Analysis of zz-sudoku-de-636873-base.sdk
Contents
Original Sudoku
level: medium
position: 8..6.9..3..........62...75..9.7.1.6..8..5..4..3.2.8.1..78...23..........4..8.5..9 initial
Autosolve
position: 8..6.9.23...5...9.9624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9....8.4..8.5.79 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G2: 1,4 => CTR => G2: 6,8 * DIS # I2: 1,4 => CTR => I2: 6,8 * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * DIS # E2: 2,7 => CTR => E2: 1,8 * DIS # E2: 2,7 => CTR => E2: 1,8 * DIS # G2: 1,4 => CTR => G2: 6,8 * DIS # I2: 1,4 => CTR => I2: 6,8 * PRF # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G8: 1,4 => CTR => G8: 5,6 * DIS # I2: 1,8 => CTR => I2: 4,6 * DIS # I4: 2,5 => CTR => I4: 8 * DIS # C6: 4,5 => CTR => C6: 6,7 * PRF # C6: 6,7 => SOL * DIS # A5: 2 => CTR => A5: 1,7 * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * PRF # C2: 1,7 => SOL * DIS # C2: 3 => CTR => C2: 1,7 * DIS # A5: 1 => CTR => A5: 2,7 * PRF # A6: 5,7 => SOL * DIS # A6: 6 => CTR => A6: 5,7 * DIS # C6: 5,7 => CTR => C6: 4,6 * DIS # B8: 1,2 => CTR => B8: 5 * PRF # B8: 5 => SOL * DIS # A8: 5,6 => CTR => A8: 1,3 * DIS # E8: 3,6 => CTR => E8: 2,7 * DIS # I7: 1,6 => CTR => I7: 5 * DIS # I8: 1,6 => CTR => I8: 4,5 * DIS # C9: 1,6 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # G2: 1,6 => CTR => G2: 4,8 * CNT 35 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:
* PRF # B1: 1,4 => SOL * STA B1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8..6.9..3..........62...75..9.7.1.6..8..5..4..3.2.8.1..78...23..........4..8.5..9 | initial |
| 8..6.9.23...5...9.9624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9....8.4..8.5.79 | autosolve |
| 815679423347512896962483751294731568781956342536248917678194235159327684423865179 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) B2: 1,4 E1: 1,7 F2: 2,7 E3: 1,8 G1: 1,4 I3: 1,8 A4: 2,5 C4: 4,5 C5: 1,7 E4: 3,4 D5: 3,9 E6: 4,9 G5: 3,9 I5: 2,7 G6: 5,9 I6: 5,7 B9: 1,2 D7: 1,9 E7: 6,9 D8: 1,3 F8: 2,7 G9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C5: 1.. / A5 = 1 => 0 pairs (X) / C5 = 1 => 25 pairs (_) D7,D8: 1.. / D7 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) E3,I3: 1.. / E3 = 1 => 0 pairs (X) / I3 = 1 => 22 pairs (_) E2,F2: 2.. / E2 = 2 => 0 pairs (X) / F2 = 2 => 20 pairs (_) A4,A5: 2.. / A4 = 2 => 22 pairs (_) / A5 = 2 => 0 pairs (X) I4,I5: 2.. / I4 = 2 => 0 pairs (X) / I5 = 2 => 22 pairs (_) B8,B9: 2.. / B8 = 2 => 0 pairs (X) / B9 = 2 => 24 pairs (_) A4,I4: 2.. / A4 = 2 => 22 pairs (_) / I4 = 2 => 0 pairs (X) A5,I5: 2.. / A5 = 2 => 0 pairs (X) / I5 = 2 => 22 pairs (_) B9,E9: 2.. / B9 = 2 => 24 pairs (_) / E9 = 2 => 0 pairs (X) F2,F8: 2.. / F2 = 2 => 20 pairs (_) / F8 = 2 => 0 pairs (X) A2,C2: 3.. / A2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) E4,D5: 3.. / E4 = 3 => 0 pairs (*) / D5 = 3 => 0 pairs (X) G4,G5: 3.. / G4 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) A8,C9: 3.. / A8 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) E4,G4: 3.. / E4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) D5,G5: 3.. / D5 = 3 => 0 pairs (X) / G5 = 3 => 0 pairs (_) C9,E9: 3.. / C9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) A2,A8: 3.. / A2 = 3 => 0 pairs (*) / A8 = 3 => 0 pairs (X) C2,C9: 3.. / C2 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) D5,D8: 3.. / D5 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) B1,B2: 4.. / B1 = 4 => 0 pairs (X) / B2 = 4 => 21 pairs (_) C4,C6: 4.. / C4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) E4,E6: 4.. / E4 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) G8,I8: 4.. / G8 = 4 => 0 pairs (X) / I8 = 4 => 22 pairs (_) B1,G1: 4.. / B1 = 4 => 0 pairs (X) / G1 = 4 => 21 pairs (_) C4,E4: 4.. / C4 = 4 => 0 pairs (*) / E4 = 4 => 0 pairs (X) C6,E6: 4.. / C6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) I2,I8: 4.. / I2 = 4 => 0 pairs (X) / I8 = 4 => 22 pairs (_) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 0 pairs (_) A7,I7: 5.. / A7 = 5 => 0 pairs (X) / I7 = 5 => 21 pairs (_) B1,B8: 5.. / B1 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) G2,I2: 6.. / G2 = 6 => 0 pairs (X) / I2 = 6 => 23 pairs (_) A6,C6: 6.. / A6 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) C6,C9: 6.. / C6 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) I5,I6: 7.. / I5 = 7 => 0 pairs (X) / I6 = 7 => 22 pairs (_) E8,F8: 7.. / E8 = 7 => 0 pairs (X) / F8 = 7 => 20 pairs (_) C1,E1: 7.. / C1 = 7 => 0 pairs (X) / E1 = 7 => 23 pairs (_) F2,F8: 7.. / F2 = 7 => 0 pairs (X) / F8 = 7 => 20 pairs (_) E2,E3: 8.. / E2 = 8 => 0 pairs (X) / E3 = 8 => 22 pairs (_) G4,I4: 8.. / G4 = 8 => 0 pairs (X) / I4 = 8 => 21 pairs (_) E3,I3: 8.. / E3 = 8 => 22 pairs (_) / I3 = 8 => 0 pairs (X) G2,G4: 8.. / G2 = 8 => 21 pairs (_) / G4 = 8 => 0 pairs (X) D5,E6: 9.. / D5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) G5,G6: 9.. / G5 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) D7,E7: 9.. / D7 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) D5,G5: 9.. / D5 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) E6,G6: 9.. / E6 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) D5,D7: 9.. / D5 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) E6,E7: 9.. / E6 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) * DURATION: 0:01:32.729637 START: 07:28:45.068709 END: 07:30:17.798346 2017-05-01 * CP COUNT: (50) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,B9,C4,C5,D5,D7,D8,E1,E3,E4,E6,E7,F2,F8,G1,G5,G6,G9,I3,I5,I6) * 8..6.9.23...5...9.9624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9....8.4..8.5.79 * PAIR B2: 1,4 BLK 1 B1: 1,4,5 # reduction candidate for 1,4 B1: 1,4 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 B1: 5 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.6..8..56.4263.2.8.17578..423.3.91..5844168.5.79 * PAIR B2: 1,4 ROW 2 G2: 1,4,6,8 # reduction candidate for 1,4 G2: 1,4 => CTR * 8..6.9.23...5...969624.3758.9.7.186..8..5634..3.2.891..78.9423...93..5844.38.5.79 G2: 6,8 # 23 pairs I2: 1,4,6,8 # reduction candidate for 1,4 I2: 1,4 => CTR * 85.6.942334.582691962413758.9.73186..8.95634..3624891.578194236619327584423865179 I2: 6,8 # 23 pairs * PAIR E1: 1,7 BLK 2 E2: 1,7,2,8 # reduction candidate for 1,7 E2: 2,8 # 23 pairs E2: 1,7 # 21 pairs * PAIR E1: 1,7 ROW 1 C1: 1,7,5 # reduction candidate for 1,7 C1: 1,7 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.6..8..56.4263.2.8.17578..423.3.91..5844168.5.79 C1: 5 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * PAIR F2: 2,7 BLK 2 E2: 2,7,1,8 # reduction candidate for 2,7 E2: 2,7 => CTR * 8576194231435...9.962483751.9.7.1.6..81.56.4..3.2.8.1..7819423.3.9....844..8.5.79 E2: 1,8 # 23 pairs * PAIR E3: 1,8 BLK 2 E2: 1,8,2,7 # reduction candidate for 1,8 E2: 2,7 => CTR * 8576194231435...9.962483751.9.7.1.6..81.56.4..3.2.8.1..7819423.3.9....844..8.5.79 E2: 1,8 # 23 pairs * PAIR G1: 1,4 BLK 3 G2: 1,4,6,8 # reduction candidate for 1,4 G2: 1,4 => CTR * 8..6.9.23...5...969624.3758.9.7.186..8..5634..3.2.891..78.9423...93..5844.38.5.79 G2: 6,8 # 23 pairs I2: 1,4,6,8 # reduction candidate for 1,4 I2: 1,4 => CTR * 85.6.942334.582691962413758.9.73186..8.95634..3624891.578194236619327584423865179 I2: 6,8 # 23 pairs * PAIR G1: 1,4 ROW 1 B1: 1,4,5 # reduction candidate for 1,4 B1: 1,4 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 B1: 5 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.6..8..56.4263.2.8.17578..423.3.91..5844168.5.79 * PAIR G1: 1,4 COL G G8: 1,4,5,6 # reduction candidate for 1,4 G8: 1,4 => CTR * 8..6.9423.4.5.2896962483751294731568.8.956342536248917678.94235..9.671844..825679 G8: 5,6 # 23 pairs * PAIR I3: 1,8 BLK 3 G2: 1,8,4,6 # reduction candidate for 1,8 G2: 1,8 # 23 pairs I2: 1,8,4,6 # reduction candidate for 1,8 I2: 1,8 => CTR * 85.6.942334.5..69.9624.375..9.73186..8.95634..3624891.5781942366193..584423865179 I2: 4,6 # 23 pairs * PAIR A4: 2,5 ROW 4 I4: 2,5,8 # reduction candidate for 2,5 I4: 2,5 => CTR * 85.6.942334.5...9.9624.375..9.73186..8.95634..3624891.5781942366193..584423865179 I4: 8 # 21 pairs * PAIR C4: 4,5 BLK 4 C6: 4,5,6,7 # reduction candidate for 4,5 C6: 4,5 => CTR * 8..6.9423.435...9.9624.375..9.741368.8.356942634298517.789642353591..684426835179 C6: 6,7 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * PAIR C5: 1,7 BLK 4 A5: 1,7,2 # reduction candidate for 1,7 A5: 2 => CTR * 8..6.9.23...5...9.9624.375..9.7.1.6.281.56.47.3.2.8.15578..423...9....8.4..8.5.79 A5: 1,7 # 22 pairs * PAIR C5: 1,7 COL C C1: 1,7,5 # reduction candidate for 1,7 C1: 1,7 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.6..8..56.4263.2.8.17578..423.3.91..5844168.5.79 C1: 5 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 C2: 1,7,3 # reduction candidate for 1,7 C2: 1,7 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 C2: 3 => CTR * 8..6.9423.435..896962483751295741368.8.356942634298517.7896423.3.91...8.426835179 * PAIR I5: 2,7 ROW 5 A5: 2,7,1 # reduction candidate for 2,7 A5: 1 => CTR * 8..679.237.35.2.9.9624.375.29.741368187356942.342985175789642313.91.7.8.4..835.79 A5: 2,7 # 25 pairs * PAIR I6: 5,7 ROW 6 A6: 5,7,6 # reduction candidate for 5,7 A6: 5,7 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 A6: 6 => CTR * 8..6.9423.435...9.9624.375..9.741368.8.356942634298517.789642353591..684426835179 C6: 5,7,4,6 # reduction candidate for 5,7 C6: 5,7 => CTR * 8..6.9.23...5...9.9624.375..94731.6..8.95634.63.24891..78194236..9367.8.4..8.5.79 C6: 4,6 # 23 pairs * PAIR B9: 1,2 BLK 7 B8: 1,2,5 # reduction candidate for 1,2 B8: 1,2 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.6..8..56.4263.2.8.17578..423.3.91..5844168.5.79 B8: 5 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * PAIR D8: 1,3 ROW 8 A8: 1,3,5,6 # reduction candidate for 1,3 A8: 5,6 => CTR * 8.5679.233.75.2.9.9624.375..94731.6.18.95634..3624891..7819423...93...8.4.38.5.79 A8: 1,3 # 24 pairs * PAIR F8: 2,7 BLK 8 E8: 2,7,3,6 # reduction candidate for 2,7 E8: 3,6 => CTR * 85.6.942334.5.2.969624.375..9.7.1.6.187.56.42.36248917.78.9423..29.67.84413825679 E8: 2,7 # 24 pairs * PAIR G9: 1,6 BLK 9 I7: 1,6,5 # reduction candidate for 1,6 I7: 1,6 => CTR * 85.6.9423.4.5...9.9624.375.29.7.1.65.8..56.42635248917578.94236..9.675844.68.5.79 I7: 5 # 21 pairs G8: 1,6,4,5 # reduction candidate for 1,6 G8: 1,6 # 21 pairs I8: 1,6,4,5 # reduction candidate for 1,6 I8: 1,6 => CTR * 845679123.1.5.26949624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9...48.4..8.5.79 I8: 4,5 # 23 pairs * PAIR G9: 1,6 ROW 9 C9: 1,6,3 # reduction candidate for 1,6 C9: 1,6 => CTR * 8..6.9423.435..896962483751295741368.8.356942634298517.7896423.3.91...8.426835179 C9: 3 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * PAIR G9: 1,6 COL G G2: 1,6,4,8 # reduction candidate for 1,6 G2: 1,6 => CTR * 85.6.942334.5...9.9624.375..9.73186..8.95634..3624891.5781942366193..584423865179 G2: 4,8 # 24 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-636873-base-pr-000.dot * REASONING * PRF # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G2: 1,4 => CTR => G2: 6,8 * DIS # I2: 1,4 => CTR => I2: 6,8 * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * DIS # E2: 2,7 => CTR => E2: 1,8 * DIS # E2: 2,7 => CTR => E2: 1,8 * DIS # G2: 1,4 => CTR => G2: 6,8 * DIS # I2: 1,4 => CTR => I2: 6,8 * PRF # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G8: 1,4 => CTR => G8: 5,6 * DIS # I2: 1,8 => CTR => I2: 4,6 * DIS # I4: 2,5 => CTR => I4: 8 * DIS # C6: 4,5 => CTR => C6: 6,7 * PRF # C6: 6,7 => SOL * DIS # A5: 2 => CTR => A5: 1,7 * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * PRF # C2: 1,7 => SOL * DIS # C2: 3 => CTR => C2: 1,7 * DIS # A5: 1 => CTR => A5: 2,7 * PRF # A6: 5,7 => SOL * DIS # A6: 6 => CTR => A6: 5,7 * DIS # C6: 5,7 => CTR => C6: 4,6 * DIS # B8: 1,2 => CTR => B8: 5 * PRF # B8: 5 => SOL * DIS # A8: 5,6 => CTR => A8: 1,3 * DIS # E8: 3,6 => CTR => E8: 2,7 * DIS # I7: 1,6 => CTR => I7: 5 * DIS # I8: 1,6 => CTR => I8: 4,5 * DIS # C9: 1,6 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # G2: 1,6 => CTR => G2: 4,8 * CNT 35 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,B9,C4,C5,D5,D7,D8,E1,E3,E4,E6,E7,F2,F8,G1,G5,G6,G9,I3,I5,I6) * 8..6.9.23...5...9.9624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9....8.4..8.5.79 * PAIR B2: 1,4 BLK 1 B1: 1,4,5 # reduction candidate for 1,4 B1: 1,4 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * DURATION: 0:00:02.359262 START: 07:31:15.985364 END: 07:31:18.344626 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-636873-base-pr-001.dot * REASONING * PRF # B1: 1,4 => SOL * STA B1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/636873.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 8..6.9.23...5...9.9624.375..9.7.1.6..8..56.4..3.2.8.1..78..423...9....8.4..8.5.79 B2: 1,4 B1: 1,4,5 # reduction candidate for 1,4 B1: 1,4 => SOLVED * 815679423347512896962483751294731568781956342536248917678194235159327684423865179 * SOLVED! -------------------------------------------------- * AUTO .. H1 = 2 # set value D2 = 5 # set value H2 = 9 # set value A3 = 9 # set value H9 = 7 # set value H8: 8 # naked single C8: 9.. # hidden single C8 = 9 # set value H8 = 8 # set value Q1: 3.. = A2,C2: 3.. => E2,F2 != 3 Q4: 2.. = A4,A5: 2.. => A8 != 2 Q4: 4.. = C4,C6: 4.. => C1,C2 != 4 Q5: 4.. = E4,E6: 4.. => E1,E2,E3,E7,E8 != 4 F5: 6 # naked single D5,G5: 3,9.. => F5 != 3,9 # naked pair F2,F8: 2,7.. => F2,F8 != 3,4,6 # hidden pair F3: 3 # naked single F2,F3,F8: 2,3,7.. => F3 != 4 # hidden triple D3: 4.. # hidden single F7: 4.. # hidden single D3 = 4 # set value F3 = 3 # set value F5 = 6 # set value F7: 4 # naked single F7 = 4 # set value Q2: 1.. = E1,E2,E3: 1.. => E7,E8,E9 != 1 * UNSOLVED! |:step:| 00 -------------------------------------------------- -------------------------------------------------- * DISABLE VALUE:: B8 != 5 B1: 5.. # hidden single * AUTO .. B1 = 5 # set value B2: 4.. # hidden single G1: 4.. # hidden single G1 = 4 # set value B2 = 4 # set value I8: 4.. # hidden single I8 = 4 # set value Q1,Q4: 1.. => A7,A8,C9 != 1 A4: 2 # naked single Q7: 5.. = A7,A8: 5.. => A4,A6 != 5 A4 = 2 # set value I5: 2.. # hidden single I5 = 2 # set value I6: 7.. # hidden single I6 = 7 # set value A6: 6 # naked single A6 = 6 # set value A7: 5 # naked single A7 = 5 # set value A8: 3 # naked single A8 = 3 # set value C9: 6 # naked single D8: 1 # naked single D8 = 1 # set value D7: 9 # naked single B8: 2 # naked single C9 = 6 # set value G9: 1 # naked single G9 = 1 # set value I7: 6 # naked single B9: 2 # naked single C2: 3.. # hidden single E9: 3.. # hidden single G8: 5.. # hidden single D5: 3.. # hidden single I4: 5.. # hidden single B8,B9 = 2 => CTR B8,B9 = 2 => CTR * CTR! => B8 = 5 |:step:| 01 --------------------------------------------------
Solution
position: 815679423347512896962483751294731568781956342536248917678194235159327684423865179 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 # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G2: 1,4 => CTR => G2: 6,8 * INC # G2: 6,8 => UNS * DIS # I2: 1,4 => CTR => I2: 6,8 * INC # I2: 6,8 => UNS * INC # E2: 1,7 => UNS * INC # E2: 2,8 => UNS * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * DIS # E2: 2,7 => CTR => E2: 1,8 * INC # E2: 1,8 => UNS * INC # E2: 1,8 => UNS * DIS # E2: 2,7 => CTR => E2: 1,8 * DIS # G2: 1,4 => CTR => G2: 6,8 * INC # G2: 6,8 => UNS * DIS # I2: 1,4 => CTR => I2: 6,8 * INC # I2: 6,8 => UNS * PRF # B1: 1,4 => SOL * DIS # B1: 5 => CTR => B1: 1,4 * DIS # G8: 1,4 => CTR => G8: 5,6 * INC # G8: 5,6 => UNS * INC # G2: 1,8 => UNS * DIS # I2: 1,8 => CTR => I2: 4,6 * INC # I2: 4,6 => UNS * DIS # I4: 2,5 => CTR => I4: 8 * INC # I4: 8 => UNS * DIS # C6: 4,5 => CTR => C6: 6,7 * PRF # C6: 6,7 => SOL * INC # A5: 1,7 => UNS * DIS # A5: 2 => CTR => A5: 1,7 * DIS # C1: 1,7 => CTR => C1: 5 * PRF # C1: 5 => SOL * PRF # C2: 1,7 => SOL * DIS # C2: 3 => CTR => C2: 1,7 * INC # A5: 2,7 => UNS * DIS # A5: 1 => CTR => A5: 2,7 * PRF # A6: 5,7 => SOL * DIS # A6: 6 => CTR => A6: 5,7 * DIS # C6: 5,7 => CTR => C6: 4,6 * INC # C6: 4,6 => UNS * DIS # B8: 1,2 => CTR => B8: 5 * PRF # B8: 5 => SOL * INC # A8: 1,3 => UNS * DIS # A8: 5,6 => CTR => A8: 1,3 * INC # E8: 2,7 => UNS * DIS # E8: 3,6 => CTR => E8: 2,7 * DIS # I7: 1,6 => CTR => I7: 5 * INC # I7: 5 => UNS * INC # G8: 1,6 => UNS * DIS # I8: 1,6 => CTR => I8: 4,5 * INC # I8: 4,5 => UNS * DIS # C9: 1,6 => CTR => C9: 3 * PRF # C9: 3 => SOL * DIS # G2: 1,6 => CTR => G2: 4,8 * INC # G2: 4,8 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B1: 1,4 => SOL * STA B1: 1,4 * CNT 1 HDP CHAINS / 1 HYP OPENED