Analysis of xx-top500-202-base.sdk
Contents
Original Sudoku
level: medium
position: .56...2.....47....3...1.....1.....6....6..8..7..........82.....2.......7.......1. initial
Autosolve
position: 1568..2749824761..34751269881..2.76..2.6.78.176.1...2..782.1..62.1.6..876..7...12 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * DIS # F4: 3,9 => CTR => F4: 4,5 * DIS # F6: 3,9 => CTR => F6: 4,5,8 * PRF # F9: 3,9 => SOL * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # H7: 3,5 => SOL * DIS # H7: 4 => CTR => H7: 3,5 * DIS # C5: 4,5 => CTR => C5: 3,9 * DIS # C6: 4,5 => CTR => C6: 3,9 * DIS # E5: 4,5 => CTR => E5: 3,9 * PRF # E5: 3,9 => SOL * PRF # H5: 4,5 => SOL * DIS # H5: 3 => CTR => H5: 4,5 * DIS # F4: 3,9 => CTR => F4: 4,5 * PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * DIS # F6: 3,9 => CTR => F6: 4,5,8 * DIS # C4: 3,9 => CTR => C4: 4,5 * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # G7: 4,5 => CTR => G7: 3,9 * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * PRF # F9: 3,9 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * PRF # G9: 4,5 => SOL * DIS # E9: 4,5 => CTR => E9: 3,8,9 * DIS # F9: 4,5 => CTR => F9: 3,8,9 * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * DIS # C5: 4,5 => CTR => C5: 3,9 * DIS # C6: 4,5 => CTR => C6: 3,9 * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * PRF # F9: 3,9 => SOL * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # E9: 4,5 => CTR => E9: 3,8,9 * DIS # F9: 4,5 => CTR => F9: 3,8,9 * DIS # F6: 4,5 => CTR => F6: 3,8,9 * DIS # G7: 4,5 => CTR => G7: 3,9 * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * DIS # G6: 4,5 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 56 HDP CHAINS / 86 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E5: 3,9 => SOL * STA E5: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .56...2.....47....3...1.....1.....6....6..8..7..........82.....2.......7.......1. | initial |
| 1568..2749824761..34751269881..2.76..2.6.78.176.1...2..782.1..62.1.6..876..7...12 | autosolve |
| 156839274982476153347512698814325769523697841769148325478251936231964587695783412 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) E1: 3,9 F1: 3,9 H2: 3,5 I2: 3,5 A5: 4,5 D4: 3,9 A7: 4,5 B8: 3,9 B9: 3,9 C9: 4,5 D8: 3,9 F8: 4,5 G8: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 3.. / E1 = 3 => 11 pairs (_) / F1 = 3 => 11 pairs (_) H2,I2: 3.. / H2 = 3 => 0 pairs (X) / I2 = 3 => 16 pairs (_) B8,B9: 3.. / B8 = 3 => 10 pairs (_) / B9 = 3 => 10 pairs (_) B8,D8: 3.. / B8 = 3 => 10 pairs (_) / D8 = 3 => 10 pairs (_) D4,D8: 3.. / D4 = 3 => 10 pairs (_) / D8 = 3 => 10 pairs (_) H5,G6: 4.. / H5 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) A7,C9: 4.. / A7 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) C4,F4: 4.. / C4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) F8,G8: 4.. / F8 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) A5,A7: 4.. / A5 = 4 => 0 pairs (X) / A7 = 4 => 0 pairs (_) H5,H7: 4.. / H5 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 16 pairs (_) / I2 = 5 => 0 pairs (X) A7,C9: 5.. / A7 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) F8,G8: 5.. / F8 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) A5,A7: 5.. / A5 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) E6,F6: 8.. / E6 = 8 => 13 pairs (_) / F6 = 8 => 13 pairs (_) E9,F9: 8.. / E9 = 8 => 13 pairs (_) / F9 = 8 => 13 pairs (_) E6,E9: 8.. / E6 = 8 => 13 pairs (_) / E9 = 8 => 13 pairs (_) F6,F9: 8.. / F6 = 8 => 13 pairs (_) / F9 = 8 => 13 pairs (_) E1,F1: 9.. / E1 = 9 => 11 pairs (_) / F1 = 9 => 11 pairs (_) I4,I6: 9.. / I4 = 9 => 16 pairs (_) / I6 = 9 => 14 pairs (_) B8,B9: 9.. / B8 = 9 => 10 pairs (_) / B9 = 9 => 10 pairs (_) G7,G9: 9.. / G7 = 9 => 13 pairs (_) / G9 = 9 => 0 pairs (X) C5,E5: 9.. / C5 = 9 => 13 pairs (_) / E5 = 9 => 0 pairs (*) E7,G7: 9.. / E7 = 9 => 0 pairs (X) / G7 = 9 => 13 pairs (_) B8,D8: 9.. / B8 = 9 => 10 pairs (_) / D8 = 9 => 10 pairs (_) D4,D8: 9.. / D4 = 9 => 10 pairs (_) / D8 = 9 => 10 pairs (_) * DURATION: 0:00:44.791235 START: 09:41:24.024127 END: 09:42:08.815362 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B8,B9,C9,D4,D8,E1,F1,F8,G8,H2,I2) * 1568..2749824761..34751269881..2.76..2.6.78.176.1...2..782.1..62.1.6..876..7...12 * PAIR E1: 3,9 COL E E5: 3,9,4,5 # reduction candidate for 3,9 E5: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E5: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E6: 3,9,4,5,8 # reduction candidate for 3,9 E6: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1.842..782.1..62.1.6..876..78..12 E6: 4,5,8 # 13 pairs E7: 3,9,4,5 # reduction candidate for 3,9 E7: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E7: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E9: 3,9,4,5,8 # reduction candidate for 3,9 E9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.78.176.18..2..782.1..62.1.6..876..7.8.12 E9: 4,5,8 # 13 pairs * PAIR F1: 3,9 COL F F4: 3,9,4,5 # reduction candidate for 3,9 F4: 3,9 => CTR * 1568..274982476153347512698814.2.7655296.78417631...294782.1..62.1.6..876.57...12 F4: 4,5 # 14 pairs F6: 3,9,4,5,8 # reduction candidate for 3,9 F6: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.18.42..782.1.462.1.645876.4758.12 F6: 4,5,8 # 13 pairs F9: 3,9,4,5,8 # reduction candidate for 3,9 F9: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 F9: 4,5,8 # 13 pairs * PAIR H2: 3,5 COL H H5: 3,5,4 # reduction candidate for 3,5 H5: 3,5 => CTR * 1568..2749824761..34751269881..2.76..2.6.78.176.1..42..782.1.462.1.645876.47...12 H5: 4 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 H7: 3,5,4 # reduction candidate for 3,5 H7: 3,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 H7: 4 => CTR * 1568..2749824761..34751269881..2.76..2.6.78.176.1...2..782.1.462.1.645876.47...12 * PAIR I2: 3,5 COL I I4: 3,5,9 # reduction candidate for 3,5 I4: 3,5 # 14 pairs I6: 3,5,9 # reduction candidate for 3,5 I6: 3,5 # 16 pairs * PAIR A5: 4,5 BLK 4 C4: 4,5,3,9 # reduction candidate for 4,5 C4: 4,5 # 16 pairs C5: 4,5,3,9 # reduction candidate for 4,5 C5: 4,5 => CTR * 1568..2749824761..34751269881..2.76..2.69783176.1..42..782.19462.19645876947..312 C5: 3,9 # 14 pairs C6: 4,5,3,9 # reduction candidate for 4,5 C6: 4,5 => CTR * 1568..27498247615334751269881..24765.2.6.78417641583294782.15362.1.654876.57...12 C6: 3,9 # 14 pairs * PAIR A5: 4,5 ROW 5 E5: 4,5,3,9 # reduction candidate for 4,5 E5: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E5: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 H5: 4,5,3 # reduction candidate for 4,5 H5: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 H5: 3 => CTR * 1568..2749824761..34751269881..2.76..2.6.783176.1..42..782.1.462.1.645876.47...12 * PAIR D4: 3,9 BLK 5 F4: 3,9,4,5 # reduction candidate for 3,9 F4: 3,9 => CTR * 1568..274982476153347512698814.2.7655296.78417631...294782.1..62.1.6..876.57...12 F4: 4,5 # 14 pairs E5: 3,9,4,5 # reduction candidate for 3,9 E5: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E5: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E6: 3,9,4,5,8 # reduction candidate for 3,9 E6: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1.842..782.1..62.1.6..876..78..12 E6: 4,5,8 # 13 pairs F6: 3,9,4,5,8 # reduction candidate for 3,9 F6: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.18.42..782.1.462.1.645876.4758.12 F6: 4,5,8 # 13 pairs * PAIR D4: 3,9 ROW 4 C4: 3,9,4,5 # reduction candidate for 3,9 C4: 3,9 => CTR * 1568..27498247615334751269881..24765.2.6.78417641583294782.15362.1.654876.57...12 C4: 4,5 # 16 pairs I4: 3,9,5 # reduction candidate for 3,9 I4: 3,9 # 18 pairs * PAIR A7: 4,5 ROW 7 E7: 4,5,3,9 # reduction candidate for 4,5 E7: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E7: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 G7: 4,5,3,9 # reduction candidate for 4,5 G7: 4,5 => CTR * 15683927498247615334751269881.92.765.2.6.78.176.1...2..78291.3629136..8763.7..912 G7: 3,9 # 14 pairs H7: 4,5,3 # reduction candidate for 4,5 H7: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 H7: 3 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 * PAIR B9: 3,9 ROW 9 E9: 3,9,4,5,8 # reduction candidate for 3,9 E9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.78.176.18..2..782.1..62.1.6..876..7.8.12 E9: 4,5,8 # 13 pairs F9: 3,9,4,5,8 # reduction candidate for 3,9 F9: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 F9: 4,5,8 # 13 pairs G9: 3,9,4,5 # reduction candidate for 3,9 G9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 G9: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 * PAIR C9: 4,5 ROW 9 E9: 4,5,3,8,9 # reduction candidate for 4,5 E9: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.18.42..782.1.462.1.645876.4758.12 E9: 3,8,9 # 13 pairs F9: 4,5,3,8,9 # reduction candidate for 4,5 F9: 4,5 => CTR * 1568..2749824761..347512698814.2.7655296478317631584294782.1.562.1.6..876..78..12 F9: 3,8,9 # 13 pairs G9: 4,5,3,9 # reduction candidate for 4,5 G9: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 G9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 * PAIR C9: 4,5 COL C C4: 4,5,3,9 # reduction candidate for 4,5 C4: 4,5 # 16 pairs C5: 4,5,3,9 # reduction candidate for 4,5 C5: 4,5 => CTR * 1568..2749824761..34751269881..2.76..2.69783176.1..42..782.19462.19645876947..312 C5: 3,9 # 14 pairs C6: 4,5,3,9 # reduction candidate for 4,5 C6: 4,5 => CTR * 1568..27498247615334751269881..24765.2.6.78417641583294782.15362.1.654876.57...12 C6: 3,9 # 14 pairs * PAIR D8: 3,9 BLK 8 E7: 3,9,4,5 # reduction candidate for 3,9 E7: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E7: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E9: 3,9,4,5,8 # reduction candidate for 3,9 E9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.78.176.18..2..782.1..62.1.6..876..7.8.12 E9: 4,5,8 # 13 pairs F9: 3,9,4,5,8 # reduction candidate for 3,9 F9: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 F9: 4,5,8 # 13 pairs * PAIR F8: 4,5 BLK 8 E7: 4,5,3,9 # reduction candidate for 4,5 E7: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 E7: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 E9: 4,5,3,8,9 # reduction candidate for 4,5 E9: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.18.42..782.1.462.1.645876.4758.12 E9: 3,8,9 # 13 pairs F9: 4,5,3,8,9 # reduction candidate for 4,5 F9: 4,5 => CTR * 1568..2749824761..347512698814.2.7655296478317631584294782.1.562.1.6..876..78..12 F9: 3,8,9 # 13 pairs * PAIR F8: 4,5 COL F F4: 4,5,3,9 # reduction candidate for 4,5 F4: 4,5 # 14 pairs F6: 4,5,3,8,9 # reduction candidate for 4,5 F6: 4,5 => CTR * 1568..2749824761..347512698814.2.76552.6.78.176.1854294782.1..62.1.645876.57.8.12 F6: 3,8,9 # 13 pairs * PAIR G8: 4,5 BLK 9 G7: 4,5,3,9 # reduction candidate for 4,5 G7: 4,5 => CTR * 15683927498247615334751269881.92.765.2.6.78.176.1...2..78291.3629136..8763.7..912 G7: 3,9 # 14 pairs H7: 4,5,3 # reduction candidate for 4,5 H7: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 H7: 3 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 G9: 4,5,3,9 # reduction candidate for 4,5 G9: 4,5 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 G9: 3,9 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 * PAIR G8: 4,5 COL G G6: 4,5,3 # reduction candidate for 4,5 G6: 4,5 => CTR * 1568..2749824761..34751269881..2.76..296.783176.1..42..782.1.462.1.645876.47...12 G6: 3 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-202-base-pr-000.dot * REASONING * PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * DIS # F4: 3,9 => CTR => F4: 4,5 * DIS # F6: 3,9 => CTR => F6: 4,5,8 * PRF # F9: 3,9 => SOL * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # H7: 3,5 => SOL * DIS # H7: 4 => CTR => H7: 3,5 * DIS # C5: 4,5 => CTR => C5: 3,9 * DIS # C6: 4,5 => CTR => C6: 3,9 * DIS # E5: 4,5 => CTR => E5: 3,9 * PRF # E5: 3,9 => SOL * PRF # H5: 4,5 => SOL * DIS # H5: 3 => CTR => H5: 4,5 * DIS # F4: 3,9 => CTR => F4: 4,5 * PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * DIS # F6: 3,9 => CTR => F6: 4,5,8 * DIS # C4: 3,9 => CTR => C4: 4,5 * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # G7: 4,5 => CTR => G7: 3,9 * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * PRF # F9: 3,9 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * PRF # G9: 4,5 => SOL * DIS # E9: 4,5 => CTR => E9: 3,8,9 * DIS # F9: 4,5 => CTR => F9: 3,8,9 * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * DIS # C5: 4,5 => CTR => C5: 3,9 * DIS # C6: 4,5 => CTR => C6: 3,9 * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * PRF # F9: 3,9 => SOL * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # E9: 4,5 => CTR => E9: 3,8,9 * DIS # F9: 4,5 => CTR => F9: 3,8,9 * DIS # F6: 4,5 => CTR => F6: 3,8,9 * DIS # G7: 4,5 => CTR => G7: 3,9 * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * DIS # G6: 4,5 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 56 HDP CHAINS / 86 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B8,B9,C9,D4,D8,E1,F1,F8,G8,H2,I2) * 1568..2749824761..34751269881..2.76..2.6.78.176.1...2..782.1..62.1.6..876..7...12 * PAIR E1: 3,9 COL E E5: 3,9,4,5 # reduction candidate for 3,9 E5: 3,9 => SOLVED * 156839274982476153347512698814325769523697841769148325478251936231964587695783412 * DURATION: 0:00:02.158482 START: 09:43:33.671104 END: 09:43:35.829586 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-202-base-pr-001.dot * REASONING * PRF # E5: 3,9 => SOL * STA E5: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 202 solution: 156839274982476153347512698814325769523697841769148325478251936231964587695783412 info: 1891 FNBTHWX S8.f 42691 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 156839274982476153347512698814325769523697841769148325478251936231964587695783412 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:
* PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * INC # E6: 4,5,8 => UNS * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * INC # E9: 4,5,8 => UNS * DIS # F4: 3,9 => CTR => F4: 4,5 * INC # F4: 4,5 => UNS * DIS # F6: 3,9 => CTR => F6: 4,5,8 * INC # F6: 4,5,8 => UNS * PRF # F9: 3,9 => SOL * INC # F9: 4,5,8 => UNS * DIS # H5: 3,5 => CTR => H5: 4 * PRF # H5: 4 => SOL * PRF # H7: 3,5 => SOL * DIS # H7: 4 => CTR => H7: 3,5 * INC # I4: 3,5 => UNS * INC # I6: 3,5 => UNS * INC # C4: 4,5 => UNS * DIS # C5: 4,5 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * DIS # C6: 4,5 => CTR => C6: 3,9 * INC # C6: 3,9 => UNS * DIS # E5: 4,5 => CTR => E5: 3,9 * PRF # E5: 3,9 => SOL * PRF # H5: 4,5 => SOL * DIS # H5: 3 => CTR => H5: 4,5 * DIS # F4: 3,9 => CTR => F4: 4,5 * INC # F4: 4,5 => UNS * PRF # E5: 3,9 => SOL * DIS # E5: 4,5 => CTR => E5: 3,9 * DIS # E6: 3,9 => CTR => E6: 4,5,8 * INC # E6: 4,5,8 => UNS * DIS # F6: 3,9 => CTR => F6: 4,5,8 * INC # F6: 4,5,8 => UNS * DIS # C4: 3,9 => CTR => C4: 4,5 * INC # C4: 4,5 => UNS * INC # I4: 3,9 => UNS * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # G7: 4,5 => CTR => G7: 3,9 * INC # G7: 3,9 => UNS * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * INC # E9: 4,5,8 => UNS * PRF # F9: 3,9 => SOL * INC # F9: 4,5,8 => UNS * DIS # G9: 3,9 => CTR => G9: 4,5 * PRF # G9: 4,5 => SOL * DIS # E9: 4,5 => CTR => E9: 3,8,9 * INC # E9: 3,8,9 => UNS * DIS # F9: 4,5 => CTR => F9: 3,8,9 * INC # F9: 3,8,9 => UNS * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * INC # C4: 4,5 => UNS * DIS # C5: 4,5 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * DIS # C6: 4,5 => CTR => C6: 3,9 * INC # C6: 3,9 => UNS * DIS # E7: 3,9 => CTR => E7: 4,5 * PRF # E7: 4,5 => SOL * DIS # E9: 3,9 => CTR => E9: 4,5,8 * INC # E9: 4,5,8 => UNS * PRF # F9: 3,9 => SOL * INC # F9: 4,5,8 => UNS * PRF # E7: 4,5 => SOL * DIS # E7: 3,9 => CTR => E7: 4,5 * DIS # E9: 4,5 => CTR => E9: 3,8,9 * INC # E9: 3,8,9 => UNS * DIS # F9: 4,5 => CTR => F9: 3,8,9 * INC # F9: 3,8,9 => UNS * INC # F4: 4,5 => UNS * DIS # F6: 4,5 => CTR => F6: 3,8,9 * INC # F6: 3,8,9 => UNS * DIS # G7: 4,5 => CTR => G7: 3,9 * INC # G7: 3,9 => UNS * DIS # H7: 4,5 => CTR => H7: 3 * PRF # H7: 3 => SOL * PRF # G9: 4,5 => SOL * DIS # G9: 3,9 => CTR => G9: 4,5 * DIS # G6: 4,5 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 86 HDP CHAINS / 86 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E5: 3,9 => SOL * STA E5: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED