Analysis of xx-top500-060-base.sdk
Contents
Original Sudoku
level: medium
position: ...8....16.....5...........4.1.5.....3.....8.......7.....1.8.4..2.3.....5.....6.. initial
Autosolve
position: .5.8....16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.5...5.....6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # C2: 2,9 => CTR => C2: 3,4,7,8 * PRF # I2: 2,9 => SOL * DIS # A1: 2,9 => CTR => A1: 3 * DIS # C6: 2 => CTR => C6: 6,9 * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * DIS # G1: 2,9 => CTR => G1: 3,4 * DIS # G3: 2,9 => CTR => G3: 3,4,8 * DIS # C7: 3,9 => CTR => C7: 6,7 * PRF # C9: 3,9 => SOL * DIS # C9: 4,7,8 => CTR => C9: 3,9 * DIS # A1: 2 => CTR => A1: 3,9 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * DIS # G3: 2,3 => CTR => G3: 4,8,9 * DIS # I8: 8,9 => CTR => I8: 7 * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * PRF # I3: 2,8 => SOL * CNT 28 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS E1: 3,4,7 # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS E1: 3,4,7 + E2: 1,3,4,7 # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 # C2: 2,9 => CTR => C2: 3,4,7,8 * PRF E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 # I2: 2,9 => SOL * STA E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 + I2: 2,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8....16.....5...........4.1.5.....3.....8.......7.....1.8.4..2.3.....5.....6.. | initial |
| .5.8....16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.5...5.....6.. | autosolve |
| 352879461678214539149536872481753296735692184296481753967128345824365917513947628 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A3: 1,8 D2: 2,9 A6: 2,9 B6: 6,9 E5: 2,9 F5: 2,9 G4: 2,9 A7: 3,9 A8: 1,8 C8: 4,6 E8: 4,6 D9: 2,9 G7: 2,3 G8: 8,9 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 15 pairs (_) / E3 = 1 => 0 pairs (X) A8,B9: 1.. / A8 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) H8,H9: 1.. / H8 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) B2,E2: 1.. / B2 = 1 => 0 pairs (X) / E2 = 1 => 15 pairs (_) A8,H8: 1.. / A8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) B9,H9: 1.. / B9 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) A3,A8: 1.. / A3 = 1 => 0 pairs (*) / A8 = 1 => 0 pairs (X) A6,C6: 2.. / A6 = 2 => 16 pairs (_) / C6 = 2 => 0 pairs (X) E5,F5: 2.. / E5 = 2 => 0 pairs (X) / F5 = 2 => 13 pairs (_) E7,G7: 2.. / E7 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) A1,A6: 2.. / A1 = 2 => 0 pairs (X) / A6 = 2 => 16 pairs (_) D2,D9: 2.. / D2 = 2 => 13 pairs (_) / D9 = 2 => 0 pairs (X) G7,H9: 3.. / G7 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) C9,H9: 3.. / C9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) A1,A7: 3.. / A1 = 3 => 17 pairs (_) / A7 = 3 => 0 pairs (X) G1,G3: 4.. / G1 = 4 => 15 pairs (_) / G3 = 4 => 0 pairs (X) C8,E8: 4.. / C8 = 4 => 13 pairs (_) / E8 = 4 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 15 pairs (_) / F3 = 6 => 16 pairs (_) B6,C6: 6.. / B6 = 6 => 16 pairs (_) / C6 = 6 => 13 pairs (_) H4,I4: 6.. / H4 = 6 => 16 pairs (_) / I4 = 6 => 16 pairs (_) E7,E8: 6.. / E7 = 6 => 0 pairs (X) / E8 = 6 => 13 pairs (_) F1,H1: 6.. / F1 = 6 => 15 pairs (_) / H1 = 6 => 16 pairs (_) C8,E8: 6.. / C8 = 6 => 0 pairs (X) / E8 = 6 => 13 pairs (_) B6,B7: 6.. / B6 = 6 => 16 pairs (_) / B7 = 6 => 13 pairs (_) I3,I4: 6.. / I3 = 6 => 16 pairs (_) / I4 = 6 => 16 pairs (_) H8,I8: 7.. / H8 = 7 => 0 pairs (X) / I8 = 7 => 16 pairs (_) A8,C9: 8.. / A8 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) C2,I2: 8.. / C2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) C9,I9: 8.. / C9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A3,A8: 8.. / A3 = 8 => 0 pairs (X) / A8 = 8 => 0 pairs (_) G3,G8: 8.. / G3 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 13 pairs (_) / F5 = 9 => 0 pairs (X) D2,D9: 9.. / D2 = 9 => 0 pairs (X) / D9 = 9 => 13 pairs (_) * DURATION: 0:00:47.558486 START: 04:43:00.826313 END: 04:43:48.384799 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A7,A8,B6,C8,D2,D9,E5,E8,F5,G4,G7,G8,I9) * .5.8....16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.5...5.....6.. * PAIR D2: 2,9 BLK 2 E1: 2,9,3,4,7 # reduction candidate for 2,9 E1: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 E1: 3,4,7 # 15 pairs F1: 2,9,4,6,7 # reduction candidate for 2,9 F1: 2,9 # 19 pairs E2: 2,9,1,3,4,7 # reduction candidate for 2,9 E2: 2,9 => CTR * .5.8....161....5..8..51....481753...7356..184...481753...1.8.4512.3.58..5.8...6.. E2: 1,3,4,7 # 15 pairs F2: 2,9,4,7 # reduction candidate for 2,9 F2: 2,9 # 19 pairs E3: 2,9,1,3,4,7 # reduction candidate for 2,9 E3: 2,9 => CTR * .5.83...16...1.5.....5.....481753...7356..184...4817533..1.8245.2.3.5...5.....638 E3: 1,3,4,7 # 15 pairs F3: 2,9,4,6,7 # reduction candidate for 2,9 F3: 2,9 # 18 pairs * PAIR D2: 2,9 ROW 2 C2: 2,9,3,4,7,8 # reduction candidate for 2,9 C2: 2,9 => CTR * .5.8....16.....5.8...5.....481753...7356..184...481753...1.8.45.2.3.58..5.8...632 C2: 3,4,7,8 # 15 pairs H2: 2,9,3,7 # reduction candidate for 2,9 H2: 2,9 # 18 pairs I2: 2,9,7,8 # reduction candidate for 2,9 I2: 2,9 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 I2: 7,8 # 16 pairs * PAIR A6: 2,9 BLK 4 C6: 2,9,6 # reduction candidate for 2,9 C6: 2,9 # 16 pairs C6: 6 # 13 pairs * PAIR A6: 2,9 COL A A1: 2,9,3 # reduction candidate for 2,9 A1: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...4817533..1.8245.2.3.5...5.....638 A1: 3 # 17 pairs * PAIR B6: 6,9 BLK 4 C6: 6,9,2 # reduction candidate for 6,9 C6: 2 => CTR * 25.8....16.....5.....5.....481753...7356..1849624817533..1.8245.2.3.5...5.....638 C6: 6,9 # 16 pairs * PAIR B6: 6,9 COL B B7: 6,9,7 # reduction candidate for 6,9 B7: 6,9 # 16 pairs B7: 7 # 15 pairs * PAIR E5: 2,9 COL E E1: 2,9,3,4,7 # reduction candidate for 2,9 E1: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 E1: 3,4,7 # 15 pairs E2: 2,9,1,3,4,7 # reduction candidate for 2,9 E2: 2,9 => CTR * .5.8....161....5..8..51....481753...7356..184...481753...1.8.4512.3.58..5.8...6.. E2: 1,3,4,7 # 15 pairs E3: 2,9,1,3,4,7 # reduction candidate for 2,9 E3: 2,9 => CTR * .5.83...16...1.5.....5.....481753...7356..184...4817533..1.8245.2.3.5...5.....638 E3: 1,3,4,7 # 15 pairs E7: 2,9,6,7 # reduction candidate for 2,9 E7: 2,9 # 19 pairs E9: 2,9,4,7 # reduction candidate for 2,9 E9: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 E9: 4,7 # 16 pairs * PAIR F5: 2,9 COL F F1: 2,9,4,6,7 # reduction candidate for 2,9 F1: 2,9 # 19 pairs F2: 2,9,4,7 # reduction candidate for 2,9 F2: 2,9 # 19 pairs F3: 2,9,4,6,7 # reduction candidate for 2,9 F3: 2,9 # 18 pairs F9: 2,9,4,7 # reduction candidate for 2,9 F9: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 F9: 4,7 # 16 pairs * PAIR G4: 2,9 BLK 6 H4: 2,9,6 # reduction candidate for 2,9 H4: 2,9 # 16 pairs I4: 2,9,6 # reduction candidate for 2,9 I4: 2,9 # 16 pairs * PAIR G4: 2,9 COL G G1: 2,9,3,4 # reduction candidate for 2,9 G1: 2,9 => CTR * .5.8....16.....5.....5..4..481753...7356..184...481753...1.8345.2.3.58..5.....6.. G1: 3,4 # 16 pairs G3: 2,9,3,4,8 # reduction candidate for 2,9 G3: 2,9 => CTR * .5.8..4.16.....5.....5.....481753...7356..184...481753...1.8345.2.3.58..5.....6.. G3: 3,4,8 # 15 pairs * PAIR A7: 3,9 BLK 7 C7: 3,9,6,7 # reduction candidate for 3,9 C7: 3,9 => CTR * .5.8....16.....5.....5.....4817539..7356..184...481753...1.8245.2.3.58..5.....6.. C7: 6,7 # 16 pairs C9: 3,9,4,7,8 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 C9: 4,7,8 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5.1751....638 * PAIR A7: 3,9 COL A A1: 3,9,2 # reduction candidate for 3,9 A1: 2 => CTR * 25.8....16.....5.....5.....481753...7356..1849624817533..1.8245.2.3.5...5.....638 A1: 3,9 # 16 pairs * PAIR D9: 2,9 BLK 8 E7: 2,9,6,7 # reduction candidate for 2,9 E7: 2,9 # 19 pairs E9: 2,9,4,7 # reduction candidate for 2,9 E9: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 E9: 4,7 # 16 pairs F9: 2,9,4,7 # reduction candidate for 2,9 F9: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 F9: 4,7 # 16 pairs * PAIR G7: 2,3 BLK 9 H9: 2,3,1 # reduction candidate for 2,3 H9: 2,3 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 H9: 1 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8345.2.3.5...5.3...61. * PAIR G7: 2,3 COL G G1: 2,3,4,9 # reduction candidate for 2,3 G1: 2,3 => CTR * .5.8....16.....5.....5..4..481753...7356..184...481753...1.8.45.2.3.58..5.8...632 G1: 4,9 # 16 pairs G3: 2,3,4,8,9 # reduction candidate for 2,3 G3: 2,3 => CTR * .5.8..4.16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.58..5.8...632 G3: 4,8,9 # 15 pairs * PAIR G8: 8,9 BLK 9 I8: 8,9,7 # reduction candidate for 8,9 I8: 8,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.834512.3.5.7.5.....61. I8: 7 # 16 pairs * PAIR G8: 8,9 COL G G3: 8,9,2,3,4 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 G3: 2,3,4 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.58..5.8...632 * PAIR I9: 2,8 COL I I2: 2,8,7,9 # reduction candidate for 2,8 I2: 2,8 # 18 pairs I3: 2,8,6,7,9 # reduction candidate for 2,8 I3: 2,8 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 I3: 6,7,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-060-base-pr-000.dot * REASONING * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # C2: 2,9 => CTR => C2: 3,4,7,8 * PRF # I2: 2,9 => SOL * DIS # A1: 2,9 => CTR => A1: 3 * DIS # C6: 2 => CTR => C6: 6,9 * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * DIS # G1: 2,9 => CTR => G1: 3,4 * DIS # G3: 2,9 => CTR => G3: 3,4,8 * DIS # C7: 3,9 => CTR => C7: 6,7 * PRF # C9: 3,9 => SOL * DIS # C9: 4,7,8 => CTR => C9: 3,9 * DIS # A1: 2 => CTR => A1: 3,9 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * DIS # G3: 2,3 => CTR => G3: 4,8,9 * DIS # I8: 8,9 => CTR => I8: 7 * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * PRF # I3: 2,8 => SOL * CNT 28 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A7,A8,B6,C8,D2,D9,E5,E8,F5,G4,G7,G8,I9) * .5.8....16.....5.....5.....481753...7356..184...481753...1.8.45.2.3.5...5.....6.. * PAIR D2: 2,9 BLK 2 E1: 2,9,3,4,7 # reduction candidate for 2,9 E1: 2,9 => CTR * .5.8....16.....5.....5.....481753...7356..184...481753...1.8245.2.3.5...5.....638 F1: 2,9,4,6,7 # reduction candidate for 2,9 F1: 2,9 # 19 pairs E2: 2,9,1,3,4,7 # reduction candidate for 2,9 E2: 2,9 => CTR * .5.8....161....5..8..51....481753...7356..184...481753...1.8.4512.3.58..5.8...6.. F2: 2,9,4,7 # reduction candidate for 2,9 F2: 2,9 # 19 pairs E3: 2,9,1,3,4,7 # reduction candidate for 2,9 E3: 2,9 => CTR * .5.83...16...1.5.....5.....481753...7356..184...4817533..1.8245.2.3.5...5.....638 F3: 2,9,4,6,7 # reduction candidate for 2,9 F3: 2,9 # 18 pairs * PAIR D2: 2,9 ROW 2 C2: 2,9,3,4,7,8 # reduction candidate for 2,9 C2: 2,9 => CTR * .5.8....16.....5.8...5.....481753...7356..184...481753...1.8.45.2.3.58..5.8...632 H2: 2,9,3,7 # reduction candidate for 2,9 H2: 2,9 # 19 pairs I2: 2,9,7,8 # reduction candidate for 2,9 I2: 2,9 => SOLVED * 352879461678214539149536872481753296735692184296481753967128345824365917513947628 * DURATION: 0:00:09.222979 START: 04:44:40.304429 END: 04:44:49.527408 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-060-base-pr-001.dot * REASONING * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS E1: 3,4,7 # E2: 2,9 => CTR => E2: 1,3,4,7 * DIS E1: 3,4,7 + E2: 1,3,4,7 # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 # C2: 2,9 => CTR => C2: 3,4,7,8 * PRF E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 # I2: 2,9 => SOL * STA E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 + I2: 2,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 060 solution: 352879461678214539149536872481753296735692184296481753967128345824365917513947628 info: 1430 FNBHWXY S8.f 11950 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 352879461678214539149536872481753296735692184296481753967128345824365917513947628 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 # E1: 2,9 => CTR => E1: 3,4,7 * INC # E1: 3,4,7 => UNS * INC # F1: 2,9 => UNS * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * INC # E2: 1,3,4,7 => UNS * INC # F2: 2,9 => UNS * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * INC # E3: 1,3,4,7 => UNS * INC # F3: 2,9 => UNS * DIS # C2: 2,9 => CTR => C2: 3,4,7,8 * INC # C2: 3,4,7,8 => UNS * INC # H2: 2,9 => UNS * PRF # I2: 2,9 => SOL * INC # I2: 7,8 => UNS * INC # C6: 2,9 => UNS * INC # C6: 6 => UNS * DIS # A1: 2,9 => CTR => A1: 3 * INC # A1: 3 => UNS * INC # C6: 6,9 => UNS * DIS # C6: 2 => CTR => C6: 6,9 * INC # B7: 6,9 => UNS * INC # B7: 7 => UNS * DIS # E1: 2,9 => CTR => E1: 3,4,7 * INC # E1: 3,4,7 => UNS * DIS # E2: 2,9 => CTR => E2: 1,3,4,7 * INC # E2: 1,3,4,7 => UNS * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * INC # E3: 1,3,4,7 => UNS * INC # E7: 2,9 => UNS * DIS # E9: 2,9 => CTR => E9: 4,7 * INC # E9: 4,7 => UNS * INC # F1: 2,9 => UNS * INC # F2: 2,9 => UNS * INC # F3: 2,9 => UNS * DIS # F9: 2,9 => CTR => F9: 4,7 * INC # F9: 4,7 => UNS * INC # H4: 2,9 => UNS * INC # I4: 2,9 => UNS * DIS # G1: 2,9 => CTR => G1: 3,4 * INC # G1: 3,4 => UNS * DIS # G3: 2,9 => CTR => G3: 3,4,8 * INC # G3: 3,4,8 => UNS * DIS # C7: 3,9 => CTR => C7: 6,7 * INC # C7: 6,7 => UNS * PRF # C9: 3,9 => SOL * DIS # C9: 4,7,8 => CTR => C9: 3,9 * INC # A1: 3,9 => UNS * DIS # A1: 2 => CTR => A1: 3,9 * INC # E7: 2,9 => UNS * DIS # E9: 2,9 => CTR => E9: 4,7 * INC # E9: 4,7 => UNS * DIS # F9: 2,9 => CTR => F9: 4,7 * INC # F9: 4,7 => UNS * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * INC # G1: 4,9 => UNS * DIS # G3: 2,3 => CTR => G3: 4,8,9 * INC # G3: 4,8,9 => UNS * DIS # I8: 8,9 => CTR => I8: 7 * INC # I8: 7 => UNS * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * INC # I2: 2,8 => UNS * PRF # I3: 2,8 => SOL * INC # I3: 6,7,9 => UNS * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 2,9 => CTR => E1: 3,4,7 * INC E1: 3,4,7 # F1: 2,9 => UNS * DIS E1: 3,4,7 # E2: 2,9 => CTR => E2: 1,3,4,7 * INC E1: 3,4,7 + E2: 1,3,4,7 # F2: 2,9 => UNS * DIS E1: 3,4,7 + E2: 1,3,4,7 # E3: 2,9 => CTR => E3: 1,3,4,7 * INC E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 # F3: 2,9 => UNS * DIS E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 # C2: 2,9 => CTR => C2: 3,4,7,8 * INC E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 # H2: 2,9 => UNS * PRF E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 # I2: 2,9 => SOL * STA E1: 3,4,7 + E2: 1,3,4,7 + E3: 1,3,4,7 + C2: 3,4,7,8 + I2: 2,9 * CNT 9 HDP CHAINS / 9 HYP OPENED