Analysis of xx-top500-425-base.sdk
Contents
Original Sudoku
level: medium
position: .....7.93.1......6.......4.3.94...........1..2...........32....5..9......7....8.. initial
Autosolve
position: .....7.93.1.....86.......413.94..6........1..2.17........32....5..97.....7....8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS # C1: 2,5 => CTR => C1: 4,6,8 * DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS # E4: 5,8 => CTR => E4: 1 * DIS # B1: 5,8 => CTR => B1: 2,4,6 * DIS # B3: 5,8 => CTR => B3: 2,3,6,9 * DIS # H5: 3,5 => CTR => H5: 2 * DIS # E6: 3,5 => CTR => E6: 6,8,9 * DIS # F6: 3,5 => CTR => F6: 6,9 * PRF # H9: 3,5 => SOL * DIS # H9: 1,2,6 => CTR => H9: 3,5 * DIS # I7: 4,9 => CTR => I7: 5,7 * DIS # I9: 4,9 => CTR => I9: 2,5 * PRF # I9: 2,5 => SOL * DIS # A7: 4,9 => CTR => A7: 1,6,8 * DIS # G6: 4,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # B8: 3,4 => SOL * DIS # B8: 2,6,8 => CTR => B8: 3,4 * DIS # C8: 3,4 => CTR => C8: 2,6,8 * PRF # G6: 3,4 => SOL * DIS # G6: 9 => CTR => G6: 3,4 * DIS # I9: 2,4 => CTR => I9: 5,9 * PRF # I9: 5,9 => SOL * DIS # B8: 2,4 => CTR => B8: 3,6,8 * DIS # C8: 2,4 => CTR => C8: 3,6,8 * DIS # I5: 2,4 => CTR => I5: 5,8,9 * CNT 27 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS D1: 1,6,8 # C1: 2,5 => CTR => C1: 4,6,8 * DIS D1: 1,6,8 + C1: 4,6,8 # B1: 4,6,8 => CTR => B1: 2,5 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # C5: 5,8 => CTR => C5: 4,6,7 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 # E4: 5,8 => CTR => E4: 1 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 # I4: 2,7 => CTR => I4: 5,8 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 # H5: 3,5 => CTR => H5: 2 * PRF D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 # H9: 3,5 => SOL * STA D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 + H9: 3,5 * CNT 8 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....7.93.1......6.......4.3.94...........1..2...........32....5..9......7....8.. | initial |
| .....7.93.1.....86.......413.94..6........1..2.17........32....5..97.....7....8.. | autosolve |
| 624187593713594286895236741359412678467853129281769354148325967536978412972641835 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) D2: 2,5 G1: 2,5 B4: 5,8 H6: 3,5 G7: 4,9 G8: 3,4 I8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 8 pairs (_) / E1 = 1 => 0 pairs (X) E4,F4: 1.. / E4 = 1 => 9 pairs (_) / F4 = 1 => 0 pairs (X) A7,A9: 1.. / A7 = 1 => 7 pairs (_) / A9 = 1 => 0 pairs (X) F8,H8: 1.. / F8 = 1 => 0 pairs (X) / H8 = 1 => 7 pairs (_) D1,D9: 1.. / D1 = 1 => 8 pairs (_) / D9 = 1 => 0 pairs (X) C9,H9: 3.. / C9 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) B3,B8: 3.. / B3 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) G6,G8: 3.. / G6 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) G2,G3: 7.. / G2 = 7 => 9 pairs (_) / G3 = 7 => 8 pairs (_) A5,C5: 7.. / A5 = 7 => 8 pairs (_) / C5 = 7 => 7 pairs (_) H4,I4: 7.. / H4 = 7 => 7 pairs (_) / I4 = 7 => 0 pairs (X) H7,I7: 7.. / H7 = 7 => 0 pairs (X) / I7 = 7 => 7 pairs (_) H4,H7: 7.. / H4 = 7 => 7 pairs (_) / H7 = 7 => 0 pairs (X) I4,I7: 7.. / I4 = 7 => 0 pairs (X) / I7 = 7 => 7 pairs (_) F7,F8: 8.. / F7 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) A9,I9: 9.. / A9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) B3,B7: 9.. / B3 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) G6,G7: 9.. / G6 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) * DURATION: 0:00:25.857178 START: 17:19:05.249666 END: 17:19:31.106844 2017-05-04 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,G1,G7,G8,H6,I8) * .....7.93.1.....86.......413.94..6........1..2.17........32....5..97.....7....8.. * PAIR D2: 2,5 BLK 2 D1: 2,5,1,6,8 # reduction candidate for 2,5 D1: 2,5 => CTR * ....17.93.1.....86.......413.94.16....7..21..2.17.....19.32.4..5..97.312.7.1..8.. D1: 1,6,8 # 7 pairs F2: 2,5,3,4,9 # reduction candidate for 2,5 F2: 2,5 # 12 pairs D3: 2,5,6,8 # reduction candidate for 2,5 D3: 2,5 # 10 pairs F3: 2,5,3,6,9 # reduction candidate for 2,5 F3: 2,5 # 9 pairs * PAIR D2: 2,5 ROW 2 C2: 2,5,3,4,7 # reduction candidate for 2,5 C2: 2,5 # 10 pairs G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 8 pairs * PAIR D2: 2,5 COL D D5: 2,5,6,8 # reduction candidate for 2,5 D5: 2,5 # 10 pairs D5: 6,8 # 8 pairs * PAIR G1: 2,5 BLK 3 G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 8 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 9 pairs * PAIR G1: 2,5 ROW 1 B1: 2,5,4,6,8 # reduction candidate for 2,5 B1: 2,5 # 8 pairs C1: 2,5,4,6,8 # reduction candidate for 2,5 C1: 2,5 => CTR * .....7.93.1.....86.......413.94..6........1..2.17......9.32.4..5..97.3.2.7....8.. C1: 4,6,8 # 7 pairs D1: 2,5,1,6,8 # reduction candidate for 2,5 D1: 2,5 => CTR * ....17.93.1.....86.......413.94.16....7..21..2.17.....19.32.4..5..97.312.7.1..8.. D1: 1,6,8 # 7 pairs * PAIR B4: 5,8 BLK 4 B5: 5,8,4,6 # reduction candidate for 5,8 B5: 5,8 # 9 pairs C5: 5,8,4,6,7 # reduction candidate for 5,8 C5: 5,8 # 12 pairs B6: 5,8,4,6 # reduction candidate for 5,8 B6: 5,8 # 9 pairs * PAIR B4: 5,8 ROW 4 E4: 5,8,1 # reduction candidate for 5,8 E4: 5,8 => CTR * .....7.93.1.....86.3.....413.94.16........1..2.17.....19.32.4..5..97.312.73...869 E4: 1 # 9 pairs I4: 5,8,2,7 # reduction candidate for 5,8 I4: 5,8 # 9 pairs * PAIR B4: 5,8 COL B B1: 5,8,2,4,6 # reduction candidate for 5,8 B1: 5,8 => CTR * .....7.93.1.....86.......413.94..6........1..2.17......9.32.4..5..97.3.2.7....8.. B1: 2,4,6 # 7 pairs B3: 5,8,2,3,6,9 # reduction candidate for 5,8 B3: 5,8 => CTR * .....7.93.1.....86.......413.94..6........1..2.17......9.32.4..53.97.....7....8.. B3: 2,3,6,9 # 7 pairs * PAIR H6: 3,5 BLK 6 H5: 3,5,2 # reduction candidate for 3,5 H5: 3,5 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.73...8.9 H5: 2 # 9 pairs * PAIR H6: 3,5 ROW 6 E6: 3,5,6,8,9 # reduction candidate for 3,5 E6: 3,5 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.73...8.9 E6: 6,8,9 # 7 pairs F6: 3,5,6,9 # reduction candidate for 3,5 F6: 3,5 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.73...8.9 F6: 6,9 # 8 pairs * PAIR H6: 3,5 COL H H9: 3,5,1,2,6 # reduction candidate for 3,5 H9: 3,5 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 H9: 1,2,6 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.73...8.9 * PAIR G7: 4,9 BLK 9 I7: 4,9,5,7 # reduction candidate for 4,9 I7: 4,9 => CTR * .....7.93.1.....86.......413.94..6.7......1..2.17........325.7.5..978.1..7....865 I7: 5,7 # 8 pairs I9: 4,9,2,5 # reduction candidate for 4,9 I9: 4,9 => CTR * .....7.93.1.....86.......413.94..6........1..2.17........32....5..97.....7....8.. I9: 2,5 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 * PAIR G7: 4,9 ROW 7 A7: 4,9,1,6,8 # reduction candidate for 4,9 A7: 4,9 => CTR * ...1.7.93.1.....86.......413.941.6........1..2.17..9.....32.4..5..97.3.217....8.9 A7: 1,6,8 # 7 pairs B7: 4,9,6,8 # reduction candidate for 4,9 B7: 4,9 # 10 pairs * PAIR G7: 4,9 COL G G6: 4,9,3 # reduction candidate for 4,9 G6: 4,9 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.73...8.9 G6: 3 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 * PAIR G8: 3,4 ROW 8 B8: 3,4,2,6,8 # reduction candidate for 3,4 B8: 3,4 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 B8: 2,6,8 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.7....8.. C8: 3,4,2,6,8 # reduction candidate for 3,4 C8: 3,4 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5.497.3.2.7....8.. C8: 2,6,8 # 7 pairs * PAIR G8: 3,4 COL G G6: 3,4,9 # reduction candidate for 3,4 G6: 3,4 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 G6: 9 => CTR * .....7.93.1.....86.......413.94..6........1..2.17..9.....32.4..5..97.3.2.7....8.. * PAIR I8: 2,4 BLK 9 I9: 2,4,5,9 # reduction candidate for 2,4 I9: 2,4 => CTR * .....7.93.1.....86.9.....413.94..6........1..2.17.....1..32....53.97.4.297....8.. I9: 5,9 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 * PAIR I8: 2,4 ROW 8 B8: 2,4,3,6,8 # reduction candidate for 2,4 B8: 2,4 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5..97.3.2.7....8.. B8: 3,6,8 # 7 pairs C8: 2,4,3,6,8 # reduction candidate for 2,4 C8: 2,4 => CTR * .....7.93.1.....86.3.....413.94..6........1..2.17......9.32.4..5.497.3.2.7....8.. C8: 3,6,8 # 7 pairs * PAIR I8: 2,4 COL I I5: 2,4,5,8,9 # reduction candidate for 2,4 I5: 2,4 => CTR * .2.1.759371..94286.9.2..741359412678..78391..2.17....91..325967536978412972641835 I5: 5,8,9 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-425-base-pr-000.dot * REASONING * DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS # C1: 2,5 => CTR => C1: 4,6,8 * DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS # E4: 5,8 => CTR => E4: 1 * DIS # B1: 5,8 => CTR => B1: 2,4,6 * DIS # B3: 5,8 => CTR => B3: 2,3,6,9 * DIS # H5: 3,5 => CTR => H5: 2 * DIS # E6: 3,5 => CTR => E6: 6,8,9 * DIS # F6: 3,5 => CTR => F6: 6,9 * PRF # H9: 3,5 => SOL * DIS # H9: 1,2,6 => CTR => H9: 3,5 * DIS # I7: 4,9 => CTR => I7: 5,7 * DIS # I9: 4,9 => CTR => I9: 2,5 * PRF # I9: 2,5 => SOL * DIS # A7: 4,9 => CTR => A7: 1,6,8 * DIS # G6: 4,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # B8: 3,4 => SOL * DIS # B8: 2,6,8 => CTR => B8: 3,4 * DIS # C8: 3,4 => CTR => C8: 2,6,8 * PRF # G6: 3,4 => SOL * DIS # G6: 9 => CTR => G6: 3,4 * DIS # I9: 2,4 => CTR => I9: 5,9 * PRF # I9: 5,9 => SOL * DIS # B8: 2,4 => CTR => B8: 3,6,8 * DIS # C8: 2,4 => CTR => C8: 3,6,8 * DIS # I5: 2,4 => CTR => I5: 5,8,9 * CNT 27 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,G1,G7,G8,H6,I8) * .....7.93.1.....86.......413.94..6........1..2.17........32....5..97.....7....8.. * PAIR D2: 2,5 BLK 2 D1: 2,5,1,6,8 # reduction candidate for 2,5 D1: 2,5 => CTR * ....17.93.1.....86.......413.94.16....7..21..2.17.....19.32.4..5..97.312.7.1..8.. F2: 2,5,3,4,9 # reduction candidate for 2,5 F2: 2,5 # 12 pairs D3: 2,5,6,8 # reduction candidate for 2,5 D3: 2,5 # 10 pairs F3: 2,5,3,6,9 # reduction candidate for 2,5 F3: 2,5 # 9 pairs * PAIR D2: 2,5 ROW 2 C2: 2,5,3,4,7 # reduction candidate for 2,5 C2: 2,5 # 10 pairs G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 8 pairs * PAIR D2: 2,5 COL D D5: 2,5,6,8 # reduction candidate for 2,5 D5: 2,5 # 10 pairs D5: 6,8 # 8 pairs * PAIR G1: 2,5 BLK 3 G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 8 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 9 pairs * PAIR G1: 2,5 ROW 1 B1: 2,5,4,6,8 # reduction candidate for 2,5 B1: 2,5 # 8 pairs C1: 2,5,4,6,8 # reduction candidate for 2,5 C1: 2,5 => CTR * .....7.93.1.....86.......413.94..6........1..2.17......9.32.4..5..97.3.2.7....8.. * RESTART * PAIR G1: 2,5 ROW 1 B1: 2,5,4,6,8 # reduction candidate for 2,5 B1: 4,6,8 => CTR * ...157293.1.2...86.......413.94..6....7...1..2.17......9.32.4..5..97.3.2.7....8.. * PAIR RESTART * PAIR G1: 2,5 BLK 3 G2: 2,5,7 # reduction candidate for 2,5 G2: 2,5 # 9 pairs G3: 2,5,7 # reduction candidate for 2,5 G3: 2,5 # 10 pairs * PAIR B4: 5,8 BLK 4 B5: 5,8,4,6 # reduction candidate for 5,8 B5: 5,8 # 10 pairs C5: 5,8,4,6,7 # reduction candidate for 5,8 C5: 5,8 => CTR * .....7.93.1.....86.......413.94..6..7.....1..2.17......9.32.4..5..97.3.2.7....8.. B6: 5,8,4,6 # reduction candidate for 5,8 B6: 5,8 # 10 pairs * PAIR B4: 5,8 ROW 4 E4: 5,8,1 # reduction candidate for 5,8 E4: 5,8 => CTR * .2...7593.1.....86.3.....413.94.16........1..2.17.....19.32.4..5.297.31..73...8.. I4: 5,8,2,7 # reduction candidate for 5,8 I4: 5,8 # 10 pairs * RESTART * PAIR B4: 5,8 ROW 4 I4: 5,8,2,7 # reduction candidate for 5,8 I4: 2,7 => CTR * .2.1.7593.1.....86.3.....4138941.6........1..2.17......9.32.4..5.297.3...73...8.. * PAIR RESTART * PAIR B4: 5,8 BLK 4 B5: 5,8,4,6 # reduction candidate for 5,8 B5: 5,8 # 12 pairs B6: 5,8,4,6 # reduction candidate for 5,8 B6: 5,8 # 13 pairs * PAIR H6: 3,5 BLK 6 H5: 3,5,2 # reduction candidate for 3,5 H5: 3,5 => CTR * .2.1.7593.1.....86.......413.941267.......1.22.17..4.9...32.9.75..97.3.4973...825 * PAIR H6: 3,5 COL H H9: 3,5,1,6 # reduction candidate for 3,5 H9: 3,5 => SOLVED * 624187593713594286895236741359412678467853129281769354148325967536978412972641835 * DURATION: 0:00:23.705752 START: 17:20:13.005171 END: 17:20:36.710923 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-425-base-pr-001.dot * REASONING * DIS # D1: 2,5 => CTR => D1: 1,6,8 * DIS D1: 1,6,8 # C1: 2,5 => CTR => C1: 4,6,8 * DIS D1: 1,6,8 + C1: 4,6,8 # B1: 4,6,8 => CTR => B1: 2,5 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # C5: 5,8 => CTR => C5: 4,6,7 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 # E4: 5,8 => CTR => E4: 1 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 # I4: 2,7 => CTR => I4: 5,8 * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 # H5: 3,5 => CTR => H5: 2 * PRF D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 # H9: 3,5 => SOL * STA D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 + H9: 3,5 * CNT 8 HDP CHAINS / 27 HYP OPENED
Header Info
Top 500 Minimum 17 425 solution: 624187593713594286895236741359412678467853129281769354148325967536978412972641835 info: 95158 FNBYK S8.f 46665 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 624187593713594286895236741359412678467853129281769354148325967536978412972641835 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 # D1: 2,5 => CTR => D1: 1,6,8 * INC # D1: 1,6,8 => UNS * INC # F2: 2,5 => UNS * INC # D3: 2,5 => UNS * INC # F3: 2,5 => UNS * INC # C2: 2,5 => UNS * INC # G2: 2,5 => UNS * INC # D5: 2,5 => UNS * INC # D5: 6,8 => UNS * INC # G2: 2,5 => UNS * INC # G3: 2,5 => UNS * INC # B1: 2,5 => UNS * DIS # C1: 2,5 => CTR => C1: 4,6,8 * INC # C1: 4,6,8 => UNS * DIS # D1: 2,5 => CTR => D1: 1,6,8 * INC # D1: 1,6,8 => UNS * INC # B5: 5,8 => UNS * INC # C5: 5,8 => UNS * INC # B6: 5,8 => UNS * DIS # E4: 5,8 => CTR => E4: 1 * INC # E4: 1 => UNS * INC # I4: 5,8 => UNS * DIS # B1: 5,8 => CTR => B1: 2,4,6 * INC # B1: 2,4,6 => UNS * DIS # B3: 5,8 => CTR => B3: 2,3,6,9 * INC # B3: 2,3,6,9 => UNS * DIS # H5: 3,5 => CTR => H5: 2 * INC # H5: 2 => UNS * DIS # E6: 3,5 => CTR => E6: 6,8,9 * INC # E6: 6,8,9 => UNS * DIS # F6: 3,5 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * PRF # H9: 3,5 => SOL * DIS # H9: 1,2,6 => CTR => H9: 3,5 * DIS # I7: 4,9 => CTR => I7: 5,7 * INC # I7: 5,7 => UNS * DIS # I9: 4,9 => CTR => I9: 2,5 * PRF # I9: 2,5 => SOL * DIS # A7: 4,9 => CTR => A7: 1,6,8 * INC # A7: 1,6,8 => UNS * INC # B7: 4,9 => UNS * DIS # G6: 4,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # B8: 3,4 => SOL * DIS # B8: 2,6,8 => CTR => B8: 3,4 * DIS # C8: 3,4 => CTR => C8: 2,6,8 * INC # C8: 2,6,8 => UNS * PRF # G6: 3,4 => SOL * DIS # G6: 9 => CTR => G6: 3,4 * DIS # I9: 2,4 => CTR => I9: 5,9 * PRF # I9: 5,9 => SOL * DIS # B8: 2,4 => CTR => B8: 3,6,8 * INC # B8: 3,6,8 => UNS * DIS # C8: 2,4 => CTR => C8: 3,6,8 * INC # C8: 3,6,8 => UNS * DIS # I5: 2,4 => CTR => I5: 5,8,9 * INC # I5: 5,8,9 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 2,5 => CTR => D1: 1,6,8 * INC D1: 1,6,8 # F2: 2,5 => UNS * INC D1: 1,6,8 # D3: 2,5 => UNS * INC D1: 1,6,8 # F3: 2,5 => UNS * INC D1: 1,6,8 # C2: 2,5 => UNS * INC D1: 1,6,8 # G2: 2,5 => UNS * INC D1: 1,6,8 # D5: 2,5 => UNS * INC D1: 1,6,8 # D5: 6,8 => UNS * INC D1: 1,6,8 # G2: 2,5 => UNS * INC D1: 1,6,8 # G3: 2,5 => UNS * INC D1: 1,6,8 # B1: 2,5 => UNS * DIS D1: 1,6,8 # C1: 2,5 => CTR => C1: 4,6,8 * INC D1: 1,6,8 + C1: 4,6,8 # B1: 2,5 => UNS * DIS D1: 1,6,8 + C1: 4,6,8 # B1: 4,6,8 => CTR => B1: 2,5 * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # G2: 2,5 => UNS * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # G3: 2,5 => UNS * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # B5: 5,8 => UNS * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 # C5: 5,8 => CTR => C5: 4,6,7 * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 # B6: 5,8 => UNS * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 # E4: 5,8 => CTR => E4: 1 * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 # I4: 5,8 => UNS * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 # I4: 5,8 => UNS * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 # I4: 2,7 => CTR => I4: 5,8 * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 # B5: 5,8 => UNS * INC D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 # B6: 5,8 => UNS * DIS D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 # H5: 3,5 => CTR => H5: 2 * PRF D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 # H9: 3,5 => SOL * STA D1: 1,6,8 + C1: 4,6,8 + B1: 2,5 + C5: 4,6,7 + E4: 1 + I4: 5,8 + H5: 2 + H9: 3,5 * CNT 27 HDP CHAINS / 27 HYP OPENED