Analysis of zz-www.sudokuoftheday.co.uk-20190131-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .3.2..9.52.7.......8...3.......2..9.....59.74.9.8.62....56...1.6.3..5.274........ initial
Autosolve
position: 13.2..9.52.7.......8...37.2....2..9..62.59.74.9.8.62....56...1.613..5.274........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * DIS # H1: 4,6 => CTR => H1: 8 * DIS # D2: 9 => CTR => D2: 4,5 * DIS # E2: 4,8 => CTR => E2: 6,9 * DIS # H2: 4,8 => CTR => H2: 3,6 * DIS # F7: 4,8 => CTR => F7: 2,7 * DIS # H1: 4,6 => CTR => H1: 8 * DIS # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * PRF # E3: 4,6 => SOL * PRF # A4: 3,8 => SOL * PRF # G5: 1 => SOL * PRF # C4: 1,4 => SOL * DIS # C4: 8 => CTR => C4: 1,4 * DIS # E6: 3,7 => CTR => E6: 1,4 * PRF # E6: 1,3 => SOL * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * DIS # G4: 3,5 => CTR => G4: 1,6,8 * DIS # A6: 3,5 => CTR => A6: 7 * DIS # G4: 1,3 => CTR => G4: 5,6,8 * DIS # I4: 1,3 => CTR => I4: 6,8 * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * PRF # E6: 1,3 => SOL * DIS # I7: 3 => CTR => I7: 8,9 * DIS # F7: 4,8 => CTR => F7: 2,7 * DIS # F9: 2,7 => CTR => F9: 1,8 * DIS # I9: 3,6 => CTR => I9: 8,9 * DIS # E8: 4,9 => CTR => E8: 8 * DIS # D2: 4,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * DIS # G7: 4,8 => CTR => G7: 3 * DIS # E8: 9 => CTR => E8: 4,8 * CNT 35 HDP CHAINS / 69 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 4,6 => CTR => C3: 9 * PRF C3: 9 => SOL * STA C3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.2..9.52.7.......8...3.......2..9.....59.74.9.8.62....56...1.6.3..5.274........ | initial |
| 13.2..9.52.7.......8...37.2....2..9..62.59.74.9.8.62....56...1.613..5.274........ | autosolve |
| 136274985247598631589163742351427896862359174794816253975642318613985427428731569 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 4,6 B2: 4,5 A3: 5,9 F2: 4,8 H3: 4,6 B4: 4,5 A5: 3,8 C6: 1,4 D5: 1,3 H6: 3,5 I6: 1,3 A7: 8,9 B7: 2,7 B9: 2,7 C9: 8,9 D8: 4,9 G8: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 1.. / D3 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) G2,I2: 1.. / G2 = 1 => 21 pairs (_) / I2 = 1 => 21 pairs (_) C4,C6: 1.. / C4 = 1 => 0 pairs (*) / C6 = 1 => 0 pairs (X) D5,G5: 1.. / D5 = 1 => 21 pairs (_) / G5 = 1 => 0 pairs (*) F4,F9: 1.. / F4 = 1 => 0 pairs (X) / F9 = 1 => 17 pairs (_) B7,B9: 2.. / B7 = 2 => 0 pairs (X) / B9 = 2 => 15 pairs (_) F7,F9: 2.. / F7 = 2 => 15 pairs (_) / F9 = 2 => 0 pairs (X) B7,F7: 2.. / B7 = 2 => 0 pairs (X) / F7 = 2 => 15 pairs (_) B9,F9: 2.. / B9 = 2 => 15 pairs (_) / F9 = 2 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 0 pairs (X) / G8 = 4 => 22 pairs (_) C6,E6: 4.. / C6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) B2,B4: 4.. / B2 = 4 => 0 pairs (*) / B4 = 4 => 0 pairs (X) B2,A3: 5.. / B2 = 5 => 0 pairs (X) / A3 = 5 => 0 pairs (_) D2,D3: 5.. / D2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) G4,H6: 5.. / G4 = 5 => 0 pairs (X) / H6 = 5 => 17 pairs (_) G9,H9: 5.. / G9 = 5 => 17 pairs (_) / H9 = 5 => 0 pairs (X) B2,D2: 5.. / B2 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) A3,D3: 5.. / A3 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) A6,H6: 5.. / A6 = 5 => 0 pairs (X) / H6 = 5 => 17 pairs (_) B2,B4: 5.. / B2 = 5 => 0 pairs (X) / B4 = 5 => 0 pairs (_) G4,G9: 5.. / G4 = 5 => 0 pairs (X) / G9 = 5 => 17 pairs (_) H6,H9: 5.. / H6 = 5 => 17 pairs (_) / H9 = 5 => 0 pairs (X) C1,C3: 6.. / C1 = 6 => 22 pairs (_) / C3 = 6 => 0 pairs (X) G4,I4: 6.. / G4 = 6 => 17 pairs (_) / I4 = 6 => 29 pairs (_) E1,F1: 7.. / E1 = 7 => 23 pairs (_) / F1 = 7 => 18 pairs (_) A4,A6: 7.. / A4 = 7 => 0 pairs (X) / A6 = 7 => 16 pairs (_) B7,B9: 7.. / B7 = 7 => 15 pairs (_) / B9 = 7 => 0 pairs (X) A6,E6: 7.. / A6 = 7 => 16 pairs (_) / E6 = 7 => 0 pairs (X) D4,D9: 7.. / D4 = 7 => 20 pairs (_) / D9 = 7 => 16 pairs (_) A7,C9: 8.. / A7 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) A5,G5: 8.. / A5 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) E8,G8: 8.. / E8 = 8 => 22 pairs (_) / G8 = 8 => 0 pairs (X) C4,C9: 8.. / C4 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) A3,C3: 9.. / A3 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) D2,E2: 9.. / D2 = 9 => 0 pairs (X) / E2 = 9 => 21 pairs (_) A7,C9: 9.. / A7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D8,E8: 9.. / D8 = 9 => 21 pairs (_) / E8 = 9 => 0 pairs (X) I7,I9: 9.. / I7 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) A7,I7: 9.. / A7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) C9,I9: 9.. / C9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) A3,A7: 9.. / A3 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) C3,C9: 9.. / C3 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D2,D8: 9.. / D2 = 9 => 0 pairs (X) / D8 = 9 => 21 pairs (_) E2,E8: 9.. / E2 = 9 => 21 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:52.257981 START: 03:21:16.945360 END: 03:22:09.203341 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B7,B9,C1,C6,C9,D5,D8,F2,G8,H3,H6,I6) * 13.2..9.52.7.......8...37.2....2..9..62.59.74.9.8.62....56...1.613..5.274........ * PAIR C1: 4,6 BLK 1 C3: 4,6,9 # reduction candidate for 4,6 C3: 4,6 => CTR * 13.2..9.5257......98.5137.2.48.2..9.362159874.918462.38.56...19613.854274.9..1... C3: 9 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 * PAIR C1: 4,6 ROW 1 E1: 4,6,7,8 # reduction candidate for 4,6 E1: 4,6 # 19 pairs H1: 4,6,8 # reduction candidate for 4,6 H1: 4,6 => CTR * 13.2..9.5257964.8198.5137.2.48.2..96362159.74.918462.3..56..41.6134958274........ H1: 8 # 18 pairs * PAIR B2: 4,5 ROW 2 D2: 4,5,9 # reduction candidate for 4,5 D2: 9 => CTR * 13.2..9.52579.....98.5137.2.4..2..9..62.59.74.918462.38.56...196134958274.9.....6 D2: 4,5 # 21 pairs * PAIR F2: 4,8 BLK 2 E1: 4,8,6,7 # reduction candidate for 4,8 E1: 4,8 # 23 pairs F1: 4,8,7 # reduction candidate for 4,8 F1: 4,8 # 23 pairs E2: 4,8,6,9 # reduction candidate for 4,8 E2: 4,8 => CTR * 13.2679852579.....986513742.4..21.98.62.59.74.9.8.62....56...1.6134958274........ E2: 6,9 # 18 pairs * PAIR F2: 4,8 ROW 2 H2: 4,8,3,6 # reduction candidate for 4,8 H2: 4,8 => CTR * 13.2..9.525796....98.5137.2.4..2..9..62.59.74.918462.38.56...196134958274........ H2: 3,6 # 18 pairs * PAIR F2: 4,8 COL F F7: 4,8,2,7 # reduction candidate for 4,8 F7: 4,8 => CTR * 13.2.79.52.7....31.8..137.2354721.9.86235917479184625392567431861398542747813256. F7: 2,7 # 18 pairs * PAIR H3: 4,6 BLK 3 H1: 4,6,8 # reduction candidate for 4,6 H1: 4,6 => CTR * 13.2..9.5257964.8198.5137.2.48.2..96362159.74.918462.3..56..41.6134958274........ H1: 8 # 18 pairs H2: 4,6,3,8 # reduction candidate for 4,6 H2: 4,6 # 27 pairs * PAIR H3: 4,6 ROW 3 C3: 4,6,9 # reduction candidate for 4,6 C3: 4,6 => CTR * 13.2..9.5257......98.5137.2.48.2..9.362159874.918462.38.56...19613.854274.9..1... C3: 9 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 E3: 4,6,1 # reduction candidate for 4,6 E3: 4,6 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 E3: 1 # 18 pairs * PAIR A5: 3,8 BLK 4 A4: 3,8,5,7 # reduction candidate for 3,8 A4: 3,8 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 A4: 5,7 # 18 pairs * PAIR A5: 3,8 ROW 5 G5: 3,8,1 # reduction candidate for 3,8 G5: 1 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 G5: 3,8 # 21 pairs * PAIR C6: 1,4 BLK 4 C4: 1,4,8 # reduction candidate for 1,4 C4: 1,4 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 C4: 8 => CTR * 13.2..9.52.7.......8...37.2..8.2..9.362159874.918462.38.56...19613.854274.9..1... * PAIR C6: 1,4 ROW 6 E6: 1,4,3,7 # reduction candidate for 1,4 E6: 3,7 => CTR * 1362..9.52475981..589.63742.51.2..9..62159.74.948.62.1..56...1.613..5.274........ E6: 1,4 # 20 pairs * PAIR D5: 1,3 BLK 5 D4: 1,3,4,7 # reduction candidate for 1,3 D4: 1,3 # 20 pairs E6: 1,3,4,7 # reduction candidate for 1,3 E6: 1,3 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 E6: 4,7 # 19 pairs * PAIR D5: 1,3 ROW 5 G5: 1,3,8 # reduction candidate for 1,3 G5: 1,3 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 G5: 8 => CTR * 13.2679852.7.98....86.13742....24.9.362159874.948.62....56.231.61398542742...1... * PAIR D5: 1,3 COL D D9: 1,3,7 # reduction candidate for 1,3 D9: 1,3 # 20 pairs D9: 7 # 16 pairs * PAIR H6: 3,5 BLK 6 G4: 3,5,1,6,8 # reduction candidate for 3,5 G4: 3,5 => CTR * 13.2..9.52.7.9.163.8...3742..1.2..96362159874.948.62.1..56..31.6139854274.8..1659 G4: 1,6,8 # 17 pairs * PAIR H6: 3,5 ROW 6 A6: 3,5,7 # reduction candidate for 3,5 A6: 3,5 => CTR * 1362.79.52475981..589.63742751.24.9.862159.74.948762.1.756.2.1.613..5.2742.7..... A6: 7 # 16 pairs * PAIR H6: 3,5 COL H H9: 3,5,6,8 # reduction candidate for 3,5 H9: 3,5 # 25 pairs H9: 6,8 # 18 pairs * PAIR I6: 1,3 BLK 6 G4: 1,3,5,6,8 # reduction candidate for 1,3 G4: 1,3 => CTR * 13.2..9.52.7.9.631.8...3742....2.196362159874791846253..56.431.6139854274.....56. G4: 5,6,8 # 17 pairs I4: 1,3,6,8 # reduction candidate for 1,3 I4: 1,3 => CTR * 13.2679852.7.98136.8651374254..2.69.36215987479.8.625...56.231.61398542742...156. I4: 6,8 # 18 pairs G5: 1,3,8 # reduction candidate for 1,3 G5: 1,3 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 G5: 8 => CTR * 13.2679852.7.98....86.13742....24.9.362159874.948.62....56.231.61398542742...1... * PAIR I6: 1,3 ROW 6 E6: 1,3,4,7 # reduction candidate for 1,3 E6: 1,3 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 E6: 4,7 # 19 pairs * PAIR I6: 1,3 COL I I2: 1,3,6,8 # reduction candidate for 1,3 I2: 6,8 # 21 pairs I2: 1,3 # 21 pairs * PAIR A7: 8,9 ROW 7 I7: 8,9,3 # reduction candidate for 8,9 I7: 3 => CTR * 1362..9.5247598136589.63742.51.2.698862159.74.9.8.62519.56...13613..5.274.8...569 I7: 8,9 # 19 pairs * PAIR B7: 2,7 ROW 7 F7: 2,7,4,8 # reduction candidate for 2,7 F7: 4,8 => CTR * 13.2.79.52.7....31.8..137.2354721.9.86235917479184625392567431861398542747813256. F7: 2,7 # 18 pairs * PAIR B9: 2,7 ROW 9 F9: 2,7,1,8 # reduction candidate for 2,7 F9: 2,7 => CTR * 13.2..9.52.7.9...158941376235.721.9.8623591747918462539.56...18613.854274.81..5.9 F9: 1,8 # 16 pairs * PAIR C9: 8,9 ROW 9 I9: 8,9,3,6 # reduction candidate for 8,9 I9: 3,6 => CTR * 13.2..9.52.7......98.5137.2..8.2..9.362159874.918462.38.56...19613.854274.9..1.86 I9: 8,9 # 20 pairs * PAIR D8: 4,9 BLK 8 E8: 4,9,8 # reduction candidate for 4,9 E8: 4,9 => CTR * 1362..985247598136589163742.51.2.698862359.74.9.8.62519.56..413613..58274.8.1.569 E8: 8 # 22 pairs * PAIR D8: 4,9 COL D D2: 4,9,5 # reduction candidate for 4,9 D2: 4,9 => CTR * 13.2..9.5257......98.5137.2.48.2..9.3621598747918462538.56...19613.854274.9..15.. D2: 5 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 * PAIR G8: 4,8 BLK 9 G7: 4,8,3 # reduction candidate for 4,8 G7: 4,8 => CTR * 1362..985247598136589163742.51.2.698862359.74.9.8.62519.56...13613..5.274.8.1.569 G7: 3 # 24 pairs * PAIR G8: 4,8 ROW 8 E8: 4,8,9 # reduction candidate for 4,8 E8: 9 => CTR * 13.2..9.52.79......8.5137.2....2..98862.59.74.9.8.62..9.56...1.613.958274........ E8: 4,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190131-absurd-base-pr-000.dot * REASONING * DIS # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * DIS # H1: 4,6 => CTR => H1: 8 * DIS # D2: 9 => CTR => D2: 4,5 * DIS # E2: 4,8 => CTR => E2: 6,9 * DIS # H2: 4,8 => CTR => H2: 3,6 * DIS # F7: 4,8 => CTR => F7: 2,7 * DIS # H1: 4,6 => CTR => H1: 8 * DIS # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * PRF # E3: 4,6 => SOL * PRF # A4: 3,8 => SOL * PRF # G5: 1 => SOL * PRF # C4: 1,4 => SOL * DIS # C4: 8 => CTR => C4: 1,4 * DIS # E6: 3,7 => CTR => E6: 1,4 * PRF # E6: 1,3 => SOL * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * DIS # G4: 3,5 => CTR => G4: 1,6,8 * DIS # A6: 3,5 => CTR => A6: 7 * DIS # G4: 1,3 => CTR => G4: 5,6,8 * DIS # I4: 1,3 => CTR => I4: 6,8 * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * PRF # E6: 1,3 => SOL * DIS # I7: 3 => CTR => I7: 8,9 * DIS # F7: 4,8 => CTR => F7: 2,7 * DIS # F9: 2,7 => CTR => F9: 1,8 * DIS # I9: 3,6 => CTR => I9: 8,9 * DIS # E8: 4,9 => CTR => E8: 8 * DIS # D2: 4,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * DIS # G7: 4,8 => CTR => G7: 3 * DIS # E8: 9 => CTR => E8: 4,8 * CNT 35 HDP CHAINS / 69 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B7,B9,C1,C6,C9,D5,D8,F2,G8,H3,H6,I6) * 13.2..9.52.7.......8...37.2....2..9..62.59.74.9.8.62....56...1.613..5.274........ * PAIR C1: 4,6 BLK 1 C3: 4,6,9 # reduction candidate for 4,6 C3: 4,6 => CTR * 13.2..9.5257......98.5137.2.48.2..9.362159874.918462.38.56...19613.854274.9..1... C3: 9 => SOLVED * 136274985247598631589163742351427896862359174794816253975642318613985427428731569 * DURATION: 0:00:02.584914 START: 03:22:55.130029 END: 03:22:57.714943 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190131-absurd-base-pr-001.dot * REASONING * DIS # C3: 4,6 => CTR => C3: 9 * PRF C3: 9 => SOL * STA C3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190131, absurd
Solution
position: 136274985247598631589163742351427896862359174794816253975642318613985427428731569 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 # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * INC # E1: 4,6 => UNS * DIS # H1: 4,6 => CTR => H1: 8 * INC # H1: 8 => UNS * INC # D2: 4,5 => UNS * DIS # D2: 9 => CTR => D2: 4,5 * INC # E1: 4,8 => UNS * INC # F1: 4,8 => UNS * DIS # E2: 4,8 => CTR => E2: 6,9 * INC # E2: 6,9 => UNS * DIS # H2: 4,8 => CTR => H2: 3,6 * INC # H2: 3,6 => UNS * DIS # F7: 4,8 => CTR => F7: 2,7 * INC # F7: 2,7 => UNS * DIS # H1: 4,6 => CTR => H1: 8 * INC # H1: 8 => UNS * INC # H2: 4,6 => UNS * DIS # C3: 4,6 => CTR => C3: 9 * PRF # C3: 9 => SOL * PRF # E3: 4,6 => SOL * INC # E3: 1 => UNS * PRF # A4: 3,8 => SOL * INC # A4: 5,7 => UNS * INC # G5: 3,8 => UNS * PRF # G5: 1 => SOL * PRF # C4: 1,4 => SOL * DIS # C4: 8 => CTR => C4: 1,4 * INC # E6: 1,4 => UNS * DIS # E6: 3,7 => CTR => E6: 1,4 * INC # D4: 1,3 => UNS * PRF # E6: 1,3 => SOL * INC # E6: 4,7 => UNS * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * INC # D9: 1,3 => UNS * INC # D9: 7 => UNS * DIS # G4: 3,5 => CTR => G4: 1,6,8 * INC # G4: 1,6,8 => UNS * DIS # A6: 3,5 => CTR => A6: 7 * INC # A6: 7 => UNS * INC # H9: 3,5 => UNS * INC # H9: 6,8 => UNS * DIS # G4: 1,3 => CTR => G4: 5,6,8 * INC # G4: 5,6,8 => UNS * DIS # I4: 1,3 => CTR => I4: 6,8 * INC # I4: 6,8 => UNS * PRF # G5: 1,3 => SOL * DIS # G5: 8 => CTR => G5: 1,3 * PRF # E6: 1,3 => SOL * INC # E6: 4,7 => UNS * INC # I2: 1,3 => UNS * INC # I2: 6,8 => UNS * INC # I7: 8,9 => UNS * DIS # I7: 3 => CTR => I7: 8,9 * INC # F7: 2,7 => UNS * DIS # F7: 4,8 => CTR => F7: 2,7 * DIS # F9: 2,7 => CTR => F9: 1,8 * INC # F9: 1,8 => UNS * INC # I9: 8,9 => UNS * DIS # I9: 3,6 => CTR => I9: 8,9 * DIS # E8: 4,9 => CTR => E8: 8 * INC # E8: 8 => UNS * DIS # D2: 4,9 => CTR => D2: 5 * PRF # D2: 5 => SOL * DIS # G7: 4,8 => CTR => G7: 3 * INC # G7: 3 => UNS * INC # E8: 4,8 => UNS * DIS # E8: 9 => CTR => E8: 4,8 * CNT 69 HDP CHAINS / 69 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 4,6 => CTR => C3: 9 * PRF C3: 9 => SOL * STA C3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED