Analysis of zz-sudoku-de-734203-base.sdk
Contents
Original Sudoku
level: medium
position: .9.1.6.5...8...2...2.8.3.7..15...82.8.......9.49...13..8.7.2.6...6...7...7.6.4.1. initial
Autosolve
position: .9.126.58..8...29.52.893.7..15...82.8......49.49..813..8.752.6..56...78..7.684.1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 3,6 => SOL * DIS # A2: 1 => CTR => A2: 3,6 * DIS # I3: 1,4 => CTR => I3: 6 * PRF # I3: 6 => SOL * DIS # C7: 3 => CTR => C7: 1,4 * DIS # E4: 3,6 => CTR => E4: 4,7 * DIS # F5: 1 => CTR => F5: 5,7 * DIS # C1: 3,4 => CTR => C1: 7 * DIS # G7: 3,4 => CTR => G7: 9 * PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # I3: 4,6 => SOL * DIS # I3: 1 => CTR => I3: 4,6 * DIS # A4: 7 => CTR => A4: 3,6 * DIS # E5: 3,6 => CTR => E5: 1,7 * DIS # D5: 3 => CTR => D5: 2,5 * DIS # E4: 6,7 => CTR => E4: 3,4 * DIS # E5: 6,7 => CTR => E5: 1,3 * PRF # A6: 6,7 => SOL * DIS # A6: 2 => CTR => A6: 6,7 * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # E4: 6,7 => CTR => E4: 3,4 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # A9: 2,3 => CTR => A9: 9 * PRF # I9: 2,3 => SOL * DIS # I9: 5 => CTR => I9: 2,3 * DIS # C5: 7 => CTR => C5: 2,3 * DIS # D4: 4 => CTR => D4: 3,9 * DIS # E5: 6,7 => CTR => E5: 1,3 * DIS # G7: 3,4 => CTR => G7: 9 * DIS # A7: 3,4 => CTR => A7: 1,9 * PRF # C7: 3,4 => SOL * DIS # C7: 1 => CTR => C7: 3,4 * CNT 36 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:
* PRF # A2: 3,6 => SOL * STA A2: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9.1.6.5...8...2...2.8.3.7..15...82.8.......9.49...13..8.7.2.6...6...7...7.6.4.1. | initial |
| .9.126.58..8...29.52.893.7..15...82.8......49.49..813..8.752.6..56...78..7.684.1. | autosolve |
| 497126358368475291521893476615349827832517649749268135184752963256931784973684512 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) B2: 3,6 C3: 1,4 D2: 4,5 E2: 4,7 F2: 5,7 G1: 3,4 I2: 1,3 G3: 4,6 B5: 3,6 F4: 7,9 D6: 2,5 E6: 6,7 I4: 6,7 G5: 5,6 A8: 2,4 C9: 2,3 D8: 3,9 E8: 1,3 F8: 1,9 I7: 3,4 I8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C3: 1.. / A2 = 1 => 0 pairs (X) / C3 = 1 => 0 pairs (_) I2,I3: 1.. / I2 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) E5,F5: 1.. / E5 = 1 => 19 pairs (_) / F5 = 1 => 0 pairs (X) A7,C7: 1.. / A7 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 0 pairs (X) / F8 = 1 => 19 pairs (_) A2,I2: 1.. / A2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) C3,I3: 1.. / C3 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) A2,A7: 1.. / A2 = 1 => 0 pairs (X) / A7 = 1 => 0 pairs (_) C3,C7: 1.. / C3 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) E5,E8: 1.. / E5 = 1 => 19 pairs (_) / E8 = 1 => 0 pairs (X) F5,F8: 1.. / F5 = 1 => 0 pairs (X) / F8 = 1 => 19 pairs (_) C5,A6: 2.. / C5 = 2 => 0 pairs (*) / A6 = 2 => 0 pairs (X) D5,D6: 2.. / D5 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) I8,I9: 2.. / I8 = 2 => 22 pairs (_) / I9 = 2 => 0 pairs (*) C5,D5: 2.. / C5 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) A6,D6: 2.. / A6 = 2 => 0 pairs (X) / D6 = 2 => 0 pairs (_) A8,I8: 2.. / A8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) C5,C9: 