Analysis of zz-www.sudokuoftheday.co.uk-20190317-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 6..8.......5..28.9.39..1..7...........8.....33...25.6.1..5.....2...1..7..7..3...4 initial
Autosolve
position: 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 1,4 => CTR => B1: 2 * PRF # B1: 2 => SOL * PRF # H2: 3 => SOL * DIS # B4: 1,4 => CTR => B4: 2,5,6,9 * DIS # B5: 1,4 => CTR => B5: 2,5,6,9 * PRF # B6: 1,4 => SOL * DIS # B6: 9 => CTR => B6: 1,4 * PRF # F1: 3 => SOL * DIS # E4: 7,9 => CTR => E4: 4,6,8 * DIS # E5: 7,9 => CTR => E5: 4,6 * PRF # D2: 6,7 => SOL * DIS # E4: 6,7 => CTR => E4: 4,8,9 * DIS # E5: 6,7 => CTR => E5: 4,9 * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # C4: 1,7 => CTR => C4: 2 * PRF # C4: 2 => SOL * DIS # G6: 1,7 => CTR => G6: 4,9 * PRF # C1: 1,7 => SOL * DIS # C1: 2 => CTR => C1: 1,7 * PRF # B8: 8,9 => SOL * DIS # B8: 5 => CTR => B8: 8,9 * DIS # E7: 8,9 => CTR => E7: 4,6,7 * DIS # F7: 8,9 => CTR => F7: 4,6,7 * DIS # B8: 5,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * DIS # G9: 5,9 => CTR => G9: 1 * PRF # H9: 5,9 => SOL * PRF # E7: 6,9 => SOL * DIS # F7: 6,9 => CTR => F7: 4,7,8 * DIS # F8: 6,9 => CTR => F8: 4,8 * DIS # D4: 6,9 => CTR => D4: 1,3,7 * DIS # E7: 8,9 => CTR => E7: 4,6,7 * DIS # F7: 8,9 => CTR => F7: 4,6,7 * DIS # F8: 8,9 => CTR => F8: 4,6 * PRF # F8: 4,6 => SOL * PRF # H9: 8,9 => SOL * DIS # H9: 1,5 => CTR => H9: 8,9 * DIS # F4: 8,9 => CTR => F4: 3,4,6,7 * CNT 39 HDP CHAINS / 71 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 1,4 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..8.......5..28.9.39..1..7...........8.....33...25.6.1..5.....2...1..7..7..3...4 | initial |
| 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 | autosolve |
| 627893415415672839839451627952386741768149253341725968194567382283914576576238194 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 4,7 B2: 1,4 E1: 7,9 E2: 6,7 I1: 1,5 C6: 1,7 B7: 8,9 C7: 3,4 C8: 3,4 A9: 5,9 D8: 6,9 F9: 8,9 I7: 2,6 I8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G9,H9: 1.. / G9 = 1 => 14 pairs (_) / H9 = 1 => 0 pairs (X) B2,H2: 1.. / B2 = 1 => 17 pairs (_) / H2 = 1 => 0 pairs (X) I1,I4: 1.. / I1 = 1 => 17 pairs (_) / I4 = 1 => 0 pairs (*) B1,C1: 2.. / B1 = 2 => 0 pairs (*) / C1 = 2 => 0 pairs (X) G7,I7: 2.. / G7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B5,G5: 2.. / B5 = 2 => 0 pairs (X) / G5 = 2 => 0 pairs (_) C1,C4: 2.. / C1 = 2 => 0 pairs (X) / C4 = 2 => 0 pairs (_) I4,I7: 2.. / I4 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) F1,D2: 3.. / F1 = 3 => 0 pairs (*) / D2 = 3 => 0 pairs (X) D4,F4: 3.. / D4 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) C7,C8: 3.. / C7 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) D2,H2: 3.. / D2 = 3 => 18 pairs (_) / H2 = 3 => 0 pairs (*) C8,G8: 3.. / C8 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) D2,D4: 3.. / D2 = 3 => 18 pairs (_) / D4 = 3 => 0 pairs (*) F1,F4: 3.. / F1 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) C7,C8: 4.. / C7 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) B6,G6: 4.. / B6 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) C8,F8: 4.. / C8 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) B8,A9: 5.. / B8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) D2,E2: 6.. / D2 = 6 => 0 pairs (*) / E2 = 6 => 0 pairs (X) B4,B5: 6.. / B4 = 6 => 14 pairs (_) / B5 = 6 => 0 pairs (*) I7,I8: 6.. / I7 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) C1,A2: 7.. / C1 = 7 => 0 pairs (*) / A2 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 14 pairs (_) / F7 = 7 => 15 pairs (_) E4,F4: 8.. / E4 = 8 => 14 pairs (_) / F4 = 8 => 0 pairs (X) B7,B8: 8.. / B7 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) H7,H9: 8.. / H7 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) B8,F8: 8.. / B8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) F9,H9: 8.. / F9 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) E4,E7: 8.. / E4 = 8 => 14 pairs (_) / E7 = 8 => 0 pairs (X) E1,F1: 9.. / E1 = 9 => 14 pairs (_) / F1 = 9 => 0 pairs (X) * DURATION: 0:00:34.801467 START: 04:35:41.490625 END: 04:36:16.292092 2019-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C6,C7,C8,D8,E1,E2,F9,I1,I7,I8) * 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 * PAIR A2: 4,7 COL A A4: 4,7,5,9 # reduction candidate for 4,7 A4: 4,7 # 16 pairs A5: 4,7,5,9 # reduction candidate for 4,7 A5: 4,7 # 16 pairs * PAIR B2: 1,4 BLK 1 B1: 1,4,2 # reduction candidate for 1,4 B1: 1,4 => CTR * 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4 B1: 2 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 * PAIR B2: 1,4 ROW 2 H2: 1,4,3 # reduction candidate for 1,4 H2: 3 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 H2: 1,4 # 18 pairs * PAIR B2: 1,4 COL B B4: 1,4,2,5,6,9 # reduction candidate for 1,4 B4: 1,4 => CTR * 6..8.......5..28.9839451627..........68...2.33...25.681..5....225..18.7697623...4 B4: 2,5,6,9 # 14 pairs B5: 1,4,2,5,6,9 # reduction candidate for 1,4 B5: 1,4 => CTR * 6..8.......5..28.9839451627.62........8...2.33...25.681..5....225..18.7697623...4 B5: 2,5,6,9 # 14 pairs B6: 1,4,9 # reduction candidate for 1,4 B6: 1,4 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 B6: 9 => CTR * 6..8.......5..28.9839451627...........8.....339..2546818.5.....25..18.7697623...4 * PAIR E1: 7,9 BLK 2 F1: 7,9,3 # reduction candidate for 7,9 F1: 3 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 F1: 7,9 # 18 pairs * PAIR E1: 7,9 COL E E4: 7,9,4,6,8 # reduction candidate for 7,9 E4: 7,9 => CTR * 6..893..1.15..2839839451627...378..2.28.46..33...25.6819.587..628..14.75576239184 E4: 4,6,8 # 14 pairs E5: 7,9,4,6 # reduction candidate for 7,9 E5: 7,9 => CTR * 6..8....1.15.628.9839451627........2.28.....33...25.681..5.72.62...1..7557623...4 E5: 4,6 # 15 pairs E7: 7,9,4,6,8 # reduction candidate for 7,9 E7: 7,9 # 15 pairs * PAIR E2: 6,7 BLK 2 D2: 6,7,3 # reduction candidate for 6,7 D2: 6,7 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 D2: 3 # 18 pairs * PAIR E2: 6,7 COL E E4: 6,7,4,8,9 # reduction candidate for 6,7 E4: 6,7 => CTR * 6..893..1.15..2839839451627...3.8..2.28.46..33...25.6819.587..628..14.75576239184 E4: 4,8,9 # 14 pairs E5: 6,7,4,9 # reduction candidate for 6,7 E5: 6,7 => CTR * 6.7893..1415..2839839451627..2........8.....33...25.681..5.7..62...1..7557623...4 E5: 4,9 # 15 pairs E7: 6,7,4,8,9 # reduction candidate for 6,7 E7: 6,7 # 15 pairs * PAIR I1: 1,5 BLK 3 G1: 1,5,3,4 # reduction candidate for 1,5 G1: 1,5 # 21 pairs H1: 1,5,3,4 # reduction candidate for 1,5 H1: 1,5 # 19 pairs * PAIR I1: 1,5 COL I I4: 1,5,2 # reduction candidate for 1,5 I4: 1,5 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 I4: 2 => CTR * 6..8....1.15..28.9839451627........2.28.....33...25.681..5..2.62...1..7557623...4 * PAIR C6: 1,7 BLK 4 C4: 1,7,2 # reduction candidate for 1,7 C4: 1,7 => CTR * 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4 C4: 2 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 * PAIR C6: 1,7 ROW 6 D6: 1,7,9 # reduction candidate for 1,7 D6: 1,7 # 17 pairs G6: 1,7,4,9 # reduction candidate for 1,7 G6: 1,7 => CTR * 6..8....1415.62839839451627...3....2.28.....334.925.681..5.....2..61..7557623...4 G6: 4,9 # 15 pairs * PAIR C6: 1,7 COL C C1: 1,7,2 # reduction candidate for 1,7 C1: 1,7 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 C1: 2 => CTR * 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4 * PAIR B7: 8,9 BLK 7 B8: 8,9,5 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 B8: 5 => CTR * 6..8.......5..28.9839451627...........8.....33...25.6818.5.....25..18.7697623...4 * PAIR B7: 8,9 ROW 7 E7: 8,9,4,6,7 # reduction candidate for 8,9 E7: 8,9 => CTR * 6..8....1.15..28.9839451627........2.28.....33...25.681.45.723628..14.7557623...4 E7: 4,6,7 # 14 pairs F7: 8,9,4,6,7 # reduction candidate for 8,9 F7: 8,9 => CTR * 6..89...1.15.628.9839451627....8...2.28.4...33...25.681.457.23628..14.7557623...4 F7: 4,6,7 # 14 pairs H7: 8,9,3 # reduction candidate for 8,9 H7: 8,9 # 16 pairs * PAIR A9: 5,9 BLK 7 B8: 5,9,8 # reduction candidate for 5,9 B8: 5,9 => CTR * 6..89...1.15.628.9839451627....8...2.28..6..334..25.6818.5.....294618375576239184 B8: 8 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 * PAIR A9: 5,9 ROW 9 G9: 5,9,1 # reduction candidate for 5,9 G9: 5,9 => CTR * 627893..1415762839839451627..2.8......8.....334.925.6819.5...8.28.619.75576238914 G9: 1 # 14 pairs H9: 5,9,1,8 # reduction candidate for 5,9 H9: 5,9 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 H9: 1,8 # 15 pairs * PAIR A9: 5,9 COL A A4: 5,9,4,7 # reduction candidate for 5,9 A4: 5,9 # 16 pairs A5: 5,9,4,7 # reduction candidate for 5,9 A5: 5,9 # 16 pairs * PAIR D8: 6,9 BLK 8 E7: 6,9,4,7,8 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 E7: 4,7,8 # 14 pairs F7: 6,9,4,7,8 # reduction candidate for 6,9 F7: 6,9 => CTR * 