Analysis of zz-sudoku-de-677379-base.sdk
Contents
Original Sudoku
level: medium
position: ...8...6263...4...2...7..41.6..3.2..4.......9..8.6..1.94..8...3...2...9551...7... initial
Autosolve
position: ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 5,9 => CTR => F1: 1,3 * PRF # G1: 5,9 => SOL * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D3: 5,9 => CTR => D3: 3,6 * PRF # F3: 5,9 => SOL * DIS # C4: 1,7 => CTR => C4: 5,9 * PRF # G2: 7,8 => SOL * DIS # G2: 5,9 => CTR => G2: 7,8 * DIS # H2: 7,8 => CTR => H2: 5 * PRF # H2: 5 => SOL * DIS # I4: 4 => CTR => I4: 7,8 * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D4: 1,7 => CTR => D4: 4,5,9 * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D6: 5,9 => CTR => D6: 4,7 * PRF # D6: 4,7 => SOL * DIS # D4: 1,5 => CTR => D4: 4,7,9 * DIS # F4: 1,5 => CTR => F4: 9 * PRF # F4: 9 => SOL * PRF # D5: 1,5 => SOL * PRF # C5: 7 => SOL * PRF # E1: 1,5 => SOL * DIS # E1: 9 => CTR => E1: 1,5 * DIS # H4: 8 => CTR => H4: 5,7 * PRF # D6: 5,7 => SOL * DIS # G1: 5,7 => CTR => G1: 3,9 * DIS # G2: 5,7 => CTR => G2: 8,9 * DIS # I4: 4,7 => CTR => I4: 8 * PRF # D6: 4,7 => SOL * DIS # D6: 5,9 => CTR => D6: 4,7 * PRF # F3: 5,9 => SOL * DIS # D3: 3,9 => CTR => D3: 5,6 * PRF # D3: 5,6 => SOL * CNT 33 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 5,9 => CTR => F1: 1,3 * PRF F1: 1,3 # G1: 5,9 => SOL * STA F1: 1,3 + G1: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8...6263...4...2...7..41.6..3.2..4.......9..8.6..1.94..8...3...2...9551...7... | initial |
| ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 | autosolve |
| 754813962631924857289675341165439278427158639398762514946581723873246195512397486 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A1: 1,7 B1: 5,9 C2: 1,7 C3: 5,9 I2: 7,8 A4: 1,7 B6: 5,9 E5: 1,5 G6: 5,7 I6: 4,7 C7: 2,6 C8: 3,6 C9: 2,3 E8: 1,4 F8: 3,6 D9: 3,9 E9: 4,9 G7: 1,7 H7: 2,7 G8: 1,4 G9: 4,8 H9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C2: 1.. / A1 = 1 => 0 pairs (X) / C2 = 1 => 22 pairs (_) G7,G8: 1.. / G7 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) C2,D2: 1.. / C2 = 1 => 22 pairs (_) / D2 = 1 => 0 pairs (X) E8,G8: 1.. / E8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) A1,A4: 1.. / A1 = 1 => 0 pairs (X) / A4 = 1 => 22 pairs (_) C7,C9: 2.. / C7 = 2 => 0 pairs (X) / C9 = 2 => 0 pairs (_) H7,H9: 2.. / H7 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) C7,H7: 2.. / C7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) C9,H9: 2.. / C9 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) G1,G3: 3.. / G1 = 3 => 26 pairs (_) / G3 = 3 => 0 pairs (*) C8,C9: 3.. / C8 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) F8,D9: 3.. / F8 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) F1,G1: 3.. / F1 = 3 => 0 pairs (*) / G1 = 3 => 0 pairs (X) C8,F8: 3.. / C8 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) C9,D9: 3.. / C9 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) D3,D9: 3.. / D3 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) D4,D6: 4.. / D4 = 4 => 22 pairs (_) / D6 = 4 => 0 pairs (X) I4,I6: 4.. / I4 = 4 => 0 pairs (X) / I6 = 4 => 22 pairs (_) E8,E9: 4.. / E8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D4,I4: 4.. / D4 = 4 => 22 pairs (_) / I4 = 4 => 0 pairs (X) D6,I6: 4.. / D6 = 4 => 0 pairs (X) / I6 = 4 => 22 pairs (_) E8,G8: 4.. / E8 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) E9,G9: 4.. / E9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) B1,C3: 5.. / B1 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) H4,G6: 5.. / H4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) D7,F7: 5.. / D7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) E1,E5: 5.. / E1 = 5 => 0 pairs (X) / E5 = 5 => 26 pairs (_) H2,H4: 5.. / H2 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) D3,F3: 6.. / D3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) C7,C8: 6.. / C7 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) C8,F8: 6.. / C8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) D3,D7: 6.. / D3 = 6 => 0 pairs (*) / D7 = 6 => 0 pairs (X) A1,C2: 7.. / A1 = 7 => 22 pairs (_) / C2 = 7 => 0 pairs (X) G7,H7: 7.. / G7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) A1,G1: 7.. / A1 = 7 => 22 pairs (_) / G1 = 7 => 0 pairs (X) C5,D5: 7.. / C5 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) A1,A4: 7.. / A1 = 7 => 22 pairs (_) / A4 = 7 => 0 pairs (X) H4,I4: 8.. / H4 = 8 => 0 pairs (X) / I4 = 8 => 22 pairs (_) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) G2,G9: 8.. / G2 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) I2,I4: 8.. / I2 = 8 => 0 pairs (X) / I4 = 8 => 22 pairs (_) B1,C3: 9.. / B1 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) C4,B6: 9.. / C4 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) D9,E9: 9.. / D9 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) D2,G2: 9.. / D2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) B6,D6: 9.. / B6 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) B1,B6: 9.. / B1 = 9 => 0 pairs (X) / B6 = 9 => 0 pairs (_) C3,C4: 9.. / C3 = 9 => 0 pairs (*) / C4 = 9 => 0 pairs (X) E1,E9: 9.. / E1 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) * DURATION: 0:01:23.487693 START: 07:43:39.069848 END: 07:45:02.557541 2017-05-01 * CP COUNT: (51) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B6,C2,C3,C7,C8,C9,D9,E5,E8,E9,F8,G6,G7,G8,G9,H7,H9,I2,I6) * ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 * PAIR B1: 5,9 ROW 1 E1: 5,9,1 # reduction candidate for 5,9 E1: 5,9 # 25 pairs F1: 5,9,1,3 # reduction candidate for 5,9 F1: 5,9 => CTR * 7.481.362631.248.728..73941169.3.2..42.1586393.8.62.1.94..8172387.24.195512397486 F1: 1,3 # 23 pairs G1: 5,9,3,7 # reduction candidate for 5,9 G1: 5,9 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 G1: 3,7 # 23 pairs * PAIR C2: 1,7 COL C C4: 1,7,5,9 # reduction candidate for 1,7 C4: 1,7 => CTR * ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486 C4: 5,9 # 25 pairs C5: 1,7,5 # reduction candidate for 1,7 C5: 1,7 # 25 pairs * PAIR C3: 5,9 ROW 3 D3: 5,9,3,6 # reduction candidate for 5,9 D3: 5,9 => CTR * ..48...6263..24...28..76341.6..3.2..42...86393.8.62.1.94.685173876213495513947826 D3: 3,6 # 23 pairs F3: 5,9,3,6 # reduction candidate for 5,9 F3: 5,9 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 F3: 3,6 # 26 pairs G3: 5,9,3 # reduction candidate for 5,9 G3: 5,9 # 26 pairs * PAIR C3: 5,9 COL C C4: 5,9,1,7 # reduction candidate for 5,9 C4: 1,7 => CTR * ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486 C4: 5,9 # 25 pairs * PAIR I2: 7,8 BLK 3 G2: 7,8,5,9 # reduction candidate for 7,8 G2: 7,8 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 G2: 5,9 => CTR * ..489.36263..249.7289376541.6..392584257186393.8.62.1.942.8..738762.3495513947826 H2: 7,8,5 # reduction candidate for 7,8 H2: 7,8 => CTR * 7.4891362631524987289.7.54116..3.25842...86393.8.6271494..8.17387.21.49551..47826 H2: 5 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 * PAIR I2: 7,8 COL I I4: 7,8,4 # reduction candidate for 7,8 I4: 4 => CTR * .548...6263..24.58289.7.341.6..3.28442..58639398462517942.8..738762.3495513947826 I4: 7,8 # 22 pairs * PAIR A4: 1,7 BLK 4 C4: 1,7,5,9 # reduction candidate for 1,7 C4: 1,7 => CTR * ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486 C4: 5,9 # 25 pairs C5: 1,7,5 # reduction candidate for 1,7 C5: 1,7 # 25 pairs * PAIR A4: 1,7 ROW 4 D4: 1,7,4,5,9 # reduction candidate for 1,7 D4: 1,7 => CTR * .548...6263..24.58289.7.341.65.3928442..58639398462517942.8..738762.3495513947826 D4: 4,5,9 # 22 pairs * PAIR B6: 5,9 BLK 4 C4: 5,9,1,7 # reduction candidate for 5,9 C4: 1,7 => CTR * ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486 C4: 5,9 # 25 pairs * PAIR B6: 5,9 ROW 6 D6: 5,9,4,7 # reduction candidate for 5,9 D6: 5,9 => CTR * 7.4891.6263..24...28..7..41.6.43.2..42.7.86393.8.6271494..8.17387.21.49551..47826 D6: 4,7 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 * PAIR E5: 1,5 BLK 5 D4: 1,5,4,7,9 # reduction candidate for 1,5 D4: 1,5 => CTR * .548...6263..24.58289.7.341.6..3928442.758639398462517942.8..738762.3495513947826 D4: 4,7,9 # 22 pairs F4: 1,5,9 # reduction candidate for 1,5 F4: 1,5 => CTR * ..48...6263..249..28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551.397..6 F4: 9 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 D5: 1,5,7 # reduction candidate for 1,5 D5: 1,5 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 D5: 7 # 25 pairs * PAIR E5: 1,5 ROW 5 C5: 1,5,7 # reduction candidate for 1,5 C5: 7 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 C5: 1,5 # 25 pairs * PAIR E5: 1,5 COL E E1: 1,5,9 # reduction candidate for 1,5 E1: 1,5 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 E1: 9 => CTR * .5489136263..249..289.7..41.6..392..42..58639398.6251.94..8...387.21.49551.947826 * PAIR G6: 5,7 BLK 6 H4: 5,7,8 # reduction candidate for 5,7 H4: 8 => CTR * .548...6263..24.58289.7.341.6..3.28.42..58639398.6251.942.8.173876213495513947826 H4: 5,7 # 22 pairs * PAIR G6: 5,7 ROW 6 D6: 5,7,4,9 # reduction candidate for 5,7 D6: 5,7 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 D6: 4,9 # 25 pairs * PAIR G6: 5,7 COL G G1: 5,7,3,9 # reduction candidate for 5,7 G1: 5,7 => CTR * ..48.3.6263..24...28..7.341.6..3.2..42...86393.8.62.1.94..8...38732.6.95512397486 G1: 3,9 # 23 pairs G2: 5,7,8,9 # reduction candidate for 5,7 G2: 5,7 => CTR * ..48...6263.924...28..7..41.6..392..42...8639398.62.1.94..8...387.2...9551.397..6 G2: 8,9 # 23 pairs * PAIR I6: 4,7 BLK 6 I4: 4,7,8 # reduction candidate for 4,7 I4: 4,7 => CTR * .548...6263..24.58289.7.341.6..3.28.42..58639398.6251.942.8..738762.3495513947826 I4: 8 # 22 pairs * PAIR I6: 4,7 ROW 6 D6: 4,7,5,9 # reduction candidate for 4,7 D6: 4,7 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 D6: 5,9 => CTR * 7.4891.6263..24...28..7..41.6.43.2..42.7.86393.8.6271494..8.17387.21.49551..47826 * PAIR F8: 3,6 COL F F3: 3,6,5,9 # reduction candidate for 3,6 F3: 5,9 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 F3: 3,6 # 26 pairs * PAIR D9: 3,9 COL D D3: 3,9,5,6 # reduction candidate for 3,9 D3: 3,9 => CTR * ..489136263152498728937654116..3.2..42...86393.8.62.1.94.685173876213495513947826 D3: 5,6 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-677379-base-pr-000.dot * REASONING * DIS # F1: 5,9 => CTR => F1: 1,3 * PRF # G1: 5,9 => SOL * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D3: 5,9 => CTR => D3: 3,6 * PRF # F3: 5,9 => SOL * DIS # C4: 1,7 => CTR => C4: 5,9 * PRF # G2: 7,8 => SOL * DIS # G2: 5,9 => CTR => G2: 7,8 * DIS # H2: 7,8 => CTR => H2: 5 * PRF # H2: 5 => SOL * DIS # I4: 4 => CTR => I4: 7,8 * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D4: 1,7 => CTR => D4: 4,5,9 * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D6: 5,9 => CTR => D6: 4,7 * PRF # D6: 4,7 => SOL * DIS # D4: 1,5 => CTR => D4: 4,7,9 * DIS # F4: 1,5 => CTR => F4: 9 * PRF # F4: 9 => SOL * PRF # D5: 1,5 => SOL * PRF # C5: 7 => SOL * PRF # E1: 1,5 => SOL * DIS # E1: 9 => CTR => E1: 1,5 * DIS # H4: 8 => CTR => H4: 5,7 * PRF # D6: 5,7 => SOL * DIS # G1: 5,7 => CTR => G1: 3,9 * DIS # G2: 5,7 => CTR => G2: 8,9 * DIS # I4: 4,7 => CTR => I4: 8 * PRF # D6: 4,7 => SOL * DIS # D6: 5,9 => CTR => D6: 4,7 * PRF # F3: 5,9 => SOL * DIS # D3: 3,9 => CTR => D3: 5,6 * PRF # D3: 5,6 => SOL * CNT 33 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B6,C2,C3,C7,C8,C9,D9,E5,E8,E9,F8,G6,G7,G8,G9,H7,H9,I2,I6) * ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 * PAIR B1: 5,9 ROW 1 E1: 5,9,1 # reduction candidate for 5,9 E1: 5,9 # 25 pairs F1: 5,9,1,3 # reduction candidate for 5,9 F1: 5,9 => CTR * 7.481.362631.248.728..73941169.3.2..42.1586393.8.62.1.94..8172387.24.195512397486 G1: 5,9,3,7 # reduction candidate for 5,9 G1: 5,9 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 * DURATION: 0:00:04.270236 START: 07:45:59.104841 END: 07:46:03.375077 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-677379-base-pr-001.dot * REASONING * DIS # F1: 5,9 => CTR => F1: 1,3 * PRF F1: 1,3 # G1: 5,9 => SOL * STA F1: 1,3 + G1: 5,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/677379.