Analysis of zz-sudoku-de-680159-base.sdk
Contents
Original Sudoku
level: medium
position: 28...6..4.5.7...32....8....1......2...5.4.6...9......1....2....72...1.6.4..3...79 initial
Autosolve
position: 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 3,9 => CTR => F3: 4,5 * DIS # D4: 6,8 => CTR => D4: 5,9 * DIS # F3: 3,5 => CTR => F3: 4,9 * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * DIS # F3: 3,5 => CTR => F3: 4,9 * PRF # A6: 3,8 => SOL * DIS # I5: 7 => CTR => I5: 3,8 * DIS # B4: 3,7 => CTR => B4: 4,6 * PRF # I5: 8 => SOL * PRF # B3: 3,7 => SOL * DIS # I4: 3,5 => CTR => I4: 7,8 * PRF # G6: 3,5 => SOL * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * DIS # F4: 3,5 => CTR => F4: 8,9 * PRF # G8: 4 => SOL * DIS # B4: 3,6 => CTR => B4: 4,7 * DIS # I8: 3,8 => CTR => I8: 5 * DIS # C9: 1,6 => CTR => C9: 8 * PRF # C9: 8 => SOL * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * DIS # E4: 3 => CTR => E4: 5,6 * PRF # F4: 5,8 => SOL * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * DIS # I8: 3,8 => CTR => I8: 5 * DIS # I4: 3,8 => CTR => I4: 5,7 * CNT 29 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F3: 3,9 => CTR => F3: 4,5 * DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9 * PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL * STA F3: 4,5 + D4: 5,9 + A6: 3,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 28...6..4.5.7...32....8....1......2...5.4.6...9......1....2....72...1.6.4..3...79 | initial |
| 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 | autosolve |
| 287536914654719832931284756146958327375142698892673541569427183723891465418365279 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A2: 6,9 C2: 4,6 A3: 3,9 D1: 5,9 E1: 3,5 F2: 4,9 G1: 7,9 H1: 1,5 G3: 7,9 H3: 1,5 A5: 3,8 B5: 3,7 G4: 3,5 H6: 4,8 B7: 3,6 C8: 3,8 B9: 1,6 D8: 4,8 E9: 5,6 F9: 5,8 H7: 4,8 I7: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 21 pairs (_) / H3 = 1 => 0 pairs (X) B9,C9: 1.. / B9 = 1 => 22 pairs (_) / C9 = 1 => 0 pairs (X) C1,H1: 1.. / C1 = 1 => 0 pairs (X) / H1 = 1 => 21 pairs (_) B3,B9: 1.. / B3 = 1 => 0 pairs (X) / B9 = 1 => 22 pairs (_) E1,F3: 3.. / E1 = 3 => 23 pairs (_) / F3 = 3 => 0 pairs (X) B7,C8: 3.. / B7 = 3 => 0 pairs (X) / C8 = 3 => 0 pairs (_) C1,E1: 3.. / C1 = 3 => 0 pairs (X) / E1 = 3 => 23 pairs (_) B7,I7: 3.. / B7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) E1,E4: 3.. / E1 = 3 => 23 pairs (_) / E4 = 3 => 0 pairs (X) F2,F3: 4.. / F2 = 4 => 22 pairs (_) / F3 = 4 => 0 pairs (*) B4,C4: 4.. / B4 = 4 => 23 pairs (_) / C4 = 4 => 0 pairs (X) G6,H6: 4.. / G6 = 4 => 27 pairs (_) / H6 = 4 => 0 pairs (*) D7,D8: 4.. / D7 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) H7,G8: 4.. / H7 = 4 => 27 pairs (_) / G8 = 4 => 0 pairs (*) C2,F2: 4.. / C2 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) D7,H7: 4.. / D7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) D8,G8: 4.. / D8 = 4 => 27 pairs (_) / G8 = 4 => 0 pairs (*) B3,B4: 4.. / B3 = 4 => 0 pairs (X) / B4 = 4 => 23 pairs (_) G6,G8: 4.. / G6 = 4 => 27 pairs (_) / G8 = 4 => 0 pairs (*) H6,H7: 4.. / H6 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) H1,H3: 5.. / H1 = 5 => 0 pairs (X) / H3 = 5 => 21 pairs (_) E9,F9: 5.. / E9 = 5 => 0 pairs (X) / F9 = 5 => 0 pairs (_) G8,I8: 5.. / G8 = 5 => 0 pairs (X) / I8 = 5 => 24 pairs (_) F3,H3: 5.. / F3 = 5 => 0 pairs (X) / H3 = 5 => 21 pairs (_) I4,I8: 5.. / I4 = 5 => 0 pairs (X) / I8 = 5 => 24 pairs (_) A2,C2: 6.. / A2 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) D7,E9: 6.. / D7 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) A6,D6: 6.. / A6 = 6 => 22 pairs (_) / D6 = 6 => 0 pairs (*) B7,D7: 6.. / B7 = 6 => 0 pairs (*) / D7 = 6 => 0 pairs (X) A2,A6: 6.. / A2 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) E4,E9: 6.. / E4 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) G1,G3: 7.. / G1 = 7 => 0 pairs (X) / G3 = 7 => 19 pairs (_) I4,I5: 7.. / I4 = 7 => 28 pairs (_) / I5 = 7 => 0 pairs (X) C1,G1: 7.. / C1 = 7 => 19 pairs (_) / G1 = 7 => 0 pairs (X) B5,I5: 7.. / B5 = 7 => 28 pairs (_) / I5 = 7 => 0 pairs (X) A5,A6: 8.. / A5 = 8 => 23 pairs (_) / A6 = 8 => 0 pairs (*) C8,C9: 8.. / C8 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) A5,I5: 8.. / A5 = 8 => 23 pairs (_) / I5 = 8 => 0 pairs (*) C9,F9: 8.. / C9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) H6,H7: 8.. / H6 = 8 => 27 pairs (_) / H7 = 8 => 0 pairs (*) A2,A3: 9.. / A2 = 9 => 22 pairs (_) / A3 = 9 => 0 pairs (*) G1,G3: 9.. / G1 = 9 => 19 pairs (_) / G3 = 9 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 19 pairs (_) / F4 = 9 => 0 pairs (X) D1,G1: 9.. / D1 = 9 => 0 pairs (X) / G1 = 9 => 19 pairs (_) A2,F2: 9.. / A2 = 9 => 22 pairs (_) / F2 = 9 => 0 pairs (*) D1,D4: 9.. / D1 = 9 => 0 pairs (X) / D4 = 9 => 19 pairs (_) * DURATION: 0:01:28.955567 START: 07:48:01.102611 END: 07:49:30.058178 2017-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,B5,B7,B9,C2,C8,D1,D8,E1,E9,F2,F9,G1,G3,G4,H1,H3,H6,H7,I7) * 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 * PAIR C2: 4,6 COL C C4: 4,6,3,7 # reduction candidate for 4,6 C4: 4,6 # 24 pairs C4: 3,7 # 24 pairs * PAIR A3: 3,9 ROW 3 F3: 3,9,4,5 # reduction candidate for 3,9 F3: 3,9 => CTR * 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279 F3: 4,5 # 24 pairs * PAIR D1: 5,9 BLK 2 F3: 5,9,3,4 # reduction candidate for 5,9 F3: 5,9 # 22 pairs F3: 3,4 # 22 pairs * PAIR D1: 5,9 COL D D4: 5,9,6,8 # reduction candidate for 5,9 D4: 6,8 => CTR * 28.9.67.49567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279 D4: 5,9 # 24 pairs * PAIR E1: 3,5 BLK 2 F3: 3,5,4,9 # reduction candidate for 3,5 F3: 3,5 => CTR * 28.9.67.49567148323..2859161....9.2.8.514269.692.73..15.9.271..72..91.6.4183..279 F3: 4,9 # 19 pairs * PAIR E1: 3,5 COL E E4: 3,5,6 # reduction candidate for 3,5 E4: 3,5 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 E4: 6 => CTR * 287.3691495671483231428975614..6..2...514269.692.7...15.962714872.491.6.461358279 * PAIR F2: 4,9 BLK 2 F3: 4,9,3,5 # reduction candidate for 4,9 F3: 3,5 => CTR * 28.9.67.49567148323..2859161....9.2.8.514269.692.73..15.9.271..72..91.6.4183..279 F3: 4,9 # 19 pairs * PAIR A5: 3,8 BLK 4 A6: 3,8,6 # reduction candidate for 3,8 A6: 3,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 