Analysis of zz-sudoku-de-767664-base.sdk
Contents
Original Sudoku
level: medium
position: .2.7.1.6...7...8...8.3.2.7..54...71.8.......2.16...93..4.9.7.5...9...2...3.8.5.9. initial
Autosolve
position: .25781.6.3.7...821.813.2.7..54...71.8.3....42.16...93..48927.5.5.9...28..328.5.9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 4,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # I1: 3 => CTR => I1: 4,9 * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E2: 6,9 => CTR => E2: 4,5 * DIS # E2: 6,9 => CTR => E2: 4,5 * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E4: 6,9 => CTR => E4: 3 * DIS # E5: 6,9 => CTR => E5: 1,5,7 * DIS # I1: 3,4 => CTR => I1: 9 * DIS # I3: 9 => CTR => I3: 4,5 * DIS # E5: 7,9 => CTR => E5: 1,5,6 * PRF # E5: 1,5,6 => SOL * DIS # E4: 6,9 => CTR => E4: 3 * DIS # F4: 6,9 => CTR => F4: 3,8 * DIS # E5: 6,9 => CTR => E5: 1,5,7 * DIS # F2: 4 => CTR => F2: 6,9 * PRF # F4: 6,8 => SOL * DIS # F4: 3,9 => CTR => F4: 6,8 * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 1,7,9 * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * DIS # G7: 3 => CTR => G7: 1,6 * DIS # A9: 1 => CTR => A9: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * PRF # E8: 4,6 => SOL * DIS # F8: 4,6 => CTR => F8: 3 * DIS # G9: 4,6 => CTR => G9: 1 * PRF # I9: 4,6 => SOL * DIS # I9: 7 => CTR => I9: 4,6 * DIS # E2: 4,6 => CTR => E2: 5,9 * DIS # G7: 1 => CTR => G7: 3,6 * CNT 34 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 4,9 => CTR => A3: 6 * PRF A3: 6 => SOL * STA A3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.7.1.6...7...8...8.3.2.7..54...71.8.......2.16...93..4.9.7.5...9...2...3.8.5.9. | initial |
| .25781.6.3.7...821.813.2.7..54...71.8.3....42.16...93..48927.5.5.9...28..328.5.9. | autosolve |
| 425781369397456821681392475954238716873619542216574938148927653569143287732865194 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 4,9 B2: 6,9 E3: 6,9 G1: 3,4 G3: 4,5 A4: 2,9 B5: 7,9 A6: 2,7 D4: 2,6 F5: 6,9 F6: 4,8 I4: 6,8 G5: 5,6 I6: 5,8 A7: 1,6 B8: 6,7 E9: 4,6 I7: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,E5: 1.. / D5 = 1 => 19 pairs (_) / E5 = 1 => 0 pairs (*) A7,A9: 1.. / A7 = 1 => 23 pairs (_) / A9 = 1 => 0 pairs (X) D8,E8: 1.. / D8 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) G7,G9: 1.. / G7 = 1 => 0 pairs (X) / G9 = 1 => 23 pairs (_) A7,G7: 1.. / A7 = 1 => 23 pairs (_) / G7 = 1 => 0 pairs (X) A9,G9: 1.. / A9 = 1 => 0 pairs (X) / G9 = 1 => 23 pairs (_) D5,D8: 1.. / D5 = 1 => 19 pairs (_) / D8 = 1 => 0 pairs (*) E5,E8: 1.. / E5 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) A4,A6: 2.. / A4 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) D4,D6: 2.. / D4 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 0 pairs (X) / D4 = 2 => 0 pairs (_) A6,D6: 2.. / A6 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) G1,I1: 3.. / G1 = 3 => 18 pairs (_) / I1 = 3 => 0 pairs (X) E4,F4: 3.. / E4 = 3 => 18 pairs (_) / F4 = 3 => 0 pairs (X) E8,F8: 3.. / E8 = 3 => 0 pairs (X) / F8 = 3 => 18 pairs (_) G7,I7: 3.. / G7 = 3 => 0 pairs (X) / I7 = 3 => 18 pairs (_) E4,E8: 3.. / E4 = 3 => 18 pairs (_) / E8 = 3 => 0 pairs (X) F4,F8: 3.. / F4 = 3 => 0 pairs (X) / F8 = 3 => 18 pairs (_) G1,G7: 3.. / G1 = 3 => 18 pairs (_) / G7 = 3 => 0 pairs (X) I1,I7: 3.. / I1 = 3 => 0 pairs (X) / I7 = 3 => 18 pairs (_) A1,A3: 4.. / A1 = 4 => 18 pairs (_) / A3 = 4 => 0 pairs (X) D2,E2: 5.. / D2 = 5 => 23 pairs (_) / E2 = 5 => 20 pairs (_) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) G5,I6: 5.. / G5 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) G3,G5: 5.. / G3 = 5 => 0 pairs (X) / G5 = 5 => 0 pairs (_) I3,I6: 5.. / I3 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) B2,A3: 6.. / B2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) I4,G5: 6.. / I4 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) A3,E3: 6.. / A3 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) B2,B8: 6.. / B2 = 6 => 0 pairs (X) / B8 = 6 => 0 pairs (_) B5,A6: 7.. / B5 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) E5,E6: 7.. / E5 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) B8,A9: 7.. / B8 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) I8,I9: 7.. / I8 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B5,E5: 7.. / B5 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) A6,E6: 7.. / A6 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) B8,I8: 7.. / B8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) A9,I9: 7.. / A9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) A6,A9: 7.. / A6 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) B5,B8: 7.. / B5 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) F4,F6: 8.. / F4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) I4,I6: 8.. / I4 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) F4,I4: 8.. / F4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) F6,I6: 8.. / F6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) I1,I3: 9.. / I1 = 9 => 18 pairs (_) / I3 = 9 => 0 pairs (X) A4,B5: 9.. / A4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) A1,I1: 9.. / A1 = 9 => 0 pairs (X) / I1 = 9 => 18 pairs (_) B2,B5: 9.. / B2 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) * DURATION: 0:01:14.036670 START: 08:37:23.541175 END: 08:38:37.577845 2017-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A7,B2,B5,B8,D4,E3,E9,F5,F6,G1,G3,G5,I4,I6,I7) * .25781.6.3.7...821.813.2.7..54...71.8.3....42.16...93..48927.5.5.9...28..328.5.9. * PAIR A1: 4,9 BLK 1 A3: 4,9,6 # reduction candidate for 4,9 A3: 4,9 => CTR * .25781.6.367...821.81362.7..54...71.893.765427162..93..48927.5.5.9...28..328.5.9. A3: 6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 * PAIR A1: 4,9 ROW 1 I1: 4,9,3 # reduction candidate for 4,9 I1: 3 => CTR * 925781463367...8214813625792546..718893....42.16...93..48927.5.5.9...28..328.5.9. I1: 4,9 # 18 pairs * PAIR B2: 6,9 BLK 1 A3: 6,9,4 # reduction candidate for 6,9 A3: 4 => CTR * .25781.6.367...821481362579.54...71.893.76.42.16...93..48927.5.5.9...28..328.5.9. A3: 6,9 # 18 pairs * PAIR B2: 6,9 ROW 2 E2: 6,9,4,5 # reduction candidate for 6,9 E2: 6,9 => CTR * .25781.6.3.75.4821.813.257..54...7188.3.5.642.16.78935.48927.5.5.9.1328.73284519. E2: 4,5 # 19 pairs F2: 6,9,4 # reduction candidate for 6,9 F2: 6,9 # 23 pairs * PAIR E3: 6,9 BLK 2 E2: 6,9,4,5 # reduction candidate for 6,9 E2: 6,9 => CTR * .25781.6.3.75.4821.813.257..54...7188.3.5.642.16.78935.48927.5.5.9.1328.73284519. E2: 4,5 # 19 pairs F2: 6,9,4 # reduction candidate for 6,9 F2: 6,9 # 23 pairs * PAIR E3: 6,9 ROW 3 A3: 6,9,4 # reduction candidate for 6,9 A3: 4 => CTR * .25781.6.367...821481362579.54...71.893.76.42.16...93..48927.5.5.9...28..328.5.9. A3: 6,9 # 18 pairs * PAIR E3: 6,9 COL E E4: 6,9,3 # reduction candidate for 6,9 E4: 6,9 => CTR * .25781463397...821.813.257..54..37188.3.19642.16.78935.48927.5.5.913.28.7328.519. E4: 3 # 18 pairs E5: 6,9,1,5,7 # reduction candidate for 6,9 E5: 6,9 => CTR * .25781.6.3.7...821.813.2.7..54...71.8731..542216.7.938.48927.5.56941.28..328.5.9. E5: 1,5,7 # 18 pairs * PAIR G1: 3,4 BLK 3 I1: 3,4,9 # reduction candidate for 3,4 I1: 3,4 => CTR * 925781.6.367...8214813625792546..718893....42.16...93..48927.5.5.9...28..328.5.9. I1: 9 # 18 pairs * PAIR G3: 4,5 BLK 3 I3: 4,5,9 # reduction candidate for 4,5 I3: 9 => CTR * 925781.6.367...8214813625792546..718893...642.16...935.48927.5.5.9...28..328.5.9. I3: 4,5 # 18 pairs * PAIR B5: 7,9 ROW 5 E5: 7,9,1,5,6 # reduction candidate for 7,9 E5: 7,9 => CTR * 4257813693.7..9821981362475254.387168.31.6542.16..4938.48927.535.9.1328..328.5.9. E5: 1,5,6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 * PAIR F5: 6,9 BLK 5 E4: 6,9,3 # reduction candidate for 6,9 E4: 6,9 => CTR * .25781463397...821.813.257..54..37188.3.19642.16.78935.48927.5.5.913.28.7328.519. E4: 3 # 18 pairs F4: 6,9,3,8 # reduction candidate for 6,9 F4: 6,9 => CTR * .25781.6.397..4821681392574954236718873..964221647893514892735.5.9..328..328.5.9. F4: 3,8 # 19 pairs E5: 6,9,1,5,7 # reduction candidate for 6,9 E5: 6,9 => CTR * .25781.6.3.7...821.813.2.7..54...71.8731..542216.7.938.48927.5.56941.28..328.5.9. E5: 1,5,7 # 18 pairs * PAIR F5: 6,9 COL F F2: 6,9,4 # reduction candidate for 6,9 F2: 4 => CTR * .25781.6.397..48216813925749542..718873..964221647893514892735.5.9...28..328.5.9. F2: 6,9 # 23 pairs * PAIR I4: 6,8 ROW 4 F4: 6,8,3,9 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 F4: 3,9 => CTR * .25781.6.397...821681392574954263718873..964221647893514892735.5.9...28..328.5.9. * PAIR G5: 5,6 ROW 5 D5: 5,6,1 # reduction candidate for 5,6 D5: 5,6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 D5: 1 # 19 pairs E5: 5,6,1,7,9 # reduction candidate for 5,6 E5: 5,6 => CTR * .25781.6.3.7...821.813.2.7..54...71.8731.9.42216.7.93..48927.5.569413287732865194 E5: 1,7,9 # 18 pairs * PAIR A7: 1,6 BLK 7 A9: 1,6,7 # reduction candidate for 1,6 A9: 1,6 => CTR * .25781.6.367...821.81362.7.2546..718893....427162..93..48927.5.579...28..328.5.97 A9: 7 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 * PAIR A7: 1,6 ROW 7 G7: 1,6,3 # reduction candidate for 1,6 G7: 3 => CTR * 925781463367..48214813625792546..7188.3...642.16..89351489273565.9...28.632845197 G7: 1,6 # 18 pairs * PAIR B8: 6,7 BLK 7 A9: 6,7,1 # reduction candidate for 6,7 A9: 1 => CTR * .25781.6.367...821.81362.7.2546..718893....427162..93..48927.5.579...28.1328.5.97 A9: 6,7 # 23 pairs * PAIR B8: 6,7 ROW 8 I8: 6,7,4 # reduction candidate for 6,7 I8: 6,7 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 I8: 4 => CTR * .25781.6.367...821.81362.7..54...71.893.765427162..93..48927.5.579...284.32845.97 * PAIR E9: 4,6 BLK 8 D8: 4,6,1 # reduction candidate for 4,6 D8: 4,6 # 19 pairs E8: 4,6,1,3 # reduction candidate for 4,6 E8: 4,6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 E8: 1,3 # 19 pairs F8: 4,6,3 # reduction candidate for 4,6 F8: 4,6 => CTR * .25781463397...821.813.257..54..37188.3.19642.16.78935.48927.5.5.913.28.7328.519. F8: 3 # 18 pairs * PAIR E9: 4,6 ROW 9 G9: 4,6,1 # reduction candidate for 4,6 G9: 4,6 => CTR * .2578136.367...821.81362.7.2546..718893....427162..93.648927153579...28.1328.5.97 G9: 1 # 23 pairs I9: 4,6,7 # reduction candidate for 4,6 I9: 4,6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 I9: 7 => CTR * .25781.6.367...821.81362.7.2546..718893....427162..93..48927.5.579...28..328.5.97 * PAIR E9: 4,6 COL E E2: 4,6,5,9 # reduction candidate for 4,6 E2: 4,6 => CTR * .25781.6.3.75..821681392.7..54.3.71.8.31...42.16...93.148927.5.569413287732865194 E2: 5,9 # 19 pairs * PAIR I7: 3,6 BLK 9 G7: 3,6,1 # reduction candidate for 3,6 G7: 1 => CTR * .2578136.367...821.81362.7.2546..718893....427162..93.648927153579...28.1328.5.97 G7: 3,6 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-767664-base-pr-000.dot * REASONING * DIS # A3: 4,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * DIS # I1: 3 => CTR => I1: 4,9 * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E2: 6,9 => CTR => E2: 4,5 * DIS # E2: 6,9 => CTR => E2: 4,5 * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E4: 6,9 => CTR => E4: 3 * DIS # E5: 6,9 => CTR => E5: 1,5,7 * DIS # I1: 3,4 => CTR => I1: 9 * DIS # I3: 9 => CTR => I3: 4,5 * DIS # E5: 7,9 => CTR => E5: 1,5,6 * PRF # E5: 1,5,6 => SOL * DIS # E4: 6,9 => CTR => E4: 3 * DIS # F4: 6,9 => CTR => F4: 3,8 * DIS # E5: 6,9 => CTR => E5: 1,5,7 * DIS # F2: 4 => CTR => F2: 6,9 * PRF # F4: 6,8 => SOL * DIS # F4: 3,9 => CTR => F4: 6,8 * PRF # D5: 5,6 => SOL * DIS # E5: 5,6 => CTR => E5: 1,7,9 * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * DIS # G7: 3 => CTR => G7: 1,6 * DIS # A9: 1 => CTR => A9: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * PRF # E8: 4,6 => SOL * DIS # F8: 4,6 => CTR => F8: 3 * DIS # G9: 4,6 => CTR => G9: 1 * PRF # I9: 4,6 => SOL * DIS # I9: 7 => CTR => I9: 4,6 * DIS # E2: 4,6 => CTR => E2: 5,9 * DIS # G7: 1 => CTR => G7: 3,6 * CNT 34 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A7,B2,B5,B8,D4,E3,E9,F5,F6,G1,G3,G5,I4,I6,I7) * .25781.6.3.7...821.813.2.7..54...71.8.3....42.16...93..48927.5.5.9...28..328.5.9. * PAIR A1: 4,9 BLK 1 A3: 4,9,6 # reduction candidate for 4,9 A3: 4,9 => CTR * .25781.6.367...821.81362.7..54...71.893.765427162..93..48927.5.5.9...28..328.5.9. A3: 6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 * DURATION: 0:00:02.800210 START: 08:39:28.244744 END: 08:39:31.044954 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-767664-base-pr-001.dot * REASONING * DIS # A3: 4,9 => CTR => A3: 6 * PRF A3: 6 => SOL * STA A3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/767664.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .25781.6.3.7...821.813.2.7..54...71.8.3....42.16...93..48927.5.5.9...28..328.5.9. A1: 4,9 A3: 4,6,9 # reduction candidate for 4,9 A3: 4,9 => CTR * .25781.6.367...821.81362.7..54...71.893.765427162..93..48927.5.5.9...28..328.5.9. A3: 6 => SOLVED * 425781369397456821681392475954238716873619542216574938148927653569143287732865194 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- * FORCE VALUE:: G7 = 3 G7 = 3 # set value I7: 6 # naked single G1: 4 # naked single I1: 3.. # hidden single G9: 1.. # hidden single A7: 1.. # hidden single |:step:| 01 --------------------------------------------------
Solution
position: 425781369397456821681392475954238716873619542216574938148927653569143287732865194 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 # A3: 4,9 => CTR => A3: 6 * PRF # A3: 6 => SOL * INC # I1: 4,9 => UNS * DIS # I1: 3 => CTR => I1: 4,9 * INC # A3: 6,9 => UNS * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E2: 6,9 => CTR => E2: 4,5 * INC # E2: 4,5 => UNS * INC # F2: 6,9 => UNS * DIS # E2: 6,9 => CTR => E2: 4,5 * INC # E2: 4,5 => UNS * INC # F2: 6,9 => UNS * INC # A3: 6,9 => UNS * DIS # A3: 4 => CTR => A3: 6,9 * DIS # E4: 6,9 => CTR => E4: 3 * INC # E4: 3 => UNS * DIS # E5: 6,9 => CTR => E5: 1,5,7 * INC # E5: 1,5,7 => UNS * DIS # I1: 3,4 => CTR => I1: 9 * INC # I1: 9 => UNS * INC # I3: 4,5 => UNS * DIS # I3: 9 => CTR => I3: 4,5 * DIS # E5: 7,9 => CTR => E5: 1,5,6 * PRF # E5: 1,5,6 => SOL * DIS # E4: 6,9 => CTR => E4: 3 * INC # E4: 3 => UNS * DIS # F4: 6,9 => CTR => F4: 3,8 * INC # F4: 3,8 => UNS * DIS # E5: 6,9 => CTR => E5: 1,5,7 * INC # E5: 1,5,7 => UNS * INC # F2: 6,9 => UNS * DIS # F2: 4 => CTR => F2: 6,9 * PRF # F4: 6,8 => SOL * DIS # F4: 3,9 => CTR => F4: 6,8 * PRF # D5: 5,6 => SOL * INC # D5: 1 => UNS * DIS # E5: 5,6 => CTR => E5: 1,7,9 * INC # E5: 1,7,9 => UNS * DIS # A9: 1,6 => CTR => A9: 7 * PRF # A9: 7 => SOL * INC # G7: 1,6 => UNS * DIS # G7: 3 => CTR => G7: 1,6 * INC # A9: 6,7 => UNS * DIS # A9: 1 => CTR => A9: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * INC # D8: 4,6 => UNS * PRF # E8: 4,6 => SOL * INC # E8: 1,3 => UNS * DIS # F8: 4,6 => CTR => F8: 3 * INC # F8: 3 => UNS * DIS # G9: 4,6 => CTR => G9: 1 * INC # G9: 1 => UNS * PRF # I9: 4,6 => SOL * DIS # I9: 7 => CTR => I9: 4,6 * DIS # E2: 4,6 => CTR => E2: 5,9 * INC # E2: 5,9 => UNS * INC # G7: 3,6 => UNS * DIS # G7: 1 => CTR => G7: 3,6 * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 4,9 => CTR => A3: 6 * PRF A3: 6 => SOL * STA A3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED