17) → 18

5₀(93) → 94

5₀(291) → 292

5₀(2) → 20

5₀(233) → 234

5₀(24) → 25

5₀(188) → 189

5₀(68) → 69

5₀(16) → 17

5₀(89) → 90

5₀(240) → 241

5₀(52) → 53

5₀(190) → 191

0₀(125) → 126

0₀(29) → 26

0₀(143) → 222

0₀(160) → 161

0₀(97) → 98

0₀(120) → 121

0₀(99) → 100

0₀(279) → 280

0₀(192) → 193

0₀(164) → 165

0₀(177) → 178

0₀(208) → 209

0₀(53) → 54

0₀(94) → 84

0₀(169) → 170

0₀(241) → 242

0₀(157) → 158

0₀(196) → 197

0₀(295) → 277

0₀(13) → 8

0₀(162) → 163

0₀(10) → 11

0₀(22) → 27

0₀(276) → 257

0₀(249) → 250

0₀(159) → 160

0₀(289) → 290

0₀(145) → 146

0₀(3) → 188

0₀(81) → 82

0₀(229) → 230

0₀(144) → 145

0₀(262) → 263

0₀(180) → 181

0₀(38) → 39

0₀(205) → 206

0₀(214) → 215

0₀(228) → 229

0₀(259) → 260

0₀(2) → 3

0₀(252) → 253

0₀(258) → 259

1₀(224) → 225

1₀(267) → 268

1₀(184) → 185

1₀(90) → 91

1₀(31) → 106

1₀(123) → 124

1₀(236) → 237

1₀(77) → 78

1₀(60) → 61

1₀(20) → 143

1₀(137) → 138

1₀(185) → 186

1₀(197) → 198

1₀(72) → 73

1₀(193) → 194

1₀(172) → 156

1₀(278) → 279

1₀(270) → 271

1₀(98) → 99

1₀(73) → 64

1₀(250) → 251

1₀(211) → 212

1₀(225) → 226

1₀(22) → 23

1₀(91) → 92

1₀(9) → 258

1₀(222) → 223

1₀(199) → 200

1₀(186) → 173

1₀(76) → 77

1₀(182) → 183

1₀(117) → 105

1₀(80) → 81

1₀(216) → 217

1₀(63) → 55

1₀(49) → 50

1₀(2) → 31

1₀(75) → 129

1₀(143) → 144

1₀(28) → 29

1₀(149) → 150

1₀(161) → 162

1₀(102) → 103

1₀(136) → 137

1₀(219) → 220

1₀(100) → 101

1₀(283) → 284

1₀(248) → 249

f6₀ → 2

2₀(2) → 9

2₀(18) → 14

2₀(237) → 221

2₀(46) → 239

2₀(227) → 228

2₀(9) → 56

2₀(10) → 15

2₀(230) → 231

2₀(175) → 176

2₀(146) → 147

2₀(54) → 45

2₀(202) → 203

2₀(213) → 214

2₀(170) → 171

2₀(79) → 80

2₀(232) → 233

2₀(247) → 248

2₀(107) → 108

2₀(25) → 19

2₀(217) → 218

2₀(43) → 44

2₀(92) → 93

2₀(124) → 125

2₀(104) → 95

2₀(244) → 245

2₀(282) → 283

2₀(284) → 285

2₀(86) → 87

2₀(147) → 148

2₀(245) → 246

2₀(256) → 238

2₀(140) → 141

2₀(23) → 24

2₀(121) → 122

2₀(269) → 270

2₀(139) → 140

2₀(7) → 1

2₀(33) → 34

2₀(15) → 16

2₀(27) → 28

2₀(129) → 130

2₀(42) → 43

2₀(75) → 76

2₀(20) → 65

2₀(174) → 175

2₀(41) → 42

2₀(58) → 59

2₀(148) → 149

2₀(122) → 123

2₀(47) → 48

2₀(153) → 154

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