A6: 6 # 22 pairs * PAIR A5: 3,8 ROW 5 I5: 3,8,7 # reduction candidate for 3,8 I5: 7 => CTR * 28..36..49567148323..28975617.....2.835142697692.7...1569.271.3723.91.6.418365279 I5: 3,8 # 28 pairs * PAIR B5: 3,7 BLK 4 B4: 3,7,4,6 # reduction candidate for 3,7 B4: 3,7 => CTR * 28..36..495671483234.2897561.4....2.8.514269.692.7...1569.271.3723.91.6.418365279 B4: 4,6 # 23 pairs C4: 3,7,4,6 # reduction candidate for 3,7 C4: 3,7 # 24 pairs * PAIR B5: 3,7 ROW 5 I5: 3,7,8 # reduction candidate for 3,7 I5: 8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 I5: 3,7 # 23 pairs * PAIR B5: 3,7 COL B B3: 3,7,1,4 # reduction candidate for 3,7 B3: 3,7 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 B3: 1,4 # 23 pairs * PAIR G4: 3,5 BLK 6 I4: 3,5,7,8 # reduction candidate for 3,5 I4: 3,5 => CTR * 28...6..4.5.71.832...28...61......2.83514269769257348156982714372349156841836.279 I4: 7,8 # 25 pairs G6: 3,5,4 # reduction candidate for 3,5 G6: 3,5 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 G6: 4 # 27 pairs * PAIR G4: 3,5 ROW 4 E4: 3,5,6 # reduction candidate for 3,5 E4: 3,5 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 E4: 6 => CTR * 287.3691495671483231428975614..6..2...514269.692.7...15.962714872.491.6.461358279 F4: 3,5,8,9 # reduction candidate for 3,5 F4: 3,5 => CTR * 28.536914.5.71.832..128.75617.9...288.5142697.92.7..415.94271837238914654.8365279 F4: 8,9 # 23 pairs * PAIR G4: 3,5 COL G G8: 3,5,4 # reduction candidate for 3,5 G8: 4 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 G8: 3,5 # 27 pairs * PAIR B7: 3,6 COL B B4: 3,6,4,7 # reduction candidate for 3,6 B4: 3,6 => CTR * 28...6..4.56714832.4.28...61.4....27.7514269.692.7...1569.271.3723891465418365279 B4: 4,7 # 24 pairs * PAIR C8: 3,8 ROW 8 I8: 3,8,5 # reduction candidate for 3,8 I8: 3,8 => CTR * 28...6..4.5.71.832...28...61.....32583514269769257348156982714372349156841836.279 I8: 5 # 24 pairs * PAIR B9: 1,6 BLK 7 C9: 1,6,8 # reduction candidate for 1,6 C9: 1,6 => CTR * 28..36..4.5.71.832...28...61..869.2.875142693692573481539627148728491365461358279 C9: 8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 * PAIR D8: 4,8 BLK 8 D7: 4,8,6 # reduction candidate for 4,8 D7: 4,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 D7: 6 => CTR * 28..36..4.5.71.832...28...61..869.2.8.514269.692573481539627148728491.6.461358279 * PAIR E9: 5,6 COL E E4: 5,6,3 # reduction candidate for 5,6 E4: 3 => CTR * 283.56714.5.71.8329..28...61...3.52...514269..92.7...15.9.271..72..91.654..365279 E4: 5,6 # 23 pairs * PAIR F9: 5,8 COL F F4: 5,8,3,9 # reduction candidate for 5,8 F4: 5,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 F4: 3,9 # 23 pairs F6: 5,8,3 # reduction candidate for 5,8 F6: 5,8 # 27 pairs * PAIR H7: 4,8 ROW 7 D7: 4,8,6 # reduction candidate for 4,8 D7: 4,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 D7: 6 => CTR * 28..36..4.5.71.832...28...61..869.2.8.514269.692573481539627148728491.6.461358279 * PAIR I7: 3,8 BLK 9 I8: 3,8,5 # reduction candidate for 3,8 I8: 3,8 => CTR * 28...6..4.5.71.832...28...61.....32583514269769257348156982714372349156841836.279 I8: 5 # 24 pairs * PