Analysis of zz-www.sudokuoftheday.co.uk-20060430-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .6..5.1...3........476...9.4..2......9..6351.....8.6........4.3....72..15.....28. initial
Autosolve
position: .6..5.1...35.......476...954.62......9..6351.....8.6........4.3.8..729.15.....28. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 2,4 => CTR => H2: 6,7 * DIS # I2: 2,4 => CTR => I2: 6,7,8 * DIS # A3: 2 => CTR => A3: 1,8 * DIS # F7: 1,8 => CTR => F7: 5,6,9 * DIS # I2: 7,8 => CTR => I2: 2,4,6 * DIS # G4: 3 => CTR => G4: 7,8 * DIS # C1: 9 => CTR => C1: 2,8 * DIS # D1: 4,7 => CTR => D1: 3,8,9 * DIS # D2: 4,7 => CTR => D2: 1,8,9 * DIS # H1: 3,7 => CTR => H1: 2,4 * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # B7: 1,7 => CTR => B7: 2 * DIS # D7: 1,9 => CTR => D7: 5,8 * DIS # F7: 1,9 => CTR => F7: 5,6,8 * DIS # F9: 1,9 => CTR => F9: 4,6 * DIS # C7: 2 => CTR => C7: 1,9 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # D9: 3,4 => CTR => D9: 1,9 * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # H7: 5,6 => SOL * DIS # H7: 7 => CTR => H7: 5,6 * PRF # H7: 6,7 => SOL * DIS # H7: 5 => CTR => H7: 6,7 * DIS # I2: 2,4,8 => CTR => I2: 6,7 * CNT 29 HDP CHAINS / 67 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 2,4 => CTR => H2: 6,7 * DIS H2: 6,7 # F7: 1,8 => CTR => F7: 5,6,9 * DIS H2: 6,7 + F7: 5,6,9 # I1: 7,8 => CTR => I1: 2,4 * DIS H2: 6,7 + F7: 5,6,9 + I1: 2,4 # I2: 7,8 => CTR => I2: 6 * PRF H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 => SOL * STA H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6..5.1...3........476...9.4..2......9..6351.....8.6........4.3....72..15.....28. | initial |
| .6..5.1...35.......476...954.62......9..6351.....8.6........4.3.8..729.15.....28. | autosolve |
| 968357142235149876147628395456291738892763514371584629729815463683472951514936287 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) E2: 2,4 E3: 2,3 F3: 1,8 G2: 7,8 G3: 3,8 C5: 2,8 E4: 1,9 D5: 4,7 H4: 3,7 A8: 3,6 C8: 3,4 B9: 1,7 E7: 1,9 E9: 3,4 H8: 5,6 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 16 pairs (_) / A3 = 1 => 13 pairs (_) A3,F3: 1.. / A3 = 1 => 13 pairs (_) / F3 = 1 => 16 pairs (_) E4,E7: 1.. / E4 = 1 => 0 pairs (X) / E7 = 1 => 23 pairs (_) E2,E3: 2.. / E2 = 2 => 0 pairs (X) / E3 = 2 => 14 pairs (_) A3,E3: 2.. / A3 = 2 => 0 pairs (X) / E3 = 2 => 14 pairs (_) B6,B7: 2.. / B6 = 2 => 0 pairs (X) / B7 = 2 => 21 pairs (_) D1,E3: 3.. / D1 = 3 => 14 pairs (_) / E3 = 3 => 0 pairs (X) H1,G3: 3.. / H1 = 3 => 0 pairs (X) / G3 = 3 => 14 pairs (_) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) G4,H4: 3.. / G4 = 3 => 0 pairs (X) / H4 = 3 => 14 pairs (_) D1,H1: 3.. / D1 = 3 => 14 pairs (_) / H1 = 3 => 0 pairs (X) E3,G3: 3.. / E3 = 3 => 0 pairs (X) / G3 = 3 => 14 pairs (_) A6,A8: 3.. / A6 = 3 => 0 pairs (*) / A8 = 3 => 0 pairs (X) E3,E9: 3.. / E3 = 3 => 0 pairs (X) / E9 = 3 => 14 pairs (_) G3,G4: 3.. / G3 = 3 => 14 pairs (_) / G4 = 3 => 0 pairs (X) H1,H4: 3.. / H1 = 3 => 0 pairs (X) / H4 = 3 => 14 pairs (_) C8,C9: 4.. / C8 = 4 => 16 pairs (_) / C9 = 4 => 0 pairs (*) D5,I5: 4.. / D5 = 4 => 16 pairs (_) / I5 = 4 => 23 pairs (_) C8,D8: 4.. / C8 = 4 => 16 pairs (_) / D8 = 4 => 0 pairs (*) E2,E9: 4.. / E2 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (X) B4,B6: 5.. / B4 = 5 => 16 pairs (_) / B6 = 5 => 23 pairs (_) H7,H8: 5.. / H7 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) B4,F4: 5.. / B4 = 5 => 16 pairs (_) / F4 = 5 => 23 pairs (_) D8,H8: 5.. / D8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) H2,I2: 6.. / H2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) A7,A8: 6.. / A7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) F7,F9: 6.. / F7 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) A8,H8: 6.. / A8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) F9,I9: 6.. / F9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) I2,I9: 6.. / I2 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) H7,I9: 7.. / H7 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) B9,I9: 7.. / B9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) G2,G4: 7.. / G2 = 7 => 16 pairs (_) / G4 = 7 => 15 pairs (_) A5,C5: 8.. / A5 = 8 => 23 pairs (_) / C5 = 8 => 17 pairs (_) G4,I4: 8.. / G4 = 8 => 15 pairs (_) / I4 = 8 => 20 pairs (_) D7,F7: 8.. / D7 = 8 => 16 pairs (_) / F7 = 8 => 0 pairs (X) C1,C5: 8.. / C1 = 8 => 23 pairs (_) / C5 = 8 => 17 pairs (_) I4,I6: 9.. / I4 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) E4,E7: 9.. / E4 = 9 => 23 pairs (_) / E7 = 9 => 0 pairs (X) * DURATION: 0:00:42.825019 START: 22:46:22.572553 END: 22:47:05.397572 2019-04-30 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C5,C8,D5,E2,E3,E4,E7,E9,F3,G2,G3,H4,H8,I9) * .6..5.1...35.......476...954.62......9..6351.....8.6........4.3.8..729.15.....28. * PAIR E2: 2,4 ROW 2 H2: 2,4,6,7 # reduction candidate for 2,4 H2: 2,4 => CTR * .6.35.1...3514.826147628395456291738.9..6351232158.6.9...81546368..7295151.936287 H2: 6,7 # 17 pairs I2: 2,4,6,7,8 # reduction candidate for 2,4 I2: 2,4 => CTR * .6..5.1...35....6..476...954.62......9..6351.3...8.6.......647368..729515.....286 I2: 6,7,8 # 16 pairs * PAIR F3: 1,8 BLK 2 D2: 1,8,4,7,9 # reduction candidate for 1,8 D2: 1,8 # 17 pairs F2: 1,8,4,7,9 # reduction candidate for 1,8 F2: 1,8 # 17 pairs * PAIR F3: 1,8 ROW 3 A3: 1,8,2 # reduction candidate for 1,8 A3: 2 => CTR * .68.5.132135.2.746247631895456219378892763514.71.8.629729...4.3.84.729.151..46287 A3: 1,8 # 14 pairs * PAIR F3: 1,8 COL F F7: 1,8,5,6,9 # reduction candidate for 1,8 F7: 1,8 => CTR * .6..5.1...351....6.476...954.62......9..6351.3.1.8.6.....5.846368..7295151...6287 F7: 5,6,9 # 16 pairs * PAIR G2: 7,8 BLK 3 I1: 7,8,2,4 # reduction candidate for 7,8 I1: 7,8 # 18 pairs I2: 7,8,2,4,6 # reduction candidate for 7,8 I2: 7,8 => CTR * .6..5.1...35....6..476...954.62......9..6351.3...8.6.......647368..729515.....286 I2: 2,4,6 # 16 pairs * PAIR G2: 7,8 ROW 2 D2: 7,8,1,4,9 # reduction candidate for 7,8 D2: 7,8 # 19 pairs F2: 7,8,1,4,9 # reduction candidate for 7,8 F2: 7,8 # 19 pairs * PAIR G2: 7,8 COL G G4: 7,8,3 # reduction candidate for 7,8 G4: 3 => CTR * .6..5.13.135.2.746247631895456219378.9..63514..1.8.629.29...4.3.8..729.151..46287 G4: 7,8 # 14 pairs * PAIR G3: 3,8 COL G G4: 3,8,7 # reduction candidate for 3,8 G4: 3,8 # 16 pairs G4: 7 # 15 pairs * PAIR C5: 2,8 BLK 4 A5: 2,8,7 # reduction candidate for 2,8 A5: 2,8 # 24 pairs A5: 7 # 18 pairs * PAIR C5: 2,8 COL C C1: 2,8,9 # reduction candidate for 2,8 C1: 9 => CTR * .69.5.13..35129.7..476...954.629....798463512321.8.649972.1.463684372951513946287 C1: 2,8 # 21 pairs * PAIR E4: 1,9 BLK 5 F4: 1,9,5,7 # reduction candidate for 1,9 F4: 1,9 # 20 pairs D6: 1,9,4,5,7 # reduction candidate for 1,9 D6: 1,9 # 18 pairs F6: 1,9,4,5,7 # reduction candidate for 1,9 F6: 1,9 # 18 pairs * PAIR D5: 4,7 BLK 5 D6: 4,7,1,5,9 # reduction candidate for 4,7 D6: 4,7 # 17 pairs F6: 4,7,1,5,9 # reduction candidate for 4,7 F6: 4,7 # 17 pairs * PAIR D5: 4,7 ROW 5 I5: 4,7,2 # reduction candidate for 4,7 I5: 4,7 # 24 pairs I5: 2 # 18 pairs * PAIR D5: 4,7 COL D D1: 4,7,3,8,9 # reduction candidate for 4,7 D1: 4,7 => CTR * .6..5.132135.2.746247631895456219378.92.63514.71.8.629729...4.3.84.729.151..46287 D1: 3,8,9 # 16 pairs D2: 4,7,1,8,9 # reduction candidate for 4,7 D2: 4,7 => CTR * .6..5.1...35.......476..3954.62...3..9..6351.....8.6........4.3.84.729.15...34286 D2: 1,8,9 # 16 pairs * PAIR H4: 3,7 BLK 6 G4: 3,7,8 # reduction candidate for 3,7 G4: 3,7 # 20 pairs G4: 8 # 15 pairs * PAIR H4: 3,7 COL H H1: 3,7,2,4 # reduction candidate for 3,7 H1: 3,7 => CTR * .6.35.17..35147826147628395456291738.9..63512321.8.6.9...81546368..7295151.936287 H1: 2,4 # 15 pairs * PAIR C8: 3,4 BLK 7 C9: 3,4,1,9 # reduction candidate for 3,4 C9: 3,4 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 C9: 1,9 => CTR * .6..5.1...35.....6.476...954.62......9..6351...3.8.6..672...45338457296151...6287 * PAIR C8: 3,4 ROW 8 D8: 3,4,5 # reduction candidate for 3,4 D8: 3,4 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 D8: 5 => CTR * .6..5.1...35.....6.476...954.62......9..6351.....8.6..672...453384572961519..6287 * PAIR B9: 1,7 BLK 7 B7: 1,7,2 # reduction candidate for 1,7 B7: 1,7 => CTR * .6..5.13..35.2....24763189545621.378798463512321.8.6499.....4.36843729515.3.4.28. B7: 2 # 21 pairs * PAIR B9: 1,7 COL B B4: 1,7,5 # reduction candidate for 1,7 B4: 1,7 # 23 pairs B6: 1,7,2,5 # reduction candidate for 1,7 B6: 1,7 # 22 pairs * PAIR E7: 1,9 BLK 8 D7: 1,9,5,8 # reduction candidate for 1,9 D7: 1,9 => CTR * .6..5.1...35.....6.476.1.954.62......9..6351.....8.6..672..8453384572961519..6287 D7: 5,8 # 17 pairs F7: 1,9,5,6,8 # reduction candidate for 1,9 F7: 1,9 => CTR * .6..5.1...35.....6.476...954.62......9..6351.....8.6..6728..453384572961519..6287 F7: 5,6,8 # 16 pairs D9: 1,9,3,4 # reduction candidate for 1,9 D9: 1,9 # 19 pairs F9: 1,9,4,6 # reduction candidate for 1,9 F9: 1,9 => CTR * .6..5.1...35.......476...954.62......9..6351.....8.6.......64.368..729515.....286 F9: 4,6 # 17 pairs * PAIR E7: 1,9 ROW 7 C7: 1,9,2 # reduction candidate for 1,9 C7: 2 => CTR * .69.5.13..35129..6.476...954562.....798463512321.8.6..9.2.1.4.3684372951513946287 C7: 1,9 # 21 pairs * PAIR E9: 3,4 BLK 8 D8: 3,4,5 # reduction candidate for 3,4 D8: 3,4 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 D8: 5 => CTR * .6..5.1...35.....6.476...954.62......9..6351.....8.6..672...453384572961519..6287 D9: 3,4,1,9 # reduction candidate for 3,4 D9: 3,4 => CTR * .6..5.1...35.....6.476...954.62......9..6351...3.8.6..672...4533845729615....6287 D9: 1,9 # 19 pairs * PAIR E9: 3,4 ROW 9 C9: 3,4,1,9 # reduction candidate for 3,4 C9: 3,4 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 C9: 1,9 => CTR * .6..5.1...35.....6.476...954.62......9..6351...3.8.6..672...45338457296151...6287 * PAIR H8: 5,6 BLK 9 H7: 5,6,7 # reduction candidate for 5,6 H7: 5,6 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 H7: 7 => CTR * .6..5.1...35....6..476...954.62...3..9..6351.....8.6.......647368..7295157....286 * PAIR I9: 6,7 BLK 9 H7: 6,7,5 # reduction candidate for 6,7 H7: 6,7 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 H7: 5 => CTR * .6..5.1...35.....6.476...954.62......9..6351.....8.6..672...453384572961519..6287 * PAIR I9: 6,7 COL I I2: 6,7,2,4,8 # reduction candidate for 6,7 I2: 2,4,8 => CTR * .6..5.1...35....6..476...954.62......9..6351.3...8.6.......647368..729515.....286 I2: 6,7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060430-absurd-base-pr-000.dot * REASONING * DIS # H2: 2,4 => CTR => H2: 6,7 * DIS # I2: 2,4 => CTR => I2: 6,7,8 * DIS # A3: 2 => CTR => A3: 1,8 * DIS # F7: 1,8 => CTR => F7: 5,6,9 * DIS # I2: 7,8 => CTR => I2: 2,4,6 * DIS # G4: 3 => CTR => G4: 7,8 * DIS # C1: 9 => CTR => C1: 2,8 * DIS # D1: 4,7 => CTR => D1: 3,8,9 * DIS # D2: 4,7 => CTR => D2: 1,8,9 * DIS # H1: 3,7 => CTR => H1: 2,4 * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # B7: 1,7 => CTR => B7: 2 * DIS # D7: 1,9 => CTR => D7: 5,8 * DIS # F7: 1,9 => CTR => F7: 5,6,8 * DIS # F9: 1,9 => CTR => F9: 4,6 * DIS # C7: 2 => CTR => C7: 1,9 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # D9: 3,4 => CTR => D9: 1,9 * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # H7: 5,6 => SOL * DIS # H7: 7 => CTR => H7: 5,6 * PRF # H7: 6,7 => SOL * DIS # H7: 5 => CTR => H7: 6,7 * DIS # I2: 2,4,8 => CTR => I2: 6,7 * CNT 29 HDP CHAINS / 67 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,C5,C8,D5,E2,E3,E4,E7,E9,F3,G2,G3,H4,H8,I9) * .6..5.1...35.......476...954.62......9..6351.....8.6........4.3.8..729.15.....28. * PAIR E2: 2,4 ROW 2 H2: 2,4,6,7 # reduction candidate for 2,4 H2: 2,4 => CTR * .6.35.1...3514.826147628395456291738.9..6351232158.6.9...81546368..7295151.936287 * PAIR RESTART * PAIR F3: 1,8 BLK 2 D2: 1,8,7,9 # reduction candidate for 1,8 D2: 1,8 # 21 pairs F2: 1,8,7,9 # reduction candidate for 1,8 F2: 1,8 # 20 pairs * PAIR F3: 1,8 COL F F7: 1,8,5,6,9 # reduction candidate for 1,8 F7: 1,8 => CTR * .6.357142235.4.8761476283954562..738.92763514.71584629729...4.3.8..729.151..36287 * PAIR RESTART * PAIR F3: 1,8 BLK 2 F2: 1,8,7,9 # reduction candidate for 1,8 F2: 1,8 # 20 pairs F2: 7,9 # 18 pairs * PAIR G2: 7,8 BLK 3 I1: 7,8,2,4 # reduction candidate for 7,8 I1: 7,8 => CTR * .6.35.14..35.4..62.4762.3954.62...3..9..6351.....8.62..2.8.64.3.8..729.15...3.286 I2: 7,8,6 # reduction candidate for 7,8 I2: 7,8 => CTR * .6.3571..235.4..6.1476283954.62...3..9..6351.....8.6.....8..4736834729.15...3.28. I2: 6 => SOLVED * 968357142235149876147628395456291738892763514371584629729815463683472951514936287 * DURATION: 0:00:06.520749 START: 22:47:42.836449 END: 22:47:49.357198 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060430-absurd-base-pr-001.dot * REASONING * DIS # H2: 2,4 => CTR => H2: 6,7 * DIS H2: 6,7 # F7: 1,8 => CTR => F7: 5,6,9 * DIS H2: 6,7 + F7: 5,6,9 # I1: 7,8 => CTR => I1: 2,4 * DIS H2: 6,7 + F7: 5,6,9 + I1: 2,4 # I2: 7,8 => CTR => I2: 6 * PRF H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 => SOL * STA H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060430, absurd
Solution
position: 968357142235149876147628395456291738892763514371584629729815463683472951514936287 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # H2: 2,4 => CTR => H2: 6,7 * INC # H2: 6,7 => UNS * DIS # I2: 2,4 => CTR => I2: 6,7,8 * INC # I2: 6,7,8 => UNS * INC # D2: 1,8 => UNS * INC # F2: 1,8 => UNS * INC # A3: 1,8 => UNS * DIS # A3: 2 => CTR => A3: 1,8 * DIS # F7: 1,8 => CTR => F7: 5,6,9 * INC # F7: 5,6,9 => UNS * INC # I1: 7,8 => UNS * DIS # I2: 7,8 => CTR => I2: 2,4,6 * INC # I2: 2,4,6 => UNS * INC # D2: 7,8 => UNS * INC # F2: 7,8 => UNS * INC # G4: 7,8 => UNS * DIS # G4: 3 => CTR => G4: 7,8 * INC # G4: 3,8 => UNS * INC # G4: 7 => UNS * INC # A5: 2,8 => UNS * INC # A5: 7 => UNS * INC # C1: 2,8 => UNS * DIS # C1: 9 => CTR => C1: 2,8 * INC # F4: 1,9 => UNS * INC # D6: 1,9 => UNS * INC # F6: 1,9 => UNS * INC # D6: 4,7 => UNS * INC # F6: 4,7 => UNS * INC # I5: 4,7 => UNS * INC # I5: 2 => UNS * DIS # D1: 4,7 => CTR => D1: 3,8,9 * INC # D1: 3,8,9 => UNS * DIS # D2: 4,7 => CTR => D2: 1,8,9 * INC # D2: 1,8,9 => UNS * INC # G4: 3,7 => UNS * INC # G4: 8 => UNS * DIS # H1: 3,7 => CTR => H1: 2,4 * INC # H1: 2,4 => UNS * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # B7: 1,7 => CTR => B7: 2 * INC # B7: 2 => UNS * INC # B4: 1,7 => UNS * INC # B6: 1,7 => UNS * DIS # D7: 1,9 => CTR => D7: 5,8 * INC # D7: 5,8 => UNS * DIS # F7: 1,9 => CTR => F7: 5,6,8 * INC # F7: 5,6,8 => UNS * INC # D9: 1,9 => UNS * DIS # F9: 1,9 => CTR => F9: 4,6 * INC # F9: 4,6 => UNS * INC # C7: 1,9 => UNS * DIS # C7: 2 => CTR => C7: 1,9 * PRF # D8: 3,4 => SOL * DIS # D8: 5 => CTR => D8: 3,4 * DIS # D9: 3,4 => CTR => D9: 1,9 * INC # D9: 1,9 => UNS * PRF # C9: 3,4 => SOL * DIS # C9: 1,9 => CTR => C9: 3,4 * PRF # H7: 5,6 => SOL * DIS # H7: 7 => CTR => H7: 5,6 * PRF # H7: 6,7 => SOL * DIS # H7: 5 => CTR => H7: 6,7 * INC # I2: 6,7 => UNS * DIS # I2: 2,4,8 => CTR => I2: 6,7 * CNT 67 HDP CHAINS / 67 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H2: 2,4 => CTR => H2: 6,7 * INC H2: 6,7 # D2: 1,8 => UNS * INC H2: 6,7 # F2: 1,8 => UNS * DIS H2: 6,7 # F7: 1,8 => CTR => F7: 5,6,9 * INC H2: 6,7 + F7: 5,6,9 # F2: 1,8 => UNS * INC H2: 6,7 + F7: 5,6,9 # F2: 7,9 => UNS * DIS H2: 6,7 + F7: 5,6,9 # I1: 7,8 => CTR => I1: 2,4 * DIS H2: 6,7 + F7: 5,6,9 + I1: 2,4 # I2: 7,8 => CTR => I2: 6 * PRF H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 => SOL * STA H2: 6,7 + F7: 5,6,9 + I1: 2,4 + I2: 6 * CNT 9 HDP CHAINS / 8 HYP OPENED