Analysis of xx-top500-188-base.sdk
Contents
Original Sudoku
level: medium
position: 3.5.....8....21...............6...5369..7..............2....71.4..3...........2.. initial
Autosolve
position: 3.57...287...213.5....35......6...5369.573.4253.2......23.5.71.4..3.258..561.723. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,4 => CTR => B3: 6,8 * DIS # C3: 1,4 => CTR => C3: 2,8,9 * DIS # G1: 9 => CTR => G1: 1,4 * DIS # B4: 1,4 => CTR => B4: 7,8 * PRF # C3: 1,2 => SOL * DIS # C3: 4,8,9 => CTR => C3: 1,2 * DIS # G3: 6,9 => CTR => G3: 1,4 * PRF # H3: 6,9 => SOL * DIS # H3: 7 => CTR => H3: 6,9 * DIS # H6: 6,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # C4: 1,2 => CTR => C4: 4,7,8 * PRF # C4: 4,7,8 => SOL * DIS # B4: 1,8 => CTR => B4: 4,7 * DIS # C4: 1,8 => CTR => C4: 2,4,7 * PRF # C6: 1,8 => SOL * DIS # C3: 1,8 => CTR => C3: 2,4,9 * DIS # G4: 1,8 => CTR => G4: 9 * DIS # G6: 1,8 => CTR => G6: 6,9 * DIS # F7: 8,9 => CTR => F7: 4,6 * PRF # B4: 1,7 => SOL * DIS # B4: 4,8 => CTR => B4: 1,7 * DIS # C4: 1,7 => CTR => C4: 2,4,8 * PRF # C4: 2,4,8 => SOL * DIS # E9: 4 => CTR => E9: 8,9 * DIS # E9: 4,9 => CTR => E9: 8 * DIS # I7: 4,9 => CTR => I7: 6 * DIS # D3: 4,9 => CTR => D3: 8 * DIS # F7: 6,9 => CTR => F7: 4,8 * DIS # E1: 4 => CTR => E1: 6,9 * DIS # I7: 4 => CTR => I7: 6,9 * DIS # I7: 4,9 => CTR => I7: 6 * DIS # E9: 4,9 => CTR => E9: 8 * 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 # B3: 1,4 => CTR => B3: 6,8 * DIS B3: 6,8 # C3: 1,4 => CTR => C3: 2,8,9 * DIS B3: 6,8 + C3: 2,8,9 # G1: 9 => CTR => G1: 1,4 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 # B4: 1,4 => CTR => B4: 7,8 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 # G3: 6,9 => CTR => G3: 1,4 * PRF B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 => SOL * STA B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 * CNT 6 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.5.....8....21...............6...5369..7..............2....71.4..3...........2.. | initial |
| 3.57...287...213.5....35......6...5369.573.4253.2......23.5.71.4..3.258..561.723. | autosolve |
| 345796128789421365162835497274618953691573842538249671823954716417362589956187234 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 1,4 A3: 1,2 H2: 6,9 I3: 1,7 A4: 1,2 C5: 1,8 G5: 1,8 I6: 1,7 A7: 8,9 B8: 1,7 C8: 1,7 A9: 8,9 D7: 4,9 E8: 6,9 I8: 6,9 I9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E6: 1.. / E4 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) B1,G1: 1.. / B1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) C5,G5: 1.. / C5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) A3,A4: 1.. / A3 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) I3,I6: 1.. / I3 = 1 => 0 pairs (X) / I6 = 1 => 0 pairs (_) A3,C3: 2.. / A3 = 2 => 0 pairs (X) / C3 = 2 => 0 pairs (_) A4,C4: 2.. / A4 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) A3,A4: 2.. / A3 = 2 => 0 pairs (X) / A4 = 2 => 0 pairs (_) C3,C4: 2.. / C3 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) G1,G3: 4.. / G1 = 4 => 0 pairs (X) / G3 = 4 => 19 pairs (_) I7,I9: 4.. / I7 = 4 => 0 pairs (X) / I9 = 4 => 17 pairs (_) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 17 pairs (_) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 18 pairs (_) E1,F1: 6.. / E1 = 6 => 0 pairs (X) / F1 = 6 => 15 pairs (_) G6,H6: 6.. / G6 = 6 => 17 pairs (_) / H6 = 6 => 0 pairs (X) F7,E8: 6.. / F7 = 6 => 0 pairs (X) / E8 = 6 => 15 pairs (_) I7,I8: 6.. / I7 = 6 => 15 pairs (_) / I8 = 6 => 0 pairs (X) B2,H2: 6.. / B2 = 6 => 0 pairs (X) / H2 = 6 => 18 pairs (_) F7,I7: 6.. / F7 = 6 => 0 pairs (X) / I7 = 6 => 15 pairs (_) E8,I8: 6.. / E8 = 6 => 15 pairs (_) / I8 = 6 => 0 pairs (X) E1,E8: 6.. / E1 = 6 => 0 pairs (X) / E8 = 6 => 15 pairs (_) F1,F7: 6.. / F1 = 6 => 15 pairs (_) / F7 = 6 => 0 pairs (X) G3,G6: 6.. / G3 = 6 => 0 pairs (X) / G6 = 6 => 17 pairs (_) H3,I3: 7.. / H3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) B4,C4: 7.. / B4 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) H6,I6: 7.. / H6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) B4,B8: 7.. / B4 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) C4,C8: 7.. / C4 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) I3,I6: 7.. / I3 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 0 pairs (X) / D3 = 8 => 17 pairs (_) A7,A9: 8.. / A7 = 8 => 14 pairs (_) / A9 = 8 => 0 pairs (X) F7,E9: 8.. / F7 = 8 => 0 pairs (X) / E9 = 8 => 14 pairs (_) C5,G5: 8.. / C5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) A7,F7: 8.. / A7 = 8 => 14 pairs (_) / F7 = 8 => 0 pairs (X) A9,E9: 8.. / A9 = 8 => 0 pairs (X) / E9 = 8 => 14 pairs (_) C2,C3: 9.. / C2 = 9 => 19 pairs (_) / C3 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 0 pairs (X) / A9 = 9 => 14 pairs (_) E8,I8: 9.. / E8 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) * DURATION: 0:01:16.606045 START: 09:06:30.948732 END: 09:07:47.554777 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A9,B1,B8,C5,C8,D7,E8,G5,H2,I3,I6,I8,I9) * 3.57...287...213.5....35......6...5369.573.4253.2......23.5.71.4..3.258..561.723. * PAIR B1: 1,4 BLK 1 B3: 1,4,6,8 # reduction candidate for 1,4 B3: 1,4 => CTR * 3.57...2876..21395..9835....8.6...5369.573.4253.2......23.5.71.4..3.258..561.723. B3: 6,8 # 17 pairs C3: 1,4,2,8,9 # reduction candidate for 1,4 C3: 1,4 => CTR * 3.57...287.9.2136526.835...1.26...5369857314253421.6.7.2395.71.4.7362589956187234 C3: 2,8,9 # 16 pairs * PAIR B1: 1,4 ROW 1 G1: 1,4,9 # reduction candidate for 1,4 G1: 9 => CTR * 3157..9287...2136526..354711.26..853698573.4253.2......23.5.71.4..3.258..561.723. G1: 1,4 # 17 pairs * PAIR B1: 1,4 COL B B4: 1,4,7,8 # reduction candidate for 1,4 B4: 1,4 => CTR * 3.57...287...213.5..2.35...2176...5369857314253421...7.23.5.71.4713.258..561.723. B4: 7,8 # 18 pairs * PAIR A3: 1,2 BLK 1 C3: 1,2,4,8,9 # reduction candidate for 1,2 C3: 1,2 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 C3: 4,8,9 => CTR * 3.57...287...213.52...35...1.26...53698573.4253.2......23.5.71.4..3.258..561.723. * PAIR H2: 6,9 BLK 3 G3: 6,9,1,4 # reduction candidate for 6,9 G3: 6,9 => CTR * 3.57..4287...213.5....35..11.26...53698573.4253.2......23.5.71.4..3.258..561.723. G3: 1,4 # 18 pairs H3: 6,9,7 # reduction candidate for 6,9 H3: 6,9 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 H3: 7 => CTR * 3.57...287...213.5....35.711.26...53698573.4253.2......23.5.71.4..3.258..561.723. * PAIR H2: 6,9 COL H H6: 6,9,7 # reduction candidate for 6,9 H6: 6,9 => CTR * 3.57...287...213.5....35.711.26...53698573.4253.2......23.5.71.4..3.258..561.723. H6: 7 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 * PAIR A4: 1,2 BLK 4 C4: 1,2,4,7,8 # reduction candidate for 1,2 C4: 1,2 => CTR * 3457..1287..4213.5...8354.7.7.6...5369.573.425342......23.5.71.4173.258..561.723. C4: 4,7,8 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 * PAIR C5: 1,8 BLK 4 B4: 1,8,4,7 # reduction candidate for 1,8 B4: 1,8 => CTR * 3.57...287...213.5..2.35...2176...5369857314253421...7.23.5.71.4713.258..561.723. B4: 4,7 # 20 pairs C4: 1,8,2,4,7 # reduction candidate for 1,8 C4: 1,8 => CTR * 3457..1287.942136516283549727.6...536915738425342..671.2395.71.417362589956187234 C4: 2,4,7 # 16 pairs C6: 1,8,4 # reduction candidate for 1,8 C6: 1,8 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 C6: 4 # 18 pairs * PAIR C5: 1,8 COL C C3: 1,8,2,4,9 # reduction candidate for 1,8 C3: 1,8 => CTR * 3.57...287.9.2136526..35...1.26...5369857314253421.6.7.23.5.71.4.73.258..561.723. C3: 2,4,9 # 16 pairs * PAIR G5: 1,8 BLK 6 G4: 1,8,9 # reduction candidate for 1,8 G4: 1,8 => CTR * 3157...287...213.52...35.711.26..853698573.4253.2......23.5.71.4..3.258..561.723. G4: 9 # 19 pairs G6: 1,8,6,9 # reduction candidate for 1,8 G6: 1,8 => CTR * 3.57..42876..21395..9.356711.26..953698573.4253.2...67.23.5.71.4..3.258..561.723. G6: 6,9 # 17 pairs * PAIR A7: 8,9 ROW 7 F7: 8,9,4,6 # reduction candidate for 8,9 F7: 8,9 => CTR * 3.57469287...21365.6..354711.26..853698573.4253.2......2345.7164..362589.561.7234 F7: 4,6 # 15 pairs * PAIR B8: 1,7 COL B B4: 1,7,4,8 # reduction candidate for 1,7 B4: 1,7 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 B4: 4,8 => CTR * 3.57...287...213.5....35.....76...5369.573.4253.2......23.5.71.4713.258..561.723. * PAIR C8: 1,7 COL C C4: 1,7,2,4,8 # reduction candidate for 1,7 C4: 1,7 => CTR * 3.57...287.9.213651628354972..6...5369.573.425342..671.2395.71.4..362589956187234 C4: 2,4,8 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 * PAIR A9: 8,9 ROW 9 E9: 8,9,4 # reduction candidate for 8,9 E9: 4 => CTR * 3.57...287...213.5....35......6...5369.573.4253.2......23.587164..362589.561.723. E9: 8,9 # 17 pairs * PAIR D7: 4,9 BLK 8 F7: 4,9,6,8 # reduction candidate for 4,9 F7: 4,9 # 13 pairs E9: 4,9,8 # reduction candidate for 4,9 E9: 4,9 => CTR * 3.57469287...21365.6..354711.268..5369.573.4253.2......23.587164..362589856197234 E9: 8 # 14 pairs * PAIR D7: 4,9 ROW 7 I7: 4,9,6 # reduction candidate for 4,9 I7: 4,9 => CTR * 3.57649287...21365.6..354711.2649853698573.4253.2.....8234567194..392586956187234 I7: 6 # 15 pairs * PAIR D7: 4,9 COL D D2: 4,9,8 # reduction candidate for 4,9 D2: 4,9 # 17 pairs D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 => CTR * 3157...287..8213.52...35...1.26...53698573.4253.2......23.5.71.4..3.258..561.723. D3: 8 # 17 pairs * PAIR E8: 6,9 BLK 8 F7: 6,9,4,8 # reduction candidate for 6,9 F7: 6,9 => CTR * 3157..9287...2136526..354711.26..853698573.4253.2.....82345.71.4..3.258.956187234 F7: 4,8 # 16 pairs * PAIR E8: 6,9 COL E E1: 6,9,4 # reduction candidate for 6,9 E1: 4 => CTR * 3.57469287...21365.6..354711.26..853698573.4253.2......23.5.71.4..3.258..561.723. E1: 6,9 # 19 pairs * PAIR I8: 6,9 BLK 9 I7: 6,9,4 # reduction candidate for 6,9 I7: 4 => CTR * 3.57...287...213.5....35......6...5369.573.4253.2......23.567144..39258..561.723. I7: 6,9 # 17 pairs * PAIR I9: 4,9 BLK 9 I7: 4,9,6 # reduction candidate for 4,9 I7: 4,9 => CTR * 3.57649287...21365.6..354711.2649853698573.4253.2.....8234567194..392586956187234 I7: 6 # 15 pairs * PAIR I9: 4,9 ROW 9 E9: 4,9,8 # reduction candidate for 4,9 E9: 4,9 => CTR * 3.57469287...21365.6..354711.268..5369.573.4253.2......23.587164..362589856197234 E9: 8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-188-base-pr-000.dot * REASONING * DIS # B3: 1,4 => CTR => B3: 6,8 * DIS # C3: 1,4 => CTR => C3: 2,8,9 * DIS # G1: 9 => CTR => G1: 1,4 * DIS # B4: 1,4 => CTR => B4: 7,8 * PRF # C3: 1,2 => SOL * DIS # C3: 4,8,9 => CTR => C3: 1,2 * DIS # G3: 6,9 => CTR => G3: 1,4 * PRF # H3: 6,9 => SOL * DIS # H3: 7 => CTR => H3: 6,9 * DIS # H6: 6,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # C4: 1,2 => CTR => C4: 4,7,8 * PRF # C4: 4,7,8 => SOL * DIS # B4: 1,8 => CTR => B4: 4,7 * DIS # C4: 1,8 => CTR => C4: 2,4,7 * PRF # C6: 1,8 => SOL * DIS # C3: 1,8 => CTR => C3: 2,4,9 * DIS # G4: 1,8 => CTR => G4: 9 * DIS # G6: 1,8 => CTR => G6: 6,9 * DIS # F7: 8,9 => CTR => F7: 4,6 * PRF # B4: 1,7 => SOL * DIS # B4: 4,8 => CTR => B4: 1,7 * DIS # C4: 1,7 => CTR => C4: 2,4,8 * PRF # C4: 2,4,8 => SOL * DIS # E9: 4 => CTR => E9: 8,9 * DIS # E9: 4,9 => CTR => E9: 8 * DIS # I7: 4,9 => CTR => I7: 6 * DIS # D3: 4,9 => CTR => D3: 8 * DIS # F7: 6,9 => CTR => F7: 4,8 * DIS # E1: 4 => CTR => E1: 6,9 * DIS # I7: 4 => CTR => I7: 6,9 * DIS # I7: 4,9 => CTR => I7: 6 * DIS # E9: 4,9 => CTR => E9: 8 * CNT 33 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A9,B1,B8,C5,C8,D7,E8,G5,H2,I3,I6,I8,I9) * 3.57...287...213.5....35......6...5369.573.4253.2......23.5.71.4..3.258..561.723. * PAIR B1: 1,4 BLK 1 B3: 1,4,6,8 # reduction candidate for 1,4 B3: 1,4 => CTR * 3.57...2876..21395..9835....8.6...5369.573.4253.2......23.5.71.4..3.258..561.723. C3: 1,4,2,8,9 # reduction candidate for 1,4 C3: 1,4 => CTR * 3.57...287.9.2136526.835...1.26...5369857314253421.6.7.2395.71.4.7362589956187234 * RESTART * PAIR B1: 1,4 ROW 1 G1: 1,4,9 # reduction candidate for 1,4 G1: 9 => CTR * 3157..9287...2136526..354711.26..853698573.4253.2......23.5.71.4..3.258..561.723. * PAIR B1: 1,4 COL B B4: 1,4,7,8 # reduction candidate for 1,4 B4: 1,4 => CTR * 3.5796.287...213.5..2.35...21764..5369857314253421...7823954716471362589956187234 * PAIR RESTART * PAIR H2: 6,9 BLK 3 G3: 6,9,1,4 # reduction candidate for 6,9 G3: 6,9 => CTR * 3.579642874.821365.684359711..6...5369.573.4253.2.....8239547164..362589956187234 G3: 1,4 => SOLVED * 345796128789421365162835497274618953691573842538249671823954716417362589956187234 * DURATION: 0:00:09.215258 START: 09:08:45.450085 END: 09:08:54.665343 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-188-base-pr-001.dot * REASONING * DIS # B3: 1,4 => CTR => B3: 6,8 * DIS B3: 6,8 # C3: 1,4 => CTR => C3: 2,8,9 * DIS B3: 6,8 + C3: 2,8,9 # G1: 9 => CTR => G1: 1,4 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 # B4: 1,4 => CTR => B4: 7,8 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 # G3: 6,9 => CTR => G3: 1,4 * PRF B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 => SOL * STA B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 * CNT 6 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 188 solution: 345796128789421365162835497274618953691573842538249671823954716417362589956187234 info: 1836 FNBTWY S8.f 29756 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 345796128789421365162835497274618953691573842538249671823954716417362589956187234 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 # B3: 1,4 => CTR => B3: 6,8 * INC # B3: 6,8 => UNS * DIS # C3: 1,4 => CTR => C3: 2,8,9 * INC # C3: 2,8,9 => UNS * INC # G1: 1,4 => UNS * DIS # G1: 9 => CTR => G1: 1,4 * DIS # B4: 1,4 => CTR => B4: 7,8 * INC # B4: 7,8 => UNS * PRF # C3: 1,2 => SOL * DIS # C3: 4,8,9 => CTR => C3: 1,2 * DIS # G3: 6,9 => CTR => G3: 1,4 * INC # G3: 1,4 => UNS * PRF # H3: 6,9 => SOL * DIS # H3: 7 => CTR => H3: 6,9 * DIS # H6: 6,9 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # C4: 1,2 => CTR => C4: 4,7,8 * PRF # C4: 4,7,8 => SOL * DIS # B4: 1,8 => CTR => B4: 4,7 * INC # B4: 4,7 => UNS * DIS # C4: 1,8 => CTR => C4: 2,4,7 * INC # C4: 2,4,7 => UNS * PRF # C6: 1,8 => SOL * INC # C6: 4 => UNS * DIS # C3: 1,8 => CTR => C3: 2,4,9 * INC # C3: 2,4,9 => UNS * DIS # G4: 1,8 => CTR => G4: 9 * INC # G4: 9 => UNS * DIS # G6: 1,8 => CTR => G6: 6,9 * INC # G6: 6,9 => UNS * DIS # F7: 8,9 => CTR => F7: 4,6 * INC # F7: 4,6 => UNS * PRF # B4: 1,7 => SOL * DIS # B4: 4,8 => CTR => B4: 1,7 * DIS # C4: 1,7 => CTR => C4: 2,4,8 * PRF # C4: 2,4,8 => SOL * INC # E9: 8,9 => UNS * DIS # E9: 4 => CTR => E9: 8,9 * INC # F7: 4,9 => UNS * DIS # E9: 4,9 => CTR => E9: 8 * INC # E9: 8 => UNS * DIS # I7: 4,9 => CTR => I7: 6 * INC # I7: 6 => UNS * INC # D2: 4,9 => UNS * DIS # D3: 4,9 => CTR => D3: 8 * INC # D3: 8 => UNS * DIS # F7: 6,9 => CTR => F7: 4,8 * INC # F7: 4,8 => UNS * INC # E1: 6,9 => UNS * DIS # E1: 4 => CTR => E1: 6,9 * INC # I7: 6,9 => UNS * DIS # I7: 4 => CTR => I7: 6,9 * DIS # I7: 4,9 => CTR => I7: 6 * INC # I7: 6 => UNS * DIS # E9: 4,9 => CTR => E9: 8 * INC # E9: 8 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 1,4 => CTR => B3: 6,8 * DIS B3: 6,8 # C3: 1,4 => CTR => C3: 2,8,9 * INC B3: 6,8 + C3: 2,8,9 # G1: 1,4 => UNS * DIS B3: 6,8 + C3: 2,8,9 # G1: 9 => CTR => G1: 1,4 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 # B4: 1,4 => CTR => B4: 7,8 * DIS B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 # G3: 6,9 => CTR => G3: 1,4 * PRF B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 => SOL * STA B3: 6,8 + C3: 2,8,9 + G1: 1,4 + B4: 7,8 + G3: 1,4 * CNT 7 HDP CHAINS / 6 HYP OPENED