Analysis of zz-sudoku-de-717677-base.sdk
Contents
Original Sudoku
level: medium
position: 6...4.81..7.63.4.......1....85...6.22.......49.3...58....4.......7.58.4..19.2...8 initial
Autosolve
position: 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I1: 3,9 => CTR => I1: 5,7 * DIS # G3: 3,9 => CTR => G3: 2,7 * PRF # G3: 2,9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * DIS # F2: 5 => CTR => F2: 2,9 * PRF # H7: 2,9 => SOL * DIS # H7: 3,7 => CTR => H7: 2,9 * DIS # I1: 5,9 => CTR => I1: 3,7 * DIS # F2: 5,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * DIS # D5: 8,9 => CTR => D5: 3,5 * PRF # D5: 3,5 => SOL * DIS # E3: 8,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # D3: 2,7 => CTR => D3: 8,9 * PRF # D3: 8,9 => SOL * DIS # H5: 3,9 => CTR => H5: 7 * DIS # D4: 3,9 => CTR => D4: 1 * PRF # D4: 1 => SOL * DIS # H7: 3,9 => CTR => H7: 2,7 * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # F7: 3,7 => SOL * DIS # F7: 9 => CTR => F7: 3,7 * DIS # G7: 1,9 => CTR => G7: 2,3,7 * PRF # G7: 2,3,7 => SOL * PRF # G7: 3,7 => SOL * DIS # H7: 3,7 => CTR => H7: 2,9 * PRF # H7: 2,9 => SOL * DIS # I7: 3,7 => CTR => I7: 9 * PRF # I7: 9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G5: 3,7 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 41 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I1: 3,9 => CTR => I1: 5,7 * PRF I1: 5,7 # H7: 2,9 => SOL * STA I1: 5,7 + H7: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...4.81..7.63.4.......1....85...6.22.......49.3...58....4.......7.58.4..19.2...8 | initial |
| 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 | autosolve |
| 632549817178632495594871263785194632261385974943267581856413729327958146419726358 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B1: 3,9 B3: 3,9 H2: 2,9 I2: 5,9 E4: 1,9 E5: 8,9 D6: 2,7 F6: 2,7 H4: 3,9 D8: 1,9 D9: 3,7 G8: 1,9 G9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,E4: 1.. / D4 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) E7,D8: 1.. / E7 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) G7,G8: 1.. / G7 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) E7,G7: 1.. / E7 = 1 => 0 pairs (*) / G7 = 1 => 0 pairs (X) D8,G8: 1.. / D8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) D4,D8: 1.. / D4 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) E4,E7: 1.. / E4 = 1 => 0 pairs (X) / E7 = 1 => 0 pairs (_) F2,D3: 2.. / F2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) H2,G3: 2.. / H2 = 2 => 0 pairs (X) / G3 = 2 => 0 pairs (_) D6,F6: 2.. / D6 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) G7,H7: 2.. / G7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) F2,H2: 2.. / F2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) D3,G3: 2.. / D3 = 2 => 0 pairs (X) / G3 = 2 => 0 pairs (_) D3,D6: 2.. / D3 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) F2,F6: 2.. / F2 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) G3,G7: 2.. / G3 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) H2,H7: 2.. / H2 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) B1,B3: 3.. / B1 = 3 => 13 pairs (_) / B3 = 3 => 0 pairs (X) F7,D9: 3.. / F7 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) B1,I1: 3.. / B1 = 3 => 13 pairs (_) / I1 = 3 => 0 pairs (X) D4,H4: 3.. / D4 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) D9,G9: 3.. / D9 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) F5,F7: 3.. / F5 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) I1,I2: 5.. / I1 = 5 => 0 pairs (X) / I2 = 5 => 13 pairs (_) D5,F5: 5.. / D5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) F2,I2: 5.. / F2 = 5 => 0 pairs (X) / I2 = 5 => 13 pairs (_) D1,D5: 5.. / D1 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) D6,F6: 7.. / D6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) G5,H5: 7.. / G5 = 7 => 0 pairs (X) / H5 = 7 => 14 pairs (_) D9,G9: 7.. / D9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) E3,E7: 7.. / E3 = 7 => 0 pairs (*) / E7 = 7 => 0 pairs (X) H5,H7: 7.. / H5 = 7 => 14 pairs (_) / H7 = 7 => 0 pairs (X) D3,E3: 8.. / D3 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) D5,E5: 8.. / D5 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) D3,D5: 8.. / D3 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) E3,E5: 8.. / E3 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) B1,B3: 9.. / B1 = 9 => 0 pairs (X) / B3 = 9 => 13 pairs (_) D8,G8: 9.. / D8 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) * DURATION: 0:01:02.031892 START: 08:12:49.573033 END: 08:13:51.604925 2017-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,D6,D8,D9,E4,E5,F6,G8,G9,H2,H4,I2) * 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 * PAIR B1: 3,9 ROW 1 I1: 3,9,5,7 # reduction candidate for 3,9 I1: 3,9 => CTR * 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758 I1: 5,7 # 15 pairs * PAIR B3: 3,9 ROW 3 G3: 3,9,2,7 # reduction candidate for 3,9 G3: 3,9 => CTR * 6.2.4.81.17863.42.5.4281.67785..46.2261895..4943762581856473...327.58.46419.26.58 G3: 2,7 # 15 pairs I3: 3,9,7 # reduction candidate for 3,9 I3: 3,9 # 17 pairs * PAIR H2: 2,9 BLK 3 G3: 2,9,3,7 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 G3: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 * PAIR H2: 2,9 ROW 2 F2: 2,9,5 # reduction candidate for 2,9 F2: 5 => CTR * 6.2.4.81.1786354295.4281.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 F2: 2,9 # 13 pairs * PAIR H2: 2,9 COL H H7: 2,9,3,7 # reduction candidate for 2,9 H7: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 H7: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 * PAIR I2: 5,9 BLK 3 I1: 5,9,3,7 # reduction candidate for 5,9 I1: 5,9 => CTR * 632.4.81.17863.4..594.81.6.785..46.2261895..4943.6.581856473...327.58.46419.26.58 I1: 3,7 # 14 pairs * PAIR I2: 5,9 ROW 2 F2: 5,9,2 # reduction candidate for 5,9 F2: 5,9 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 F2: 2 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR E4: 1,9 BLK 5 D4: 1,9,3 # reduction candidate for 1,9 D4: 1,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 D4: 3 => CTR * 6.2.4.81.17863.4..5.4..1.6.785314692261.....4943.6.5818564.312.327.58.46419.26.58 * PAIR E4: 1,9 COL E E7: 1,9,7 # reduction candidate for 1,9 E7: 1,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 E7: 7 => CTR * 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758 * PAIR E5: 8,9 BLK 5 D5: 8,9,3,5 # reduction candidate for 8,9 D5: 8,9 => CTR * 6.254.81.17863.4.55.4.71.6.785314692261.857349432675818564.3...327.58.46419726358 D5: 3,5 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR E5: 8,9 COL E E3: 8,9,7 # reduction candidate for 8,9 E3: 8,9 => CTR * 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758 E3: 7 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR D6: 2,7 COL D D3: 2,7,8,9 # reduction candidate for 2,7 D3: 2,7 => CTR * 6.2.4.81.17863.4..5.4.81.6.785..46.2261895..4943.6.581856473...327.58.46419.26.58 D3: 8,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR H4: 3,9 BLK 6 G5: 3,9,7 # reduction candidate for 3,9 G5: 3,9 # 14 pairs H5: 3,9,7 # reduction candidate for 3,9 H5: 3,9 => CTR * 6.2.4.81.17863.42.5.42.1.6.785..46.2261...7.4943.6.5818564...7.327.58.46419726358 H5: 7 # 14 pairs * PAIR H4: 3,9 ROW 4 D4: 3,9,1 # reduction candidate for 3,9 D4: 3,9 => CTR * 6.2.4.81.1786324955.4..126.785914632261.8.7.4943.6.5818564..12.327158946419.26.58 D4: 1 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR H4: 3,9 COL H H7: 3,9,2,7 # reduction candidate for 3,9 H7: 3,9 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895.74943762581856473...327.58.46419.26.58 H7: 2,7 # 15 pairs * PAIR D8: 1,9 BLK 8 E7: 1,9,7 # reduction candidate for 1,9 E7: 1,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 E7: 7 => CTR * 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758 * PAIR D8: 1,9 COL D D4: 1,9,3 # reduction candidate for 1,9 D4: 1,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 D4: 3 => CTR * 6.2.4.81.17863.4..5.4..1.6.785314692261.....4943.6.5818564.312.327.58.46419.26.58 * PAIR D9: 3,7 BLK 8 F7: 3,7,9 # reduction candidate for 3,7 F7: 3,7 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 F7: 9 => CTR * 6.2.4.81.17863.4..5.4..1.6.785..46.2261..3..4943.6.5818564.9...327158946419326758 * PAIR G8: 1,9 BLK 9 G7: 1,9,2,3,7 # reduction candidate for 1,9 G7: 1,9 => CTR * 6.2.4.81.1786324955.4..126.785..4632261...9749432675818564..12.327.58.46419.26.58 G7: 2,3,7 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR G9: 3,7 BLK 9 G7: 3,7,1,2,9 # reduction candidate for 3,7 G7: 3,7 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 G7: 1,2,9 # 13 pairs H7: 3,7,2,9 # reduction candidate for 3,7 H7: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 H7: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 I7: 3,7,9 # reduction candidate for 3,7 I7: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 I7: 9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * PAIR G9: 3,7 COL G G3: 3,7,2,9 # reduction candidate for 3,7 G3: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 G3: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 G5: 3,7,9 # reduction candidate for 3,7 G5: 3,7 => CTR * 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58 G5: 9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-717677-base-pr-000.dot * REASONING * DIS # I1: 3,9 => CTR => I1: 5,7 * DIS # G3: 3,9 => CTR => G3: 2,7 * PRF # G3: 2,9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * DIS # F2: 5 => CTR => F2: 2,9 * PRF # H7: 2,9 => SOL * DIS # H7: 3,7 => CTR => H7: 2,9 * DIS # I1: 5,9 => CTR => I1: 3,7 * DIS # F2: 5,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * DIS # D5: 8,9 => CTR => D5: 3,5 * PRF # D5: 3,5 => SOL * DIS # E3: 8,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # D3: 2,7 => CTR => D3: 8,9 * PRF # D3: 8,9 => SOL * DIS # H5: 3,9 => CTR => H5: 7 * DIS # D4: 3,9 => CTR => D4: 1 * PRF # D4: 1 => SOL * DIS # H7: 3,9 => CTR => H7: 2,7 * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # F7: 3,7 => SOL * DIS # F7: 9 => CTR => F7: 3,7 * DIS # G7: 1,9 => CTR => G7: 2,3,7 * PRF # G7: 2,3,7 => SOL * PRF # G7: 3,7 => SOL * DIS # H7: 3,7 => CTR => H7: 2,9 * PRF # H7: 2,9 => SOL * DIS # I7: 3,7 => CTR => I7: 9 * PRF # I7: 9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G5: 3,7 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 41 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,D6,D8,D9,E4,E5,F6,G8,G9,H2,H4,I2) * 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 * PAIR B1: 3,9 ROW 1 I1: 3,9,5,7 # reduction candidate for 3,9 I1: 3,9 => CTR * 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758 * PAIR RESTART * PAIR H2: 2,9 COL H H7: 2,9,3,7 # reduction candidate for 2,9 H7: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * DURATION: 0:00:04.300861 START: 08:14:44.050270 END: 08:14:48.351131 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-717677-base-pr-001.dot * REASONING * DIS # I1: 3,9 => CTR => I1: 5,7 * PRF I1: 5,7 # H7: 2,9 => SOL * STA I1: 5,7 + H7: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokus.de/717677.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 B1: 3,9 I1: 3,5,7,9 # reduction candidate for 3,9 I1: 3,9 => CTR * 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758 H2: 2,9 H7: 2,3,7,9 # reduction candidate for 2,9 H7: 2,9 => SOLVED * 632549817178632495594871263785194632261385974943267581856413729327958146419726358 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- highlight 1 * FORCE VALUE:: F7 = 9 F7 = 9 # set value D8: 1 # naked single D9: 3.. # hidden single G8: 9.. # hidden single F5: 3.. # hidden single * FORCE VALUE:: D9 = 3 D9 = 3 # set value G9: 7 # naked single E7: 7.. # hidden single H4: 3.. # hidden single * FORCE VALUE:: G7 = 1 G7 = 1 # set value G8: 9 # naked single E7: 7 # naked single H7: 2.. # hidden single E4: 1.. # hidden single G3: 2.. # hidden single * FORCE VALUE:: G3 = 2 G3 = 2 # set value H2: 9 # naked single F2: 2.. # hidden single D6: 2.. # hidden single G5: 3.. # hidden single * ANALYZE .. F2: 2 # naked single E4: 1 # naked single H4: 3 # naked single F5: 3 # naked single G5: 3 # naked single D6: 2 # naked single H7: 2 # naked single D5: 5.. # hidden single F6: 7.. # hidden single H5: 7.. # hidden single H5 = 7,9 => CTR I7: 3.. # hidden single I2: 5.. # hidden single D4: 9.. # hidden single F1: 5.. # hidden single * CTR! |:step:| 01 --------------------------------------------------
Solution
position: 632549817178632495594871263785194632261385974943267581856413729327958146419726358 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 # I1: 3,9 => CTR => I1: 5,7 * INC # I1: 5,7 => UNS * DIS # G3: 3,9 => CTR => G3: 2,7 * INC # G3: 2,7 => UNS * INC # I3: 3,9 => UNS * PRF # G3: 2,9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * INC # F2: 2,9 => UNS * DIS # F2: 5 => CTR => F2: 2,9 * PRF # H7: 2,9 => SOL * DIS # H7: 3,7 => CTR => H7: 2,9 * DIS # I1: 5,9 => CTR => I1: 3,7 * INC # I1: 3,7 => UNS * DIS # F2: 5,9 => CTR => F2: 2 * PRF # F2: 2 => SOL * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * DIS # D5: 8,9 => CTR => D5: 3,5 * PRF # D5: 3,5 => SOL * DIS # E3: 8,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # D3: 2,7 => CTR => D3: 8,9 * PRF # D3: 8,9 => SOL * INC # G5: 3,9 => UNS * DIS # H5: 3,9 => CTR => H5: 7 * INC # H5: 7 => UNS * DIS # D4: 3,9 => CTR => D4: 1 * PRF # D4: 1 => SOL * DIS # H7: 3,9 => CTR => H7: 2,7 * INC # H7: 2,7 => UNS * PRF # E7: 1,9 => SOL * DIS # E7: 7 => CTR => E7: 1,9 * PRF # D4: 1,9 => SOL * DIS # D4: 3 => CTR => D4: 1,9 * PRF # F7: 3,7 => SOL * DIS # F7: 9 => CTR => F7: 3,7 * DIS # G7: 1,9 => CTR => G7: 2,3,7 * PRF # G7: 2,3,7 => SOL * PRF # G7: 3,7 => SOL * INC # G7: 1,2,9 => UNS * DIS # H7: 3,7 => CTR => H7: 2,9 * PRF # H7: 2,9 => SOL * DIS # I7: 3,7 => CTR => I7: 9 * PRF # I7: 9 => SOL * DIS # G3: 3,7 => CTR => G3: 2,9 * PRF # G3: 2,9 => SOL * DIS # G5: 3,7 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I1: 3,9 => CTR => I1: 5,7 * PRF I1: 5,7 # H7: 2,9 => SOL * STA I1: 5,7 + H7: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED