Analysis of xx-top500-277-base.sdk
Contents
Original Sudoku
level: medium
position: .3.2...4.1...8..............2.67.........21........5.87.1.........4...3.5........ initial
Autosolve
position: 93.2...4.1...84...4........825671.9.3948521..617.4.5287.1......2.94...3.5.3...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 2 => CTR => C3: 6,8 * DIS # G1: 6,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # H2: 5,7 => CTR => H2: 6 * DIS # I2: 5,7 => CTR => I2: 2,3,6,9 * DIS # C3: 8 => CTR => C3: 2,6 * DIS # G2: 2,6 => CTR => G2: 3,7,9 * DIS # I2: 2,6 => CTR => I2: 3,5,7,9 * DIS # D3: 5,7 => CTR => D3: 1,3,9 * DIS # F3: 5,7 => CTR => F3: 3,6,9 * PRF # H3: 5,7 => SOL * DIS # I3: 5,7 => CTR => I3: 1,2,3,6,9 * PRF # I1: 1,6 => SOL * DIS # I1: 5,7 => CTR => I1: 1,6 * DIS # D2: 3,9 => CTR => D2: 5,7 * DIS # D3: 3,9 => CTR => D3: 1,5,7 * PRF # F3: 3,9 => SOL * DIS # G3: 3,9 => CTR => G3: 2,6,7,8 * DIS # I3: 3,9 => CTR => I3: 1,2,5,6,7 * DIS # D2: 3,9 => CTR => D2: 5,7 * DIS # D3: 3,9 => CTR => D3: 1,5,7 * DIS # D7: 3,9 => CTR => D7: 5 * PRF # D7: 5 => SOL * PRF # F3: 3,9 => SOL * DIS # F7: 3,9 => CTR => F7: 5,6,8 * DIS # H3: 6,7 => CTR => H3: 1,5,8 * DIS # H9: 6,7 => CTR => H9: 1,8 * DIS # I1: 6,7 => CTR => I1: 1,5 * DIS # I2: 6,7 => CTR => I2: 2,3,5,9 * DIS # I8: 6,7 => CTR => I8: 1,5 * DIS # F8: 6,8 => CTR => F8: 5,7 * PRF # G8: 6,8 => SOL * DIS # G8: 7 => CTR => G8: 6,8 * DIS # I8: 1,6 => CTR => I8: 5,7 * PRF # I8: 5,7 => SOL * CNT 35 HDP CHAINS / 72 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 2 => CTR => C3: 6,8 * DIS C3: 6,8 # H2: 5,7 => CTR => H2: 6 * DIS C3: 6,8 + H2: 6 # I2: 5,7 => CTR => I2: 3,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 # D2: 3,9 => CTR => D2: 5,7 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 # D3: 5,7 => CTR => D3: 1,3,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 # F3: 5,7 => CTR => F3: 3,6,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 # I3: 5,7 => CTR => I3: 1,2 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 # D3: 3,9 => CTR => D3: 1 * PRF C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 => SOL * STA C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 * CNT 9 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.2...4.1...8..............2.67.........21........5.87.1.........4...3.5........ | initial |
| 93.2...4.1...84...4........825671.9.3948521..617.4.5287.1......2.94...3.5.3...... | autosolve |
| 938265741152784963476193852825671394394852176617349528741536289289417635563928417 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 6,8 B2: 5,7 C2: 2,6 B3: 5,7 E1: 1,6 E3: 3,9 D6: 3,9 F6: 3,9 G4: 3,4 I4: 3,4 H5: 6,7 I5: 6,7 B8: 6,8 E8: 1,6 E9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D3: 1.. / E1 = 1 => 0 pairs (X) / D3 = 1 => 0 pairs (_) E8,D9: 1.. / E8 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) E1,I1: 1.. / E1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) E8,I8: 1.. / E8 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) D3,D9: 1.. / D3 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) E1,E8: 1.. / E1 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) H3,H9: 1.. / H3 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) C2,C3: 2.. / C2 = 2 => 16 pairs (_) / C3 = 2 => 0 pairs (X) E7,E9: 2.. / E7 = 2 => 15 pairs (_) / E9 = 2 => 15 pairs (_) D6,F6: 3.. / D6 = 3 => 14 pairs (_) / F6 = 3 => 15 pairs (_) G4,I4: 3.. / G4 = 3 => 13 pairs (_) / I4 = 3 => 13 pairs (_) E3,E7: 3.. / E3 = 3 => 17 pairs (_) / E7 = 3 => 14 pairs (_) G4,I4: 4.. / G4 = 4 => 13 pairs (_) / I4 = 4 => 13 pairs (_) B7,B9: 4.. / B7 = 4 => 16 pairs (_) / B9 = 4 => 16 pairs (_) B2,B3: 5.. / B2 = 5 => 16 pairs (_) / B3 = 5 => 16 pairs (_) F1,I1: 5.. / F1 = 5 => 0 pairs (*) / I1 = 5 => 0 pairs (X) F8,I8: 5.. / F8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 14 pairs (_) E1,E8: 6.. / E1 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) B2,B3: 7.. / B2 = 7 => 16 pairs (_) / B3 = 7 => 16 pairs (_) H5,I5: 7.. / H5 = 7 => 14 pairs (_) / I5 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 16 pairs (_) / C3 = 8 => 0 pairs (X) C1,G1: 8.. / C1 = 8 => 16 pairs (_) / G1 = 8 => 0 pairs (X) D6,F6: 9.. / D6 = 9 => 15 pairs (_) / F6 = 9 => 14 pairs (_) * DURATION: 0:00:35.866295 START: 12:24:19.823688 END: 12:24:55.689983 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D6,E1,E3,E8,E9,F6,G4,H5,I4,I5) * 93.2...4.1...84...4........825671.9.3948521..617.4.5287.1......2.94...3.5.3...... * PAIR C1: 6,8 BLK 1 C3: 6,8,2 # reduction candidate for 6,8 C3: 2 => CTR * 938265741176.84.5.4521.7...825671.9.394852176617.4.5287.15.....2.941..355.37...1. C3: 6,8 # 16 pairs * PAIR C1: 6,8 ROW 1 G1: 6,8,7 # reduction candidate for 6,8 G1: 6,8 => CTR * 93.21..4.1...84...4....6.1.825671.9.3948521..617.4.5287.1......2894657315.31.7... G1: 7 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 * PAIR B2: 5,7 ROW 2 D2: 5,7,3,9 # reduction candidate for 5,7 D2: 5,7 # 19 pairs H2: 5,7,6 # reduction candidate for 5,7 H2: 5,7 => CTR * 93.265.411...84...4..1.7...825671.9.3948521.7617.4.5287.15.....2.941.7355.37...1. H2: 6 # 16 pairs I2: 5,7,2,3,6,9 # reduction candidate for 5,7 I2: 5,7 => CTR * 93.2.584.1.2.84.6.4........825671.9.394852176617.4.5287.15...8.2.94...355.3....1. I2: 2,3,6,9 # 15 pairs * PAIR C2: 2,6 BLK 1 C3: 2,6,8 # reduction candidate for 2,6 C3: 8 => CTR * 9362158471.2.84...4.8..6.1.825671.9.394852176617.4.5287.15.....28946.7315.31.7... C3: 2,6 # 16 pairs * PAIR C2: 2,6 ROW 2 G2: 2,6,3,7,9 # reduction candidate for 2,6 G2: 2,6 => CTR * 93.265.411...84...4..1.7...825671.9.3948521.7617.4.5287.15.....2.941.7355.37...1. G2: 3,7,9 # 15 pairs I2: 2,6,3,5,7,9 # reduction candidate for 2,6 I2: 2,6 => CTR * 93.265.411...84...4..1.7...825671.9.3948521.7617.4.5287.15.....2.941.7355.37...1. I2: 3,5,7,9 # 15 pairs * PAIR B3: 5,7 ROW 3 D3: 5,7,1,3,9 # reduction candidate for 5,7 D3: 5,7 => CTR * 93.21..4.1...84...4......1.825671.9.3948521..617.4.5287.1......2894657315.31.7... D3: 1,3,9 # 15 pairs F3: 5,7,3,6,9 # reduction candidate for 5,7 F3: 5,7 => CTR * 9382..74.1...84...4........825671.9.3948521..617.4.5287.1......2.94...3.5.3...... F3: 3,6,9 # 15 pairs H3: 5,7,1,6,8 # reduction candidate for 5,7 H3: 5,7 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 H3: 1,6,8 # 15 pairs I3: 5,7,1,2,3,6,9 # reduction candidate for 5,7 I3: 5,7 => CTR * 93.2.7845172584.6.458..6217825671.9.394852176617.4.5287.1....5.289465.3.5.3...... I3: 1,2,3,6,9 # 15 pairs * PAIR E1: 1,6 ROW 1 I1: 1,6,5,7 # reduction candidate for 1,6 I1: 1,6 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 I1: 5,7 => CTR * 93.21..4.1...84...4......1.825671.9.3948521..617.4.5287.1......2894657315.31.7... * PAIR E3: 3,9 BLK 2 D2: 3,9,5,7 # reduction candidate for 3,9 D2: 3,9 => CTR * 93.265.411...84...4..1.7...825671.9.3948521..617.4.5287.15.....2.941.7355.37...1. D2: 5,7 # 19 pairs D3: 3,9,1,5,7 # reduction candidate for 3,9 D3: 3,9 => CTR * 93.21..4.1..784...47.....1.825671.9.3948521..617.4.5287.15.....289467.315.31..... D3: 1,5,7 # 15 pairs F3: 3,9,5,6,7 # reduction candidate for 3,9 F3: 3,9 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 F3: 5,6,7 # 15 pairs * PAIR E3: 3,9 ROW 3 G3: 3,9,2,6,7,8 # reduction candidate for 3,9 G3: 3,9 => CTR * 93.265.411...84...4..1.7...825671.9.3948521..617.4.5287.15.....2.941.7355.37...1. G3: 2,6,7,8 # 15 pairs I3: 3,9,1,2,5,6,7 # reduction candidate for 3,9 I3: 3,9 => CTR * 93.265.411...84...4..1.7...825671.9.3948521..617.4.5287.15.....2.941.7355.37...1. I3: 1,2,5,6,7 # 15 pairs * PAIR E3: 3,9 COL E E7: 3,9,2 # reduction candidate for 3,9 E7: 3,9 # 15 pairs E7: 2 # 15 pairs * PAIR D6: 3,9 COL D D2: 3,9,5,7 # reduction candidate for 3,9 D2: 3,9 => CTR * 93.265.411...84...4..1.7...825671.9.3948521..617.4.5287.15.....2.941.7355.37...1. D2: 5,7 # 19 pairs D3: 3,9,1,5,7 # reduction candidate for 3,9 D3: 3,9 => CTR * 93.21..4.1..784...47.....1.825671.9.3948521..617.4.5287.15.....289467.315.31..... D3: 1,5,7 # 15 pairs D7: 3,9,5 # reduction candidate for 3,9 D7: 3,9 => CTR * 93.2167451...84.6.4.6....1.825671.9.39485217.617.4.5287.1....5.2.9465.315.31.7... D7: 5 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 * PAIR F6: 3,9 COL F F3: 3,9,5,6,7 # reduction candidate for 3,9 F3: 3,9 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 F3: 5,6,7 # 15 pairs F7: 3,9,5,6,8 # reduction candidate for 3,9 F7: 3,9 => CTR * 93.265.411...84...4..1.7...825671.9.3948521..617.4.5287.15.....2.941.7355.37...1. F7: 5,6,8 # 15 pairs * PAIR H5: 6,7 COL H H2: 6,7,5 # reduction candidate for 6,7 H2: 6,7 # 18 pairs H3: 6,7,1,5,8 # reduction candidate for 6,7 H3: 6,7 => CTR * 93826574117..84.5.45.1.786.825671.9.394852176617.4.5287.15...8.2.941.6355.37...1. H3: 1,5,8 # 15 pairs H9: 6,7,1,8 # reduction candidate for 6,7 H9: 6,7 => CTR * 93.21..4.1...84.5.45.....1.825671.9.3948521..617.4.5287.15...8.2.946..3.5.31..... H9: 1,8 # 16 pairs * PAIR I5: 6,7 COL I I1: 6,7,1,5 # reduction candidate for 6,7 I1: 6,7 => CTR * 93.215.4.1...84...4....6...825671.9.3948521..617.4.5287.15.....2.946..3.5.3...... I1: 1,5 # 16 pairs I2: 6,7,2,3,5,9 # reduction candidate for 6,7 I2: 6,7 => CTR * 93.2.5741172.84.5645.1.7.8.825671.9.3948521..617.4.5287.15.....2.94...355.3....1. I2: 2,3,5,9 # 15 pairs I3: 6,7,1,2,3,5,9 # reduction candidate for 6,7 I3: 6,7 # 18 pairs I8: 6,7,1,5 # reduction candidate for 6,7 I8: 6,7 => CTR * 93.2...4.1...84...4........825671.9.3948521..617.4.5287.1......2.9415.3.5.3...... I8: 1,5 # 16 pairs I9: 6,7,1,2,4,9 # reduction candidate for 6,7 I9: 6,7 # 18 pairs * PAIR B8: 6,8 BLK 7 B7: 6,8,4 # reduction candidate for 6,8 B7: 6,8 # 16 pairs B9: 6,8,4 # reduction candidate for 6,8 B9: 6,8 # 16 pairs * PAIR B8: 6,8 ROW 8 F8: 6,8,5,7 # reduction candidate for 6,8 F8: 6,8 => CTR * 93.2.5.4.1...84...4........825671.9.3948521..617.4.5287.15.....2.941.7355.3...... F8: 5,7 # 16 pairs G8: 6,8,7 # reduction candidate for 6,8 G8: 6,8 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 G8: 7 => CTR * 93.215.471...84...4....6.1.825671.9.394852176617.4.5287.15.....28946.7315.31.7... * PAIR E8: 1,6 ROW 8 I8: 1,6,5,7 # reduction candidate for 1,6 I8: 1,6 => CTR * 93.217.451...84...4....6...825671.9.3948521..617.4.5287.1....5.28946573.5.3...... I8: 5,7 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 * PAIR E9: 2,9 BLK 8 E7: 2,9,3 # reduction candidate for 2,9 E7: 2,9 # 17 pairs E7: 3 # 14 pairs * PAIR E9: 2,9 ROW 9 G9: 2,9,4,6,7,8 # reduction candidate for 2,9 G9: 2,9 # 17 pairs I9: 2,9,1,4,6,7 # reduction candidate for 2,9 I9: 2,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-277-base-pr-000.dot * REASONING * DIS # C3: 2 => CTR => C3: 6,8 * DIS # G1: 6,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * DIS # H2: 5,7 => CTR => H2: 6 * DIS # I2: 5,7 => CTR => I2: 2,3,6,9 * DIS # C3: 8 => CTR => C3: 2,6 * DIS # G2: 2,6 => CTR => G2: 3,7,9 * DIS # I2: 2,6 => CTR => I2: 3,5,7,9 * DIS # D3: 5,7 => CTR => D3: 1,3,9 * DIS # F3: 5,7 => CTR => F3: 3,6,9 * PRF # H3: 5,7 => SOL * DIS # I3: 5,7 => CTR => I3: 1,2,3,6,9 * PRF # I1: 1,6 => SOL * DIS # I1: 5,7 => CTR => I1: 1,6 * DIS # D2: 3,9 => CTR => D2: 5,7 * DIS # D3: 3,9 => CTR => D3: 1,5,7 * PRF # F3: 3,9 => SOL * DIS # G3: 3,9 => CTR => G3: 2,6,7,8 * DIS # I3: 3,9 => CTR => I3: 1,2,5,6,7 * DIS # D2: 3,9 => CTR => D2: 5,7 * DIS # D3: 3,9 => CTR => D3: 1,5,7 * DIS # D7: 3,9 => CTR => D7: 5 * PRF # D7: 5 => SOL * PRF # F3: 3,9 => SOL * DIS # F7: 3,9 => CTR => F7: 5,6,8 * DIS # H3: 6,7 => CTR => H3: 1,5,8 * DIS # H9: 6,7 => CTR => H9: 1,8 * DIS # I1: 6,7 => CTR => I1: 1,5 * DIS # I2: 6,7 => CTR => I2: 2,3,5,9 * DIS # I8: 6,7 => CTR => I8: 1,5 * DIS # F8: 6,8 => CTR => F8: 5,7 * PRF # G8: 6,8 => SOL * DIS # G8: 7 => CTR => G8: 6,8 * DIS # I8: 1,6 => CTR => I8: 5,7 * PRF # I8: 5,7 => SOL * CNT 35 HDP CHAINS / 72 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D6,E1,E3,E8,E9,F6,G4,H5,I4,I5) * 93.2...4.1...84...4........825671.9.3948521..617.4.5287.1......2.94...3.5.3...... * PAIR C1: 6,8 BLK 1 C3: 6,8,2 # reduction candidate for 6,8 C3: 2 => CTR * 938265741176.84.5.4521.7...825671.9.394852176617.4.5287.15.....2.941..355.37...1. * PAIR B2: 5,7 ROW 2 D2: 5,7,3,9 # reduction candidate for 5,7 D2: 5,7 # 19 pairs H2: 5,7,6 # reduction candidate for 5,7 H2: 5,7 => CTR * 93.265.411.2.84...4.61.7.8.825671.9.3948521.7617.4.5287.15...6.2.941..355.37..... I2: 5,7,3,9 # reduction candidate for 5,7 I2: 5,7 => CTR * 93.2.584.1.2.84.6.4........825671.9.394852176617.4.5287.15...8.2.94...355.3....1. * RESTART * PAIR B2: 5,7 ROW 2 D2: 5,7,3,9 # reduction candidate for 5,7 D2: 3,9 => CTR * 93.2.7845152.8476.4781.....825671.9.394852176617.4.5287.1......2.94...3.5.37..... * PAIR RESTART * PAIR B3: 5,7 ROW 3 D3: 5,7,1,3,9 # reduction candidate for 5,7 D3: 5,7 => CTR * 93.21..4.1.2.84.6.4......1.825671.9.394852176617.4.5287.1....5.2894657315.31.7.8. F3: 5,7,3,6,9 # reduction candidate for 5,7 F3: 5,7 => CTR * 9382..74.1.2.84.6.4.6......825671.9.394852176617.4.5287.1......2.94...3.5.3...... I3: 5,7,1,2 # reduction candidate for 5,7 I3: 5,7 => CTR * 93.2.7845172584.6.458..6217825671.9.394852176617.4.5287.1....5.289465.3.5.3...... * RESTART * PAIR RESTART * PAIR E3: 3,9 BLK 2 D3: 3,9,1 # reduction candidate for 3,9 D3: 3,9 => CTR * 93621.84.1.2784.6.478..6...825671.9.394852176617.4.5287.1......2.946..315.31...8. D3: 1 => SOLVED * 938265741152784963476193852825671394394852176617349528741536289289417635563928417 * DURATION: 0:00:12.232439 START: 12:25:55.380943 END: 12:26:07.613382 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-277-base-pr-001.dot * REASONING * DIS # C3: 2 => CTR => C3: 6,8 * DIS C3: 6,8 # H2: 5,7 => CTR => H2: 6 * DIS C3: 6,8 + H2: 6 # I2: 5,7 => CTR => I2: 3,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 # D2: 3,9 => CTR => D2: 5,7 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 # D3: 5,7 => CTR => D3: 1,3,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 # F3: 5,7 => CTR => F3: 3,6,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 # I3: 5,7 => CTR => I3: 1,2 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 # D3: 3,9 => CTR => D3: 1 * PRF C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 => SOL * STA C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 * CNT 9 HDP CHAINS / 11 HYP OPENED
Header Info
Top 500 Minimum 17 277 solution: 938265741152784963476193852825671394394852176617349528741536289289417635563928417 info: 2208 FNBTHWY S8.f 17898 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 938265741152784963476193852825671394394852176617349528741536289289417635563928417 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 # C3: 6,8 => UNS * DIS # C3: 2 => CTR => C3: 6,8 * DIS # G1: 6,8 => CTR => G1: 7 * PRF # G1: 7 => SOL * INC # D2: 5,7 => UNS * DIS # H2: 5,7 => CTR => H2: 6 * INC # H2: 6 => UNS * DIS # I2: 5,7 => CTR => I2: 2,3,6,9 * INC # I2: 2,3,6,9 => UNS * INC # C3: 2,6 => UNS * DIS # C3: 8 => CTR => C3: 2,6 * DIS # G2: 2,6 => CTR => G2: 3,7,9 * INC # G2: 3,7,9 => UNS * DIS # I2: 2,6 => CTR => I2: 3,5,7,9 * INC # I2: 3,5,7,9 => UNS * DIS # D3: 5,7 => CTR => D3: 1,3,9 * INC # D3: 1,3,9 => UNS * DIS # F3: 5,7 => CTR => F3: 3,6,9 * INC # F3: 3,6,9 => UNS * PRF # H3: 5,7 => SOL * INC # H3: 1,6,8 => UNS * DIS # I3: 5,7 => CTR => I3: 1,2,3,6,9 * INC # I3: 1,2,3,6,9 => UNS * PRF # I1: 1,6 => SOL * DIS # I1: 5,7 => CTR => I1: 1,6 * DIS # D2: 3,9 => CTR => D2: 5,7 * INC # D2: 5,7 => UNS * DIS # D3: 3,9 => CTR => D3: 1,5,7 * INC # D3: 1,5,7 => UNS * PRF # F3: 3,9 => SOL * INC # F3: 5,6,7 => UNS * DIS # G3: 3,9 => CTR => G3: 2,6,7,8 * INC # G3: 2,6,7,8 => UNS * DIS # I3: 3,9 => CTR => I3: 1,2,5,6,7 * INC # I3: 1,2,5,6,7 => UNS * INC # E7: 3,9 => UNS * INC # E7: 2 => UNS * DIS # D2: 3,9 => CTR => D2: 5,7 * INC # D2: 5,7 => UNS * DIS # D3: 3,9 => CTR => D3: 1,5,7 * INC # D3: 1,5,7 => UNS * DIS # D7: 3,9 => CTR => D7: 5 * PRF # D7: 5 => SOL * PRF # F3: 3,9 => SOL * INC # F3: 5,6,7 => UNS * DIS # F7: 3,9 => CTR => F7: 5,6,8 * INC # F7: 5,6,8 => UNS * INC # H2: 6,7 => UNS * DIS # H3: 6,7 => CTR => H3: 1,5,8 * INC # H3: 1,5,8 => UNS * DIS # H9: 6,7 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * DIS # I1: 6,7 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * DIS # I2: 6,7 => CTR => I2: 2,3,5,9 * INC # I2: 2,3,5,9 => UNS * INC # I3: 6,7 => UNS * DIS # I8: 6,7 => CTR => I8: 1,5 * INC # I8: 1,5 => UNS * INC # I9: 6,7 => UNS * INC # B7: 6,8 => UNS * INC # B9: 6,8 => UNS * DIS # F8: 6,8 => CTR => F8: 5,7 * INC # F8: 5,7 => UNS * PRF # G8: 6,8 => SOL * DIS # G8: 7 => CTR => G8: 6,8 * DIS # I8: 1,6 => CTR => I8: 5,7 * PRF # I8: 5,7 => SOL * INC # E7: 2,9 => UNS * INC # E7: 3 => UNS * INC # G9: 2,9 => UNS * INC # I9: 2,9 => UNS * CNT 72 HDP CHAINS / 72 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 6,8 => UNS * DIS # C3: 2 => CTR => C3: 6,8 * INC C3: 6,8 # D2: 5,7 => UNS * DIS C3: 6,8 # H2: 5,7 => CTR => H2: 6 * DIS C3: 6,8 + H2: 6 # I2: 5,7 => CTR => I2: 3,9 * INC C3: 6,8 + H2: 6 + I2: 3,9 # D2: 5,7 => UNS * DIS C3: 6,8 + H2: 6 + I2: 3,9 # D2: 3,9 => CTR => D2: 5,7 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 # D3: 5,7 => CTR => D3: 1,3,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 # F3: 5,7 => CTR => F3: 3,6,9 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 # I3: 5,7 => CTR => I3: 1,2 * DIS C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 # D3: 3,9 => CTR => D3: 1 * PRF C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 => SOL * STA C3: 6,8 + H2: 6 + I2: 3,9 + D2: 5,7 + D3: 1,3,9 + F3: 3,6,9 + I3: 1,2 + D3: 1 * CNT 12 HDP CHAINS / 11 HYP OPENED