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 A1: 1,7 B1: 5,9 E1: 1,5,9 # reduction candidate for 5,9 E1: 1 => SOLVED * 754813962631924857289675341165439278427158639398762514946581723873246195512397486 * SOLVED! -------------------------------------------------- * AUTO .. C1 = 4 # set value E2 = 2 # set value B3 = 8 # set value B8: 7 # naked single G5 = 6 # set value H5 = 3 # set value A8 = 8 # set value B8 = 7 # set value I9 = 6 # set value A6: 3.. # hidden single F5: 8.. # hidden single F5 = 8 # set value A6 = 3 # set value F6: 2.. # hidden single F6 = 2 # set value B5: 2.. # hidden single B5 = 2 # set value Q5: 4.. = D4,D6: 4.. => D9 != 4 Q9: 4.. = G8,G9: 4.. => G6 != 4 A1,C2: 1,7.. => C2 != 5,9 # hidden pair C8,F8: 3,6.. => F8 != 1 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: H2 != 5 * FORCE VALUE:: H2 = 5 |:step:| 01 --------------------------------------------------
Solution
position: 754813962631924857289675341165439278427158639398762514946581723873246195512397486 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 # E1: 5,9 => UNS * DIS # F1: 5,9 => CTR => F1: 1,3 * INC # F1: 1,3 => UNS * PRF # G1: 5,9 => SOL * INC # G1: 3,7 => UNS * DIS # C4: 1,7 => CTR => C4: 5,9 * INC # C4: 5,9 => UNS * INC # C5: 1,7 => UNS * DIS # D3: 5,9 => CTR => D3: 3,6 * INC # D3: 3,6 => UNS * PRF # F3: 5,9 => SOL * INC # F3: 3,6 => UNS * INC # G3: 5,9 => UNS * INC # C4: 5,9 => UNS * DIS # C4: 1,7 => CTR => C4: 5,9 * PRF # G2: 7,8 => SOL * DIS # G2: 5,9 => CTR => G2: 7,8 * DIS # H2: 7,8 => CTR => H2: 5 * PRF # H2: 5 => SOL * INC # I4: 7,8 => UNS * DIS # I4: 4 => CTR => I4: 7,8 * DIS # C4: 1,7 => CTR => C4: 5,9 * INC # C4: 5,9 => UNS * INC # C5: 1,7 => UNS * DIS # D4: 1,7 => CTR => D4: 4,5,9 * INC # D4: 4,5,9 => UNS * INC # C4: 5,9 => UNS * DIS # C4: 1,7 => CTR => C4: 5,9 * DIS # D6: 5,9 => CTR => D6: 4,7 * PRF # D6: 4,7 => SOL * DIS # D4: 1,5 => CTR => D4: 4,7,9 * INC # D4: 4,7,9 => UNS * DIS # F4: 1,5 => CTR => F4: 9 * PRF # F4: 9 => SOL * PRF # D5: 1,5 => SOL * INC # D5: 7 => UNS * INC # C5: 1,5 => UNS * PRF # C5: 7 => SOL * PRF # E1: 1,5 => SOL * DIS # E1: 9 => CTR => E1: 1,5 * INC # H4: 5,7 => UNS * DIS # H4: 8 => CTR => H4: 5,7 * PRF # D6: 5,7 => SOL * INC # D6: 4,9 => UNS * DIS # G1: 5,7 => CTR => G1: 3,9 * INC # G1: 3,9 => UNS * DIS # G2: 5,7 => CTR => G2: 8,9 * INC # G2: 8,9 => UNS * DIS # I4: 4,7 => CTR => I4: 8 * INC # I4: 8 => UNS * PRF # D6: 4,7 => SOL * DIS # D6: 5,9 => CTR => D6: 4,7 * INC # F3: 3,6 => UNS * PRF # F3: 5,9 => SOL * DIS # D3: 3,9 => CTR => D3: 5,6 * PRF # D3: 5,6 => SOL * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 5,9 => UNS * DIS # F1: 5,9 => CTR => F1: 1,3 * PRF F1: 1,3 # G1: 5,9 => SOL * STA F1: 1,3 + G1: 5,9 * CNT 3 HDP CHAINS / 3 HYP OPENED