6..89.4..415762839839451627...38..4...864..13347125968194576382283914576576238194 F7: 4,7,8 # 14 pairs F8: 6,9,4,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 6..8....1.15..28.9839451627........2.28.....33...25.6819.5.....284.1.37557623...4 F8: 4,8 # 15 pairs * PAIR D8: 6,9 COL D D4: 6,9,1,3,7 # reduction candidate for 6,9 D4: 6,9 => CTR * 6..8.....7.53628.98394516274...83...5.8.....339..2546818.5.....25..18.7697623...4 D4: 1,3,7 # 14 pairs D5: 6,9,1,7 # reduction candidate for 6,9 D5: 6,9 # 18 pairs * PAIR F9: 8,9 BLK 8 E7: 8,9,4,6,7 # reduction candidate for 8,9 E7: 8,9 => CTR * 6..8....1.15..28.9839451627........2.28.....33...25.681.45.723628..14.7557623...4 E7: 4,6,7 # 14 pairs F7: 8,9,4,6,7 # reduction candidate for 8,9 F7: 8,9 => CTR * 6..89...1.15.628.9839451627....8...2.28.4...33...25.681.457.23628..14.7557623...4 F7: 4,6,7 # 14 pairs F8: 8,9,4,6 # reduction candidate for 8,9 F8: 8,9 => CTR * 6..89...1.15.628.9839451627....8...2.28..6..33...25.681.35..2.62.461.37557623...4 F8: 4,6 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 * PAIR F9: 8,9 ROW 9 H9: 8,9,1,5 # reduction candidate for 8,9 H9: 8,9 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 H9: 1,5 => CTR * 627893..1415762839839451627..2.8......8.....334.925.6819.5...8.28.619.75576238914 * PAIR F9: 8,9 COL F F4: 8,9,3,4,6,7 # reduction candidate for 8,9 F4: 8,9 => CTR * 627893...415672839839451627..2389.....81..2.33.1725.681..5.7.8228.914576576238..4 F4: 3,4,6,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190317-absurd-base-pr-000.dot * REASONING * DIS # B1: 1,4 => CTR => B1: 2 * PRF # B1: 2 => SOL * PRF # H2: 3 => SOL * DIS # B4: 1,4 => CTR => B4: 2,5,6,9 * DIS # B5: 1,4 => CTR => B5: 2,5,6,9 * PRF # B6: 1,4 => SOL * DIS # B6: 9 => CTR => B6: 1,4 * PRF # F1: 3 => SOL * DIS # E4: 7,9 => CTR => E4: 4,6,8 * DIS # E5: 7,9 => CTR => E5: 4,6 * PRF # D2: 6,7 => SOL * DIS # E4: 6,7 => CTR => E4: 4,8,9 * DIS # E5: 6,7 => CTR => E5: 4,9 * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # C4: 1,7 => CTR => C4: 2 * PRF # C4: 2 => SOL * DIS # G6: 1,7 => CTR => G6: 4,9 * PRF # C1: 1,7 => SOL * DIS # C1: 2 => CTR => C1: 1,7 * PRF # B8: 8,9 => SOL * DIS # B8: 5 => CTR => B8: 8,9 * DIS # E7: 8,9 => CTR => E7: 4,6,7 * DIS # F7: 8,9 => CTR => F7: 4,6,7 * DIS # B8: 5,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * DIS # G9: 5,9 => CTR => G9: 1 * PRF # H9: 5,9 => SOL * PRF # E7: 6,9 => SOL * DIS # F7: 6,9 => CTR => F7: 4,7,8 * DIS # F8: 6,9 => CTR => F8: 4,8 * DIS # D4: 6,9 => CTR => D4: 1,3,7 * DIS # E7: 8,9 => CTR => E7: 4,6,7 * DIS # F7: 8,9 => CTR => F7: 4,6,7 * DIS # F8: 8,9 => CTR => F8: 4,6 * PRF # F8: 4,6 => SOL * PRF # H9: 8,9 => SOL * DIS # H9: 1,5 => CTR => H9: 8,9 * DIS # F4: 8,9 => CTR => F4: 3,4,6,7 * CNT 39 HDP CHAINS / 71 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,B7,C6,C7,C8,D8,E1,E2,F9,I1,I7,I8) * 6..8.......5..28.9839451627...........8.....33...25.681..5.....2...1..7..7623...4 * PAIR A2: 4,7 COL A A4: 4,7,5,9 # reduction candidate for 4,7 A4: 4,7 # 16 pairs A5: 4,7,5,9 # reduction candidate for 4,7 A5: 4,7 # 16 pairs * PAIR B2: 1,4 BLK 1 B1: 1,4,2 # reduction candidate for 1,4 B1: 1,4 => CTR * 6.28.....7.53628.98394516274...83.....8.....339..2546818.5.....25..18.7697623...4 B1: 2 => SOLVED * 627893415415672839839451627952386741768149253341725968194567382283914576576238194 * DURATION: 0:00:03.280911 START: 04:36:57.533860 END: 04:37:00.814771 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190317-absurd-base-pr-001.dot * REASONING * DIS # B1: 1,4 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190317, absurd
Solution
position: 627893415415672839839451627952386741768149253341725968194567382283914576576238194 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:
* INC # A4: 4,7 => UNS * INC # A5: 4,7 => UNS * DIS # B1: 1,4 => CTR => B1: 2 * PRF # B1: 2 => SOL * INC # H2: 1,4 => UNS * PRF # H2: 3 => SOL * DIS # B4: 1,4 => CTR => B4: 2,5,6,9 * INC # B4: 2,5,6,9 => UNS * DIS # B5: 1,4 => CTR => B5: 2,5,6,9 * INC # B5: 2,5,6,9 => UNS * PRF # B6: 1,4 => SOL * DIS # B6: 9 => CTR => B6: 1,4 * INC # F1: 7,9 => UNS * PRF # F1: 3 => SOL * DIS # E4: 7,9 => CTR => E4: 4,6,8 * INC # E4: 4,6,8 => UNS * DIS # E5: 7,9 => CTR => E5: 4,6 * INC # E5: 4,6 => UNS * INC # E7: 7,9 => UNS * PRF # D2: 6,7 => SOL * INC # D2: 3 => UNS * DIS # E4: 6,7 => CTR => E4: 4,8,9 * INC # E4: 4,8,9 => UNS * DIS # E5: 6,7 => CTR => E5: 4,9 * INC # E5: 4,9 => UNS * INC # E7: 6,7 => UNS * INC # G1: 1,5 => UNS * INC # H1: 1,5 => UNS * PRF # I4: 1,5 => SOL * DIS # I4: 2 => CTR => I4: 1,5 * DIS # C4: 1,7 => CTR => C4: 2 * PRF # C4: 2 => SOL * INC # D6: 1,7 => UNS * DIS # G6: 1,7 => CTR => G6: 4,9 * INC # G6: 4,9 => UNS * PRF # C1: 1,7 => SOL * DIS # C1: 2 => CTR => C1: 1,7 * PRF # B8: 8,9 => SOL * DIS # B8: 5 => CTR => B8: 8,9 * DIS # E7: 8,9 => CTR => E7: 4,6,7 * INC # E7: 4,6,7 => UNS * DIS # F7: 8,9 => CTR => F7: 4,6,7 * INC # F7: 4,6,7 => UNS * INC # H7: 8,9 => UNS * DIS # B8: 5,9 => CTR => B8: 8 * PRF # B8: 8 => SOL * DIS # G9: 5,9 => CTR => G9: 1 * INC # G9: 1 => UNS * PRF # H9: 5,9 => SOL * INC # H9: 1,8 => UNS * INC # A4: 5,9 => UNS * INC # A5: 5,9 => UNS * PRF # E7: 6,9 => SOL * INC # E7: 4,7,8 => UNS * DIS # F7: 6,9 => CTR => F7: 4,7,8 * INC # F7: 4,7,8 => UNS * DIS # F8: 6,9 => CTR => F8: 4,8 * INC # F8: 4,8 => UNS * DIS # D4: 6,9 => CTR => D4: 1,3,7 * INC # D4: 1,3,7 => UNS * INC # D5: 6,9 => UNS * DIS # E7: 8,9 => CTR => E7: 4,6,7 * INC # E7: 4,6,7 => UNS * DIS # F7: 8,9 => CTR => F7: 4,6,7 * INC # F7: 4,6,7 => UNS * DIS # F8: 8,9 => CTR => F8: 4,6 * PRF # F8: 4,6 => SOL * PRF # H9: 8,9 => SOL * DIS # H9: 1,5 => CTR => H9: 8,9 * DIS # F4: 8,9 => CTR => F4: 3,4,6,7 * INC # F4: 3,4,6,7 => UNS * CNT 71 HDP CHAINS / 71 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 4,7 => UNS * INC # A5: 4,7 => UNS * DIS # B1: 1,4 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 4 HDP CHAINS / 3 HYP OPENED