Analysis of xx-top500-276-base.sdk
Contents
Original Sudoku
level: medium
position: .3.7...4.1...9..............2.68.........21........5.98.1.........4...3.5........ initial
Autosolve
position: 23.7...4.1...94...4........925681.7.3749521..6183475298.1......7.24...3.5.3...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 7 => CTR => C3: 6,9 * DIS # G1: 6,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # H2: 5,8 => CTR => H2: 6 * DIS # I2: 5,8 => CTR => I2: 2,3,6,7 * DIS # C3: 9 => CTR => C3: 6,7 * DIS # G2: 6,7 => CTR => G2: 2,3,8 * DIS # I2: 6,7 => CTR => I2: 2,3,5,8 * DIS # D3: 5,8 => CTR => D3: 1,2 * DIS # F3: 5,8 => CTR => F3: 3,6 * PRF # H3: 5,8 => SOL * DIS # I3: 5,8 => CTR => I3: 1,2,6,7 * PRF # I1: 1,6 => SOL * DIS # I1: 5,8 => CTR => I1: 1,6 * DIS # E7: 7 => CTR => E7: 2,3 * DIS # H3: 6,8 => CTR => H3: 1,5,9 * DIS # H9: 6,8 => CTR => H9: 1,9 * DIS # I1: 6,8 => CTR => I1: 1,5 * DIS # I2: 6,8 => CTR => I2: 2,3,5,7 * DIS # I8: 6,8 => CTR => I8: 1,5 * DIS # F8: 6,9 => CTR => F8: 5,8 * PRF # G8: 6,9 => SOL * DIS # G8: 8 => CTR => G8: 6,9 * PRF # I7: 2,5 => SOL * DIS # D3: 2,5 => CTR => D3: 1,8 * DIS # I8: 1,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * DIS # E7: 2,7 => CTR => E7: 3 * PRF # E7: 3 => SOL * CNT 29 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 7 => CTR => C3: 6,9 * DIS C3: 6,9 # H2: 5,8 => CTR => H2: 6 * DIS C3: 6,9 + H2: 6 # I2: 5,8 => CTR => I2: 2,3 * DIS C3: 6,9 + H2: 6 + I2: 2,3 # D2: 2 => CTR => D2: 5,8 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 # D3: 5,8 => CTR => D3: 1,2 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 # F3: 5,8 => CTR => F3: 3,6 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 # I3: 5,8 => CTR => I3: 1,7 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 # E7: 7 => CTR => E7: 2,3 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 # F8: 6,9 => CTR => F8: 5,8 * PRF C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 # G8: 6,9 => SOL * STA C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 + G8: 6,9 * CNT 10 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.7...4.1...9..............2.68.........21........5.98.1.........4...3.5........ | initial |
| 23.7...4.1...94...4........925681.7.3749521..6183475298.1......7.24...3.5.3...... | autosolve |
| 239765841157894263486123957925681374374952186618347529841536792792418635563279418 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 6,9 B2: 5,8 C2: 6,7 B3: 5,8 E1: 1,6 E3: 2,3 G4: 3,4 I4: 3,4 H5: 6,8 I5: 6,8 B8: 6,9 D7: 2,5 E8: 1,6 E9: 2,7 -------------------------------------------------- * 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 (_) E3,F3: 3.. / E3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) G2,I2: 3.. / G2 = 3 => 12 pairs (_) / I2 = 3 => 12 pairs (_) G4,I4: 3.. / G4 = 3 => 12 pairs (_) / I4 = 3 => 12 pairs (_) E7,F7: 3.. / E7 = 3 => 0 pairs (*) / F7 = 3 => 0 pairs (X) E3,E7: 3.. / E3 = 3 => 0 pairs (X) / E7 = 3 => 0 pairs (_) F3,F7: 3.. / F3 = 3 => 0 pairs (*) / F7 = 3 => 0 pairs (X) G2,G4: 3.. / G2 = 3 => 12 pairs (_) / G4 = 3 => 12 pairs (_) I2,I4: 3.. / I2 = 3 => 12 pairs (_) / I4 = 3 => 12 pairs (_) G4,I4: 4.. / G4 = 4 => 12 pairs (_) / I4 = 4 => 12 pairs (_) B7,B9: 4.. / B7 = 4 => 15 pairs (_) / B9 = 4 => 15 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 => 13 pairs (_) E1,E8: 6.. / E1 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 15 pairs (_) / C3 = 7 => 0 pairs (X) E7,E9: 7.. / E7 = 7 => 0 pairs (X) / E9 = 7 => 14 pairs (_) B2,B3: 8.. / B2 = 8 => 16 pairs (_) / B3 = 8 => 16 pairs (_) H5,I5: 8.. / H5 = 8 => 13 pairs (_) / I5 = 8 => 0 pairs (X) C1,C3: 9.. / C1 = 9 => 15 pairs (_) / C3 = 9 => 0 pairs (X) C1,G1: 9.. / C1 = 9 => 15 pairs (_) / G1 = 9 => 0 pairs (X) * DURATION: 0:00:45.234550 START: 12:22:08.002699 END: 12:22:53.237249 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D7,E1,E3,E8,E9,G4,H5,I4,I5) * 23.7...4.1...94...4........925681.7.3749521..6183475298.1......7.24...3.5.3...... * PAIR C1: 6,9 BLK 1 C3: 6,9,7 # reduction candidate for 6,9 C3: 7 => CTR * 239765841186294.5.457138...925681.7.3749521866183475298.15.3...7.241..355.38...1. C3: 6,9 # 15 pairs * PAIR C1: 6,9 ROW 1 G1: 6,9,8 # reduction candidate for 6,9 G1: 6,9 => CTR * 23.71..4.1...94...4...36.1.925681.7.3749521..6183475298.1..3...7924658315.31..... G1: 8 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 * PAIR B2: 5,8 ROW 2 D2: 5,8,2 # reduction candidate for 5,8 D2: 5,8 # 18 pairs H2: 5,8,6 # reduction candidate for 5,8 H2: 5,8 => CTR * 23.765.411..294...4..138...925681.7.3749521.86183475298.15.3...7.241.8355.38...1. H2: 6 # 15 pairs I2: 5,8,2,3,6,7 # reduction candidate for 5,8 I2: 5,8 => CTR * 23.7.5.4.15729436848.136...9256814733749521866183475298.15.3.9.7.24...355.3....1. I2: 2,3,6,7 # 14 pairs * PAIR C2: 6,7 BLK 1 C3: 6,7,9 # reduction candidate for 6,7 C3: 9 => CTR * 23671.94.1.7.94...4.9..6...925681.7.3749521..6183475298.1..3...7.246.8315.31.8... C3: 6,7 # 15 pairs * PAIR C2: 6,7 ROW 2 G2: 6,7,2,3,8 # reduction candidate for 6,7 G2: 6,7 => CTR * 23.765.411..294..34..138...9256813743749521.86183475298.15.3...7.241.8355.38...1. G2: 2,3,8 # 14 pairs I2: 6,7,2,3,5,8 # reduction candidate for 6,7 I2: 6,7 => CTR * 23.765.411..2943..4..138...9256814733749521.86183475298.15.3...7.241.8355.38...1. I2: 2,3,5,8 # 14 pairs * PAIR B3: 5,8 ROW 3 D3: 5,8,1,2 # reduction candidate for 5,8 D3: 5,8 => CTR * 23.71..4.1...94...4......1.925681.7.3749521..6183475298.1......7924658315.31.8... D3: 1,2 # 15 pairs F3: 5,8,3,6 # reduction candidate for 5,8 F3: 5,8 => CTR * 2397.58411...94...4..138...925681.7.3749521..6183475298.15.3...7.241..355.38...1. F3: 3,6 # 15 pairs H3: 5,8,1,6,9 # reduction candidate for 5,8 H3: 5,8 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 H3: 1,6,9 # 14 pairs I3: 5,8,1,2,6,7 # reduction candidate for 5,8 I3: 5,8 => CTR * 23.7.8945187594.6.459..6718925681.7.3749521866183475298.12...5.7.24.5.3.5.3...... I3: 1,2,6,7 # 14 pairs * PAIR E1: 1,6 ROW 1 I1: 1,6,5,8 # reduction candidate for 1,6 I1: 1,6 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 I1: 5,8 => CTR * 23.71..4.1...94...4......1.925681.7.3749521..6183475298.1......7924658315.31.8... * PAIR E3: 2,3 COL E E7: 2,3,7 # reduction candidate for 2,3 E7: 7 => CTR * 23.765.411..294...4..138...925681.7.3749521..6183475298.1573...7.241.8355.382..1. E7: 2,3 # 14 pairs * PAIR H5: 6,8 COL H H2: 6,8,5 # reduction candidate for 6,8 H2: 6,8 # 17 pairs H3: 6,8,1,5,9 # reduction candidate for 6,8 H3: 6,8 => CTR * 23976584118.294.5.45.138962925681.7.3749521866183475298.15.3.9.7.241.6355.38.6.1. H3: 1,5,9 # 14 pairs H9: 6,8,1,9 # reduction candidate for 6,8 H9: 6,8 => CTR * 23.71..4.1...94.5.45.....1.925681.7.3749521..6183475298.15...9.7.246..3.5.31..... H9: 1,9 # 15 pairs * PAIR I5: 6,8 COL I I1: 6,8,1,5 # reduction candidate for 6,8 I1: 6,8 => CTR * 23.715.4.1...94...4....6...925681.7.3749521..6183475298.15.3...7.246..3.5.3...... I1: 1,5 # 15 pairs I2: 6,8,2,3,5,7 # reduction candidate for 6,8 I2: 6,8 => CTR * 23.765.411.72943..4.6138...9256814733749521..6183475298.15.3...7.241.8355.38...1. I2: 2,3,5,7 # 14 pairs I3: 6,8,1,2,5,7 # reduction candidate for 6,8 I3: 6,8 # 18 pairs I8: 6,8,1,5 # reduction candidate for 6,8 I8: 6,8 => CTR * 23.7...4.1...94...4........925681.7.3749521..6183475298.1......7.2415.3.5.3...... I8: 1,5 # 15 pairs I9: 6,8,1,2,4,7 # reduction candidate for 6,8 I9: 6,8 # 18 pairs * PAIR B8: 6,9 BLK 7 B7: 6,9,4 # reduction candidate for 6,9 B7: 6,9 # 15 pairs B9: 6,9,4 # reduction candidate for 6,9 B9: 6,9 # 15 pairs * PAIR B8: 6,9 ROW 8 F8: 6,9,5,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 23.7.5.4.1...94...4........925681.7.3749521..6183475298.15.....7.241.8355.3...... F8: 5,8 # 15 pairs G8: 6,9,8 # reduction candidate for 6,9 G8: 6,9 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 G8: 8 => CTR * 23.71..4.1...94...4....6...925681.7.3749521..6183475298.1..3...7.246.8315.31.8... * PAIR D7: 2,5 ROW 7 I7: 2,5,4,6,7 # reduction candidate for 2,5 I7: 2,5 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 I7: 4,6,7 # 14 pairs * PAIR D7: 2,5 COL D D2: 2,5,8 # reduction candidate for 2,5 D2: 2,5 # 17 pairs D3: 2,5,1,8 # reduction candidate for 2,5 D3: 2,5 => CTR * 23.71..4.1..894...48.....1.925681.7.3749521..6183475298.1......7924658315.31.8... D3: 1,8 # 15 pairs * PAIR E8: 1,6 ROW 8 I8: 1,6,5,8 # reduction candidate for 1,6 I8: 1,6 => CTR * 23.718.451..594...4........925681.7.3749521..6183475298.12...5.7924.583.5.3.7.... I8: 5,8 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 * PAIR E9: 2,7 BLK 8 E7: 2,7,3 # reduction candidate for 2,7 E7: 2,7 => CTR * 23.765.411..294...4..138...925681.7.3749521..6183475298.15.3...7.241.8355.38...1. E7: 3 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 * PAIR E9: 2,7 ROW 9 G9: 2,7,4,6,8,9 # reduction candidate for 2,7 G9: 2,7 # 16 pairs I9: 2,7,1,4,6,8 # reduction candidate for 2,7 I9: 2,7 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-276-base-pr-000.dot * REASONING * DIS # C3: 7 => CTR => C3: 6,9 * DIS # G1: 6,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # H2: 5,8 => CTR => H2: 6 * DIS # I2: 5,8 => CTR => I2: 2,3,6,7 * DIS # C3: 9 => CTR => C3: 6,7 * DIS # G2: 6,7 => CTR => G2: 2,3,8 * DIS # I2: 6,7 => CTR => I2: 2,3,5,8 * DIS # D3: 5,8 => CTR => D3: 1,2 * DIS # F3: 5,8 => CTR => F3: 3,6 * PRF # H3: 5,8 => SOL * DIS # I3: 5,8 => CTR => I3: 1,2,6,7 * PRF # I1: 1,6 => SOL * DIS # I1: 5,8 => CTR => I1: 1,6 * DIS # E7: 7 => CTR => E7: 2,3 * DIS # H3: 6,8 => CTR => H3: 1,5,9 * DIS # H9: 6,8 => CTR => H9: 1,9 * DIS # I1: 6,8 => CTR => I1: 1,5 * DIS # I2: 6,8 => CTR => I2: 2,3,5,7 * DIS # I8: 6,8 => CTR => I8: 1,5 * DIS # F8: 6,9 => CTR => F8: 5,8 * PRF # G8: 6,9 => SOL * DIS # G8: 8 => CTR => G8: 6,9 * PRF # I7: 2,5 => SOL * DIS # D3: 2,5 => CTR => D3: 1,8 * DIS # I8: 1,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * DIS # E7: 2,7 => CTR => E7: 3 * PRF # E7: 3 => SOL * CNT 29 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B8,C1,C2,D7,E1,E3,E8,E9,G4,H5,I4,I5) * 23.7...4.1...94...4........925681.7.3749521..6183475298.1......7.24...3.5.3...... * PAIR C1: 6,9 BLK 1 C3: 6,9,7 # reduction candidate for 6,9 C3: 7 => CTR * 239765841186294.5.457138...925681.7.3749521866183475298.15.3...7.241..355.38...1. * PAIR B2: 5,8 ROW 2 D2: 5,8,2 # reduction candidate for 5,8 D2: 5,8 # 18 pairs H2: 5,8,6 # reduction candidate for 5,8 H2: 5,8 => CTR * 23.765.411.7294...4.6138.9.925681.7.3749521.86183475298.15.3.6.7.241..355.38..... I2: 5,8,2,3 # reduction candidate for 5,8 I2: 5,8 => CTR * 23.7.5.4.15729436848.136...9256814733749521866183475298.15.3.9.7.24...355.3....1. * RESTART * PAIR B2: 5,8 ROW 2 D2: 5,8,2 # reduction candidate for 5,8 D2: 2 => CTR * 23.7...4.15729486348..3....9256813743749521866183475298.15.3.9.7.24..6355.38.6... * PAIR RESTART * PAIR B3: 5,8 ROW 3 D3: 5,8,1,2 # reduction candidate for 5,8 D3: 5,8 => CTR * 23.716.451.7.94.6.4.6.23917925681.7.3749521866183475298.123.7547924658315.317..9. F3: 5,8,3,6 # reduction candidate for 5,8 F3: 5,8 => CTR * 2397..84.1.7.94.6.4.623....925681.7.3749521866183475298.15.3.9.7.24..6355.31..... I3: 5,8,1,7 # reduction candidate for 5,8 I3: 5,8 => CTR * 23.7.8945187594.6.459..6718925681.7.3749521866183475298.12...5.7.24.5.3.5.3...... * RESTART * PAIR RESTART * PAIR E3: 2,3 COL E E7: 2,3,7 # reduction candidate for 2,3 E7: 7 => CTR * 23.7...4.1.7.94.6.4...36...925681.7.3749521866183475298.1.73...7.246..315.312..9. * PAIR RESTART * PAIR B8: 6,9 BLK 7 B7: 6,9,4 # reduction candidate for 6,9 B7: 6,9 # 26 pairs B9: 6,9,4 # reduction candidate for 6,9 B9: 6,9 # 23 pairs * PAIR B8: 6,9 ROW 8 F8: 6,9,5,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 23.7.5.4.157894.6.48.....5.925681.7.3749521866183475298.15...9.7.241.8355.3278.14 G8: 6,9,8 # reduction candidate for 6,9 G8: 6,9 => SOLVED * 239765841157894263486123957925681374374952186618347529841536792792418635563279418 * DURATION: 0:00:19.544284 START: 12:23:44.593660 END: 12:24:04.137944 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-276-base-pr-001.dot * REASONING * DIS # C3: 7 => CTR => C3: 6,9 * DIS C3: 6,9 # H2: 5,8 => CTR => H2: 6 * DIS C3: 6,9 + H2: 6 # I2: 5,8 => CTR => I2: 2,3 * DIS C3: 6,9 + H2: 6 + I2: 2,3 # D2: 2 => CTR => D2: 5,8 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 # D3: 5,8 => CTR => D3: 1,2 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 # F3: 5,8 => CTR => F3: 3,6 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 # I3: 5,8 => CTR => I3: 1,7 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 # E7: 7 => CTR => E7: 2,3 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 # F8: 6,9 => CTR => F8: 5,8 * PRF C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 # G8: 6,9 => SOL * STA C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 + G8: 6,9 * CNT 10 HDP CHAINS / 16 HYP OPENED
Header Info
Top 500 Minimum 17 276 solution: 239765841157894263486123957925681374374952186618347529841536792792418635563279418 info: 2205 FNBTHWY S8.f 18054 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 239765841157894263486123957925681374374952186618347529841536792792418635563279418 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: 6,9 => UNS * DIS # C3: 7 => CTR => C3: 6,9 * DIS # G1: 6,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * INC # D2: 5,8 => UNS * DIS # H2: 5,8 => CTR => H2: 6 * INC # H2: 6 => UNS * DIS # I2: 5,8 => CTR => I2: 2,3,6,7 * INC # I2: 2,3,6,7 => UNS * INC # C3: 6,7 => UNS * DIS # C3: 9 => CTR => C3: 6,7 * DIS # G2: 6,7 => CTR => G2: 2,3,8 * INC # G2: 2,3,8 => UNS * DIS # I2: 6,7 => CTR => I2: 2,3,5,8 * INC # I2: 2,3,5,8 => UNS * DIS # D3: 5,8 => CTR => D3: 1,2 * INC # D3: 1,2 => UNS * DIS # F3: 5,8 => CTR => F3: 3,6 * INC # F3: 3,6 => UNS * PRF # H3: 5,8 => SOL * INC # H3: 1,6,9 => UNS * DIS # I3: 5,8 => CTR => I3: 1,2,6,7 * INC # I3: 1,2,6,7 => UNS * PRF # I1: 1,6 => SOL * DIS # I1: 5,8 => CTR => I1: 1,6 * INC # E7: 2,3 => UNS * DIS # E7: 7 => CTR => E7: 2,3 * INC # H2: 6,8 => UNS * DIS # H3: 6,8 => CTR => H3: 1,5,9 * INC # H3: 1,5,9 => UNS * DIS # H9: 6,8 => CTR => H9: 1,9 * INC # H9: 1,9 => UNS * DIS # I1: 6,8 => CTR => I1: 1,5 * INC # I1: 1,5 => UNS * DIS # I2: 6,8 => CTR => I2: 2,3,5,7 * INC # I2: 2,3,5,7 => UNS * INC # I3: 6,8 => UNS * DIS # I8: 6,8 => CTR => I8: 1,5 * INC # I8: 1,5 => UNS * INC # I9: 6,8 => UNS * INC # B7: 6,9 => UNS * INC # B9: 6,9 => UNS * DIS # F8: 6,9 => CTR => F8: 5,8 * INC # F8: 5,8 => UNS * PRF # G8: 6,9 => SOL * DIS # G8: 8 => CTR => G8: 6,9 * PRF # I7: 2,5 => SOL * INC # I7: 4,6,7 => UNS * INC # D2: 2,5 => UNS * DIS # D3: 2,5 => CTR => D3: 1,8 * INC # D3: 1,8 => UNS * DIS # I8: 1,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * DIS # E7: 2,7 => CTR => E7: 3 * PRF # E7: 3 => SOL * INC # G9: 2,7 => UNS * INC # I9: 2,7 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 6,9 => UNS * DIS # C3: 7 => CTR => C3: 6,9 * INC C3: 6,9 # D2: 5,8 => UNS * DIS C3: 6,9 # H2: 5,8 => CTR => H2: 6 * DIS C3: 6,9 + H2: 6 # I2: 5,8 => CTR => I2: 2,3 * INC C3: 6,9 + H2: 6 + I2: 2,3 # D2: 5,8 => UNS * DIS C3: 6,9 + H2: 6 + I2: 2,3 # D2: 2 => CTR => D2: 5,8 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 # D3: 5,8 => CTR => D3: 1,2 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 # F3: 5,8 => CTR => F3: 3,6 * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 # I3: 5,8 => CTR => I3: 1,7 * INC C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 # E7: 2,3 => UNS * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 # E7: 7 => CTR => E7: 2,3 * INC C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 # B7: 6,9 => UNS * INC C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 # B9: 6,9 => UNS * DIS C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 # F8: 6,9 => CTR => F8: 5,8 * PRF C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 # G8: 6,9 => SOL * STA C3: 6,9 + H2: 6 + I2: 2,3 + D2: 5,8 + D3: 1,2 + F3: 3,6 + I3: 1,7 + E7: 2,3 + F8: 5,8 + G8: 6,9 * CNT 16 HDP CHAINS / 16 HYP OPENED