2.. / C5 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) G1,I2: 3.. / G1 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) D8,E8: 3.. / D8 = 3 => 0 pairs (X) / E8 = 3 => 19 pairs (_) B2,B5: 3.. / B2 = 3 => 0 pairs (X) / B5 = 3 => 0 pairs (_) D2,E2: 4.. / D2 = 4 => 23 pairs (_) / E2 = 4 => 0 pairs (X) D4,E4: 4.. / D4 = 4 => 0 pairs (X) / E4 = 4 => 23 pairs (_) A8,I8: 4.. / A8 = 4 => 22 pairs (_) / I8 = 4 => 0 pairs (*) D2,D4: 4.. / D2 = 4 => 23 pairs (_) / D4 = 4 => 0 pairs (X) E2,E4: 4.. / E2 = 4 => 0 pairs (X) / E4 = 4 => 23 pairs (_) D2,F2: 5.. / D2 = 5 => 0 pairs (X) / F2 = 5 => 23 pairs (_) G5,I6: 5.. / G5 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) G9,I9: 5.. / G9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) D6,I6: 5.. / D6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) F2,F5: 5.. / F2 = 5 => 23 pairs (_) / F5 = 5 => 0 pairs (X) G5,G9: 5.. / G5 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) I6,I9: 5.. / I6 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) A2,B2: 6.. / A2 = 6 => 0 pairs (X) / B2 = 6 => 0 pairs (_) G3,I3: 6.. / G3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) B2,B5: 6.. / B2 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) G3,G5: 6.. / G3 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) A1,C1: 7.. / A1 = 7 => 0 pairs (X) / C1 = 7 => 20 pairs (_) E2,F2: 7.. / E2 = 7 => 23 pairs (_) / F2 = 7 => 0 pairs (X) I4,I6: 7.. / I4 = 7 => 23 pairs (_) / I6 = 7 => 0 pairs (X) C1,C5: 7.. / C1 = 7 => 20 pairs (_) / C5 = 7 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 0 pairs (X) / F4 = 9 => 19 pairs (_) A7,A9: 9.. / A7 = 9 => 0 pairs (X) / A9 = 9 => 23 pairs (_) D8,F8: 9.. / D8 = 9 => 19 pairs (_) / F8 = 9 => 0 pairs (X) G7,G9: 9.. / G7 = 9 => 23 pairs (_) / G9 = 9 => 0 pairs (X) A7,G7: 9.. / A7 = 9 => 0 pairs (X) / G7 = 9 => 23 pairs (_) A9,G9: 9.. / A9 = 9 => 23 pairs (_) / G9 = 9 => 0 pairs (X) D4,D8: 9.. / D4 = 9 => 0 pairs (X) / D8 = 9 => 19 pairs (_) F4,F8: 9.. / F4 = 9 => 19 pairs (_) / F8 = 9 => 0 pairs (X) * DURATION: 0:01:28.054960 START: 08:21:23.009717 END: 08:22:51.064677 2017-05-01 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B5,C3,C9,D2,D6,D8,E2,E6,E8,F2,F4,F8,G1,G3,G5,I2,I4,I7,I8) * .9.126.58..8...29.52.893.7..15...82.8......49.49..813..8.752.6..56...78..7.684.1. * PAIR B2: 3,6 BLK 1 A2: 3,6,1 # reduction candidate for 3,6 A2: 3,6 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 A2: 1 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136.81752.64456.1978..7.684.1. * PAIR C3: 1,4 ROW 3 I3: 1,4,6 # reduction candidate for 1,4 I3: 1,4 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 I3: 6 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 * PAIR C3: 1,4 COL C C7: 1,4,3 # reduction candidate for 1,4 C7: 3 => CTR * .94126358..8...291521893476.15...8278.72..6492495.813.183752964456...782972684.1. C7: 1,4 # 23 pairs * PAIR E2: 4,7 COL E E4: 4,7,3,6 # reduction candidate for 4,7 E4: 3,6 => CTR * .9.126.58..8.4729.52.893.7..154.982.8....5649.492.8135.8.752.6..5693178..7.68451. E4: 4,7 # 24 pairs * PAIR F2: 5,7 COL F F5: 5,7,1 # reduction candidate for 5,7 F5: 1 => CTR * 79.126.58638475291521893674315947826867231549249568137183752.6.456.19782.72684.15 F5: 5,7 # 19 pairs * PAIR G1: 3,4 ROW 1 A1: 3,4,7 # reduction candidate for 3,4 A1: 3,4 # 20 pairs C1: 3,4,7 # reduction candidate for 3,4 C1: 3,4 => CTR * 79.126.58638475291521893674315947826867231549249568137183752.6.456319782.72684.15 C1: 7 # 20 pairs * PAIR G1: 3,4 COL G G7: 3,4,9 # reduction candidate for 3,4 G7: 3,4 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136981752364456.19782.7.684915 G7: 9 # 23 pairs * PAIR I2: 1,3 ROW 2 A2: 1,3,6 # reduction candidate for 1,3 A2: 1,3 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 A2: 6 => CTR * .9.126.58638...291521893.7..15...82.86....549.495.813.18.75296..56...78.97.684315 * PAIR G3: 4,6 BLK 3 I3: 4,6,1 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 I3: 1 => CTR * .9.126458168475293524893671.15.4.82.83.26.549.495.813..81752.6..56...78..7.684.15 * PAIR B5: 3,6 BLK 4 A4: 3,6,7 # reduction candidate for 3,6 A4: 7 => CTR * 3971264586.847529.52.89367.7153498268..217549249568137.8.752.6.456931782.72684.15 A4: 3,6 # 24 pairs * PAIR B5: 3,6 ROW 5 E5: 3,6,1,7 # reduction candidate for 3,6 E5: 3,6 => CTR * 79.126.58638475291521893674315947826867231549249568137183752.6.456319782.72684.15 E5: 1,7 # 22 pairs * PAIR D6: 2,5 BLK 5 D5: 2,5,3 # reduction candidate for 2,5 D5: 3 => CTR * .9.126.58..8...29.52.893.7..15...82.8.23...49.492.8135.8.752.6..5693178..73684512 D5: 2,5 # 23 pairs * PAIR E6: 6,7 BLK 5 E4: 6,7,3,4 # reduction candidate for 6,7 E4: 6,7 => CTR * .9.126.58..8.4729.52.893.7..154.982.8....5649.492.8135.8.752.6..5693178..7.68451. E4: 3,4 # 22 pairs E5: 6,7,1,3 # reduction candidate for 6,7 E5: 6,7 => CTR * .9.126.58..8..529.52.893.7..159..82.8....1.49.49..813..8.752.6..56.1978..7.684.1. E5: 1,3 # 22 pairs * PAIR E6: 6,7 ROW 6 A6: 6,7,2 # reduction candidate for 6,7 A6: 6,7 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 A6: 2 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 I6: 6,7,5 # reduction candidate for 6,7 I6: 6,7 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 I6: 5 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 * PAIR I4: 6,7 BLK 6 I6: 6,7,5 # reduction candidate for 6,7 I6: 6,7 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 I6: 5 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 * PAIR I4: 6,7 ROW 4 A4: 6,7,3 # reduction candidate for 6,7 A4: 6,7 # 20 pairs E4: 6,7,3,4 # reduction candidate for 6,7 E4: 6,7 => CTR * .9.126.58..8.4729.52.893.7..154.982.8....5649.492.8135.8.752.6..5693178..7.68451. E4: 3,4 # 22 pairs * PAIR G5: 5,6 BLK 6 I6: 5,6,7 # reduction candidate for 5,6 I6: 7 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 I6: 5,6 # 23 pairs * PAIR C9: 2,3 BLK 7 A9: 2,3,9 # reduction candidate for 2,3 A9: 2,3 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136981752364456.19782.7.684915 A9: 9 # 23 pairs * PAIR C9: 2,3 ROW 9 I9: 2,3,5 # reduction candidate for 2,3 I9: 2,3 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 I9: 5 => CTR * .9.126.58638475291521893674.15.4.82686.2..549249568137183752.6.456...782.72684.15 * PAIR C9: 2,3 COL C C5: 2,3,7 # reduction candidate for 2,3 C5: 7 => CTR * 79.126.58638475291521893674315947826867231549249568137183752.6.456319782.72684.15 C5: 2,3 # 20 pairs * PAIR D8: 3,9 COL D D4: 3,9,4 # reduction candidate for 3,9 D4: 4 => CTR * .9.126.58..854729.52.893.7.3154.982.86.315.49.49..813..8.752.6..5693178..7.684.1. D4: 3,9 # 23 pairs * PAIR E8: 1,3 COL E E5: 1,3,6,7 # reduction candidate for 1,3 E5: 6,7 => CTR * .9.126.58..8..529.52.893.7..159..82.8....1.49.49..813..8.752.6..56.1978..7.684.1. E5: 1,3 # 22 pairs * PAIR I7: 3,4 BLK 9 G7: 3,4,9 # reduction candidate for 3,4 G7: 3,4 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136981752364456.19782.7.684915 G7: 9 # 23 pairs * PAIR I7: 3,4 ROW 7 A7: 3,4,1,9 # reduction candidate for 3,4 A7: 3,4 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136.81752964456.1978..7.684.1. A7: 1,9 # 22 pairs C7: 3,4,1 # reduction candidate for 3,4 C7: 3,4 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 C7: 1 => CTR * .9.126.58168...293524893671.15...82.83..61549.49578136.81752.64456.1978..7.684.1. * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-734203-base-pr-000.dot * REASONING * PRF # A2: 3,6 => SOL * DIS # A2: 1 => CTR => A2: 3,6 * DIS # I3: 1,4 => CTR => I3: 6 * PRF # I3: 6 => SOL * DIS # C7: 3 => CTR => C7: 1,4 * DIS # E4: 3,6 => CTR => E4: 4,7 * DIS # F5: 1 => CTR => F5: 5,7 * DIS # C1: 3,4 => CTR => C1: 7 * DIS # G7: 3,4 => CTR => G7: 9 * PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # I3: 4,6 => SOL * DIS # I3: 1 => CTR => I3: 4,6 * DIS # A4: 7 => CTR => A4: 3,6 * DIS # E5: 3,6 => CTR => E5: 1,7 * DIS # D5: 3 => CTR => D5: 2,5 * DIS # E4: 6,7 => CTR => E4: 3,4 * DIS # E5: 6,7 => CTR => E5: 1,3 * PRF # A6: 6,7 => SOL * DIS # A6: 2 => CTR => A6: 6,7 * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # E4: 6,7 => CTR => E4: 3,4 * DIS # I6: 7 => CTR => I6: 5,6 * DIS # A9: 2,3 => CTR => A9: 9 * PRF # I9: 2,3 => SOL * DIS # I9: 5 => CTR => I9: 2,3 * DIS # C5: 7 => CTR => C5: 2,3 * DIS # D4: 4 => CTR => D4: 3,9 * DIS # E5: 6,7 => CTR => E5: 1,3 * DIS # G7: 3,4 => CTR => G7: 9 * DIS # A7: 3,4 => CTR => A7: 1,9 * PRF # C7: 3,4 => SOL * DIS # C7: 1 => CTR => C7: 3,4 * CNT 36 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B5,C3,C9,D2,D6,D8,E2,E6,E8,F2,F4,F8,G1,G3,G5,I2,I4,I7,I8) * .9.126.58..8...29.52.893.7..15...82.8......49.49..813..8.752.6..56...78..7.684.1. * PAIR B2: 3,6 BLK 1 A2: 3,6,1 # reduction candidate for 3,6 A2: 3,6 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 * DURATION: 0:00:02.225695 START: 08:23:46.557558 END: 08:23:48.783253 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-734203-base-pr-001.dot * REASONING * PRF # A2: 3,6 => SOL * STA A2: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/734203.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .9.126.58..8...29.52.893.7..15...82.8......49.49..813..8.752.6..56...78..7.684.1. B2: 3,6 A2: 1,3,6 # reduction candidate for 3,6 A2: 3,6 => SOLVED * 497126358368475291521893476615349827832517649749268135184752963256931784973684512 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- higlight 2 A9: 2,3,9 C9: 2,3 I9: 2,3,5 => A9 = 9 or I9 = 5 I9 = 5 => * DISABLE VALUE:: I9 != 2 * DISABLE VALUE:: I9 != 3 I9: 5 # naked single * ANALYZE .. I8: 2.. # hidden single I8: 2 # naked single A8: 4.. # hidden single A8: 4 # naked single Q9: 4.. = G7,I7: 4.. => A7,C7 != 4 * UNSOLVED! * DISABLE VALUE:: G9 != 5 * ANALYZE .. G5: 5.. # hidden single G5: 5 # naked single G3: 6.. # hidden single G3: 6 # naked single Q6: 6.. = I4,I6: 6.. => I3 != 6 * UNSOLVED! * DISABLE VALUE:: I6 != 5 * ANALYZE .. D6: 5.. # hidden single D6: 5 # naked single D5: 2.. # hidden single A6: 2.. # hidden single D5: 2 # naked single A6: 2 # naked single * UNSOLVED! * DISABLE VALUE:: C5 != 2 * ANALYZE .. C9: 2.. # hidden single C9: 2 # naked single * UNSOLVED! * DISABLE VALUE:: A9 != 2 * ANALYZE .. * UNSOLVED! * DISABLE VALUE:: F5 != 5 * ANALYZE .. F2: 5.. # hidden single F2: 5 # naked single E2: 7.. # hidden single E2: 7 # naked single D2: 4.. # hidden single E4: 4.. # hidden single D2: 4 # naked single E4: 4 # naked single E5,E8: 1,3.. => E5 != 6,7 # hidden pair * UNSOLVED! * DISABLE VALUE:: E6 != 7 E6: 6 # naked single * ANALYZE .. I6: 7.. # hidden single I4: 6 # naked single Q4,Q5: 7.. => I4 != 7 I6: 7 # naked single * UNSOLVED! * DISABLE VALUE:: E5 != 6 * DISABLE VALUE:: E5 != 7 |:step:| 01 -------------------------------------------------- |:step:| 02 --------------------------------------------------
Solution
position: 497126358368475291521893476615349827832517649749268135184752963256931784973684512 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:
* PRF # A2: 3,6 => SOL * DIS # A2: 1 => CTR => A2: 3,6 * DIS # I3: 1,4 => CTR => I3: 6 * PRF # I3: 6 => SOL * INC # C7: 1,4 => UNS * DIS # C7: 3 => CTR => C7: 1,4 * INC # E4: 4,7 => UNS * DIS # E4: 3,6 => CTR => E4: 4,7 * INC # F5: 5,7 => UNS * DIS # F5: 1 => CTR => F5: 5,7 * INC # A1: 3,4 => UNS * DIS # C1: 3,4 => CTR => C1: 7 * INC # C1: 7 => UNS * DIS # G7: 3,4 => CTR => G7: 9 * INC # G7: 9 => UNS * PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # I3: 4,6 => SOL * DIS # I3: 1 => CTR => I3: 4,6 * INC # A4: 3,6 => UNS * DIS # A4: 7 => CTR => A4: 3,6 * DIS # E5: 3,6 => CTR => E5: 1,7 * INC # E5: 1,7 => UNS * INC # D5: 2,5 => UNS * DIS # D5: 3 => CTR => D5: 2,5 * DIS # E4: 6,7 => CTR => E4: 3,4 * INC # E4: 3,4 => UNS * DIS # E5: 6,7 => CTR => E5: 1,3 * INC # E5: 1,3 => UNS * PRF # A6: 6,7 => SOL * DIS # A6: 2 => CTR => A6: 6,7 * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 6,7 => CTR => I6: 5 * PRF # I6: 5 => SOL * INC # A4: 6,7 => UNS * DIS # E4: 6,7 => CTR => E4: 3,4 * INC # E4: 3,4 => UNS * INC # I6: 5,6 => UNS * DIS # I6: 7 => CTR => I6: 5,6 * DIS # A9: 2,3 => CTR => A9: 9 * INC # A9: 9 => UNS * PRF # I9: 2,3 => SOL * DIS # I9: 5 => CTR => I9: 2,3 * INC # C5: 2,3 => UNS * DIS # C5: 7 => CTR => C5: 2,3 * INC # D4: 3,9 => UNS * DIS # D4: 4 => CTR => D4: 3,9 * INC # E5: 1,3 => UNS * DIS # E5: 6,7 => CTR => E5: 1,3 * DIS # G7: 3,4 => CTR => G7: 9 * INC # G7: 9 => UNS * DIS # A7: 3,4 => CTR => A7: 1,9 * INC # A7: 1,9 => UNS * PRF # C7: 3,4 => SOL * DIS # C7: 1 => CTR => C7: 3,4 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 3,6 => SOL * STA A2: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED