Analysis of zz-www.sudokuoftheday.co.uk-20060505-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: 4.62..9......56...8....4........8..3........5.2.....7..9..1.53.23......41.74...6. initial
Autosolve
position: 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2 => SOL * DIS # A6: 3,9 => CTR => A6: 5 * DIS # B1: 1,7 => CTR => B1: 5 * DIS # D2: 1,7 => CTR => D2: 8 * PRF # D2: 8 => SOL * DIS # G2: 1,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * PRF # I2: 1,7 => SOL * DIS # D2: 1 => CTR => D2: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * DIS # D3: 7,9 => CTR => D3: 1 * DIS # E4: 7,9 => CTR => E4: 2,4,6 * DIS # E5: 7,9 => CTR => E5: 2,4,6 * DIS # E8: 7,9 => CTR => E8: 6,8 * DIS # H1: 1,5 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # B3: 1,5 => CTR => B3: 7 * DIS # E4: 4,6 => CTR => E4: 2,7,9 * PRF # C6: 1,9 => SOL * DIS # G5: 4,6 => CTR => G5: 1,8 * DIS # F5: 1,9 => CTR => F5: 7 * PRF # F5: 7 => SOL * PRF # C6: 1,9 => SOL * DIS # D8: 7,8 => CTR => D8: 6,9 * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * DIS # D2: 1 => CTR => D2: 7,8 * DIS # D8: 7,9 => CTR => D8: 6,8 * DIS # E8: 7,9 => CTR => E8: 6,8 * PRF # F5: 7,9 => SOL * DIS # F5: 1 => CTR => F5: 7,9 * PRF # G8: 7,8 => SOL * DIS # G8: 1 => CTR => G8: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # I2: 7,8 => SOL * DIS # G8: 1,8 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # H1: 5 => CTR => H1: 1,8 * CNT 42 HDP CHAINS / 73 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2 => SOL * STA C2: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.62..9......56...8....4........8..3........5.2.....7..9..1.53.23......41.74...6. | initial |
| 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 | autosolve |
| 456273981912856347873194652761528493348967125529341876694712538235689714187435269 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 3,9 B2: 1,7 C3: 2,3 E1: 7,8 E3: 7,9 G3: 3,6 H3: 1,5 I3: 2,6 B4: 4,6 C4: 1,9 B5: 4,6 F6: 1,9 H4: 2,9 H5: 2,9 D7: 7,8 F8: 7,9 I7: 7,8 H8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 0 pairs (X) / D3 = 1 => 19 pairs (_) F5,F6: 1.. / F5 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) G8,H8: 1.. / G8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) C4,G4: 1.. / C4 = 1 => 18 pairs (_) / G4 = 1 => 0 pairs (X) C2,C3: 2.. / C2 = 2 => 0 pairs (*) / C3 = 2 => 0 pairs (X) I2,I3: 2.. / I2 = 2 => 17 pairs (_) / I3 = 2 => 0 pairs (*) E4,E5: 2.. / E4 = 2 => 18 pairs (_) / E5 = 2 => 18 pairs (_) H4,H5: 2.. / H4 = 2 => 18 pairs (_) / H5 = 2 => 18 pairs (_) C2,I2: 2.. / C2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) C3,I3: 2.. / C3 = 2 => 17 pairs (_) / I3 = 2 => 0 pairs (*) E4,H4: 2.. / E4 = 2 => 18 pairs (_) / H4 = 2 => 18 pairs (_) E5,H5: 2.. / E5 = 2 => 18 pairs (_) / H5 = 2 => 18 pairs (_) G2,G3: 3.. / G2 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) D5,D6: 3.. / D5 = 3 => 19 pairs (_) / D6 = 3 => 19 pairs (_) C3,G3: 3.. / C3 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) B4,B5: 4.. / B4 = 4 => 17 pairs (_) / B5 = 4 => 17 pairs (_) E6,G6: 4.. / E6 = 4 => 18 pairs (_) / G6 = 4 => 24 pairs (_) B1,B3: 5.. / B1 = 5 => 19 pairs (_) / B3 = 5 => 0 pairs (X) H1,H3: 5.. / H1 = 5 => 0 pairs (X) / H3 = 5 => 19 pairs (_) A4,A6: 5.. / A4 = 5 => 0 pairs (X) / A6 = 5 => 19 pairs (_) D4,D6: 5.. / D4 = 5 => 19 pairs (_) / D6 = 5 => 0 pairs (X) B1,H1: 5.. / B1 = 5 => 19 pairs (_) / H1 = 5 => 0 pairs (X) B3,H3: 5.. / B3 = 5 => 0 pairs (X) / H3 = 5 => 19 pairs (_) A4,D4: 5.. / A4 = 5 => 0 pairs (X) / D4 = 5 => 19 pairs (_) A6,D6: 5.. / A6 = 5 => 19 pairs (_) / D6 = 5 => 0 pairs (X) G3,I3: 6.. / G3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) B4,B5: 6.. / B4 = 6 => 17 pairs (_) / B5 = 6 => 17 pairs (_) D8,E8: 6.. / D8 = 6 => 21 pairs (_) / E8 = 6 => 0 pairs (X) I3,I6: 6.. / I3 = 6 => 17 pairs (_) / I6 = 6 => 0 pairs (*) A4,A5: 7.. / A4 = 7 => 19 pairs (_) / A5 = 7 => 0 pairs (X) I7,G8: 7.. / I7 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) D7,I7: 7.. / D7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) F5,F8: 7.. / F5 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) G2,G8: 7.. / G2 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) E1,D2: 8.. / E1 = 8 => 0 pairs (X) / D2 = 8 => 0 pairs (_) C5,C6: 8.. / C5 = 8 => 18 pairs (_) / C6 = 8 => 23 pairs (_) C5,G5: 8.. / C5 = 8 => 18 pairs (_) / G5 = 8 => 23 pairs (_) D7,I7: 8.. / D7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) E1,E8: 8.. / E1 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) H1,H8: 8.. / H1 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 22 pairs (_) / C2 = 9 => 19 pairs (_) D3,E3: 9.. / D3 = 9 => 0 pairs (X) / E3 = 9 => 20 pairs (_) H4,H5: 9.. / H4 = 9 => 18 pairs (_) / H5 = 9 => 18 pairs (_) * DURATION: 0:00:59.574732 START: 22:54:57.415902 END: 22:55:56.990634 2019-04-30 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B4,B5,C3,C4,D7,E1,E3,F6,F8,G3,H3,H4,H5,H8,I3,I7) * 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 * PAIR A2: 3,9 BLK 1 C2: 3,9,2 # reduction candidate for 3,9 C2: 2 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 C2: 3,9 # 17 pairs * PAIR A2: 3,9 COL A A5: 3,9,7 # reduction candidate for 3,9 A5: 3,9 # 19 pairs A6: 3,9,5 # reduction candidate for 3,9 A6: 3,9 => CTR * 4.62.39......5674.8....43.65....8..37..3....5.2.5...7.694812537235..7..4187435269 A6: 5 # 19 pairs * PAIR B2: 1,7 BLK 1 B1: 1,7,5 # reduction candidate for 1,7 B1: 1,7 => CTR * 416283957....56.4.85...4.1......8..3........5.2.....71694.1253.235...184187435269 B1: 5 # 19 pairs B3: 1,7,5 # reduction candidate for 1,7 B3: 1,7 # 19 pairs * PAIR B2: 1,7 ROW 2 D2: 1,7,8 # reduction candidate for 1,7 D2: 1,7 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269 D2: 8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 G2: 1,7,3,8 # reduction candidate for 1,7 G2: 1,7 => CTR * 4.62.39.....856.428.2194356.....8..3........5.2.....7.694712538235.89714187435269 G2: 3,8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 I2: 1,7,2,8 # reduction candidate for 1,7 I2: 1,7 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 I2: 2,8 # 19 pairs * PAIR C3: 2,3 BLK 1 C2: 2,3,9 # reduction candidate for 2,3 C2: 2,3 # 22 pairs C2: 9 # 19 pairs * PAIR E1: 7,8 BLK 2 D2: 7,8,1 # reduction candidate for 7,8 D2: 1 => CTR * 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269 D2: 7,8 # 19 pairs * PAIR E1: 7,8 ROW 1 I1: 7,8,1 # reduction candidate for 7,8 I1: 7,8 => CTR * 4.62839.7....56.4.8....4........8..3........5.2.....7.694.1253.235...184187435269 I1: 1 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 * PAIR E1: 7,8 COL E E8: 7,8,6,9 # reduction candidate for 7,8 E8: 7,8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 E8: 6,9 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269 * PAIR E3: 7,9 BLK 2 D3: 7,9,1 # reduction candidate for 7,9 D3: 7,9 => CTR * 4.62839...7.156.4.8....4........8..3........5.2.....7.694.1253.235...7.4187435269 D3: 1 # 19 pairs * PAIR E3: 7,9 COL E E4: 7,9,2,4,6 # reduction candidate for 7,9 E4: 7,9 => CTR * 476283951....56.4.8....4........8.23....2..95.2..4..7.694812537235.6.184187435269 E4: 2,4,6 # 20 pairs E5: 7,9,2,4,6 # reduction candidate for 7,9 E5: 7,9 => CTR * 476283951....56.4.8....4.....1.28.93.......25.2..4..7.694812537235.6.184187435269 E5: 2,4,6 # 18 pairs E8: 7,9,6,8 # reduction candidate for 7,9 E8: 7,9 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.6948125372356..184187435269 E8: 6,8 # 19 pairs * PAIR H3: 1,5 BLK 3 H1: 1,5,8 # reduction candidate for 1,5 H1: 1,5 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269 H1: 8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 * PAIR H3: 1,5 ROW 3 B3: 1,5,7 # reduction candidate for 1,5 B3: 1,5 => CTR * 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269 B3: 7 # 19 pairs * PAIR B4: 4,6 ROW 4 E4: 4,6,2,7,9 # reduction candidate for 4,6 E4: 4,6 => CTR * 45627398191.8563478731946527.95.81233..62..95.2.....7.694712538235.89714187435269 E4: 2,7,9 # 18 pairs G4: 4,6,1 # reduction candidate for 4,6 G4: 4,6 # 18 pairs * PAIR C4: 1,9 BLK 4 C5: 1,9,3,8 # reduction candidate for 1,9 C5: 1,9 # 26 pairs C6: 1,9,3,8 # reduction candidate for 1,9 C6: 1,9 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 C6: 3,8 # 19 pairs * PAIR B5: 4,6 ROW 5 E5: 4,6,2,7,9 # reduction candidate for 4,6 E5: 4,6 # 20 pairs G5: 4,6,1,8 # reduction candidate for 4,6 G5: 4,6 => CTR * 4.62.39......5674.8....43.6.....8..3..8..1..5.2...9.7.694812537235..7..4187435269 G5: 1,8 # 19 pairs * PAIR F6: 1,9 BLK 5 F5: 1,9,7 # reduction candidate for 1,9 F5: 1,9 => CTR * 4.62.39......5674.8....43.6.....8..3........5.2.....7.694812537235..7..4187435269 F5: 7 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 * PAIR F6: 1,9 ROW 6 C6: 1,9,3,8 # reduction candidate for 1,9 C6: 1,9 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 C6: 3,8 # 19 pairs * PAIR H4: 2,9 ROW 4 E4: 2,9,4,6,7 # reduction candidate for 2,9 E4: 2,9 # 21 pairs E4: 4,6,7 # 18 pairs * PAIR H5: 2,9 ROW 5 E5: 2,9,4,6,7 # reduction candidate for 2,9 E5: 2,9 # 21 pairs E5: 4,6,7 # 18 pairs * PAIR D7: 7,8 BLK 8 D8: 7,8,6,9 # reduction candidate for 7,8 D8: 7,8 => CTR * 4.62839......56.4.8...74...7..5.8..3.....7..552...1.7.694812537235769184187435269 D8: 6,9 # 19 pairs E8: 7,8,6,9 # reduction candidate for 7,8 E8: 7,8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 E8: 6,9 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269 * PAIR D7: 7,8 COL D D2: 7,8,1 # reduction candidate for 7,8 D2: 1 => CTR * 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269 D2: 7,8 # 19 pairs * PAIR F8: 7,9 BLK 8 D8: 7,9,6,8 # reduction candidate for 7,9 D8: 7,9 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.694812537235.6..84187435269 D8: 6,8 # 19 pairs E8: 7,9,6,8 # reduction candidate for 7,9 E8: 7,9 => CTR * 476283951....56.4.8....4........8..3........5.2.....7.6948125372356..184187435269 E8: 6,8 # 19 pairs * PAIR F8: 7,9 COL F F5: 7,9,1 # reduction candidate for 7,9 F5: 7,9 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 F5: 1 => CTR * 4.62.39......5674.8....43.6.....8..3.....1..5.2...9.7.694812537235..7..4187435269 * PAIR I7: 7,8 BLK 9 G8: 7,8,1 # reduction candidate for 7,8 G8: 7,8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 G8: 1 => CTR * 4.62839.1....5674.8....43.6.....8..3........5.2.....7.694.12537235...184187435269 * PAIR I7: 7,8 COL I I1: 7,8,1 # reduction candidate for 7,8 I1: 7,8 => CTR * 4.62839.7....56.4.8....4........8..3........5.2.....7.694.1253.235...184187435269 I1: 1 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 I2: 7,8,1,2 # reduction candidate for 7,8 I2: 7,8 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 I2: 1,2 # 19 pairs * PAIR H8: 1,8 BLK 9 G8: 1,8,7 # reduction candidate for 1,8 G8: 1,8 => CTR * 4.62.39...1.85674.8....43.6.....8..3........5.2.....7.694.12537235.....4187435269 G8: 7 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 * PAIR H8: 1,8 COL H H1: 1,8,5 # reduction candidate for 1,8 H1: 5 => CTR * 416283957....56.4.85...4.1......8..3........5.2.....71694.1253.235...184187435269 H1: 1,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060505-absurd-base-pr-000.dot * REASONING * PRF # C2: 2 => SOL * DIS # A6: 3,9 => CTR => A6: 5 * DIS # B1: 1,7 => CTR => B1: 5 * DIS # D2: 1,7 => CTR => D2: 8 * PRF # D2: 8 => SOL * DIS # G2: 1,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * PRF # I2: 1,7 => SOL * DIS # D2: 1 => CTR => D2: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * DIS # D3: 7,9 => CTR => D3: 1 * DIS # E4: 7,9 => CTR => E4: 2,4,6 * DIS # E5: 7,9 => CTR => E5: 2,4,6 * DIS # E8: 7,9 => CTR => E8: 6,8 * DIS # H1: 1,5 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # B3: 1,5 => CTR => B3: 7 * DIS # E4: 4,6 => CTR => E4: 2,7,9 * PRF # C6: 1,9 => SOL * DIS # G5: 4,6 => CTR => G5: 1,8 * DIS # F5: 1,9 => CTR => F5: 7 * PRF # F5: 7 => SOL * PRF # C6: 1,9 => SOL * DIS # D8: 7,8 => CTR => D8: 6,9 * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * DIS # D2: 1 => CTR => D2: 7,8 * DIS # D8: 7,9 => CTR => D8: 6,8 * DIS # E8: 7,9 => CTR => E8: 6,8 * PRF # F5: 7,9 => SOL * DIS # F5: 1 => CTR => F5: 7,9 * PRF # G8: 7,8 => SOL * DIS # G8: 1 => CTR => G8: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # I2: 7,8 => SOL * DIS # G8: 1,8 => CTR => G8: 7 * PRF # G8: 7 => SOL * DIS # H1: 5 => CTR => H1: 1,8 * CNT 42 HDP CHAINS / 73 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B4,B5,C3,C4,D7,E1,E3,F6,F8,G3,H3,H4,H5,H8,I3,I7) * 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 * PAIR A2: 3,9 BLK 1 C2: 3,9,2 # reduction candidate for 3,9 C2: 2 => SOLVED * 456273981912856347873194652761528493348967125529341876694712538235689714187435269 * DURATION: 0:00:02.598470 START: 22:56:56.057284 END: 22:56:58.655754 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060505-absurd-base-pr-001.dot * REASONING * PRF # C2: 2 => SOL * STA C2: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060505, absurd
Solution
position: 456273981912856347873194652761528493348967125529341876694712538235689714187435269 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 # C2: 3,9 => UNS * PRF # C2: 2 => SOL * INC # A5: 3,9 => UNS * DIS # A6: 3,9 => CTR => A6: 5 * INC # A6: 5 => UNS * DIS # B1: 1,7 => CTR => B1: 5 * INC # B1: 5 => UNS * INC # B3: 1,7 => UNS * DIS # D2: 1,7 => CTR => D2: 8 * PRF # D2: 8 => SOL * DIS # G2: 1,7 => CTR => G2: 3,8 * PRF # G2: 3,8 => SOL * PRF # I2: 1,7 => SOL * INC # I2: 2,8 => UNS * INC # C2: 2,3 => UNS * INC # C2: 9 => UNS * INC # D2: 7,8 => UNS * DIS # D2: 1 => CTR => D2: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * DIS # D3: 7,9 => CTR => D3: 1 * INC # D3: 1 => UNS * DIS # E4: 7,9 => CTR => E4: 2,4,6 * INC # E4: 2,4,6 => UNS * DIS # E5: 7,9 => CTR => E5: 2,4,6 * INC # E5: 2,4,6 => UNS * DIS # E8: 7,9 => CTR => E8: 6,8 * INC # E8: 6,8 => UNS * DIS # H1: 1,5 => CTR => H1: 8 * PRF # H1: 8 => SOL * DIS # B3: 1,5 => CTR => B3: 7 * INC # B3: 7 => UNS * DIS # E4: 4,6 => CTR => E4: 2,7,9 * INC # E4: 2,7,9 => UNS * INC # G4: 4,6 => UNS * INC # C5: 1,9 => UNS * PRF # C6: 1,9 => SOL * INC # C6: 3,8 => UNS * INC # E5: 4,6 => UNS * DIS # G5: 4,6 => CTR => G5: 1,8 * INC # G5: 1,8 => UNS * DIS # F5: 1,9 => CTR => F5: 7 * PRF # F5: 7 => SOL * PRF # C6: 1,9 => SOL * INC # C6: 3,8 => UNS * INC # E4: 2,9 => UNS * INC # E4: 4,6,7 => UNS * INC # E5: 2,9 => UNS * INC # E5: 4,6,7 => UNS * DIS # D8: 7,8 => CTR => D8: 6,9 * INC # D8: 6,9 => UNS * PRF # E8: 7,8 => SOL * DIS # E8: 6,9 => CTR => E8: 7,8 * INC # D2: 7,8 => UNS * DIS # D2: 1 => CTR => D2: 7,8 * DIS # D8: 7,9 => CTR => D8: 6,8 * INC # D8: 6,8 => UNS * DIS # E8: 7,9 => CTR => E8: 6,8 * INC # E8: 6,8 => UNS * PRF # F5: 7,9 => SOL * DIS # F5: 1 => CTR => F5: 7,9 * PRF # G8: 7,8 => SOL * DIS # G8: 1 => CTR => G8: 7,8 * DIS # I1: 7,8 => CTR => I1: 1 * PRF # I1: 1 => SOL * PRF # I2: 7,8 => SOL * INC # I2: 1,2 => UNS * DIS # G8: 1,8 => CTR => G8: 7 * PRF # G8: 7 => SOL * INC # H1: 1,8 => UNS * DIS # H1: 5 => CTR => H1: 1,8 * CNT 73 HDP CHAINS / 73 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 3,9 => UNS * PRF # C2: 2 => SOL * STA C2: 2 * CNT 2 HDP CHAINS / 2 HYP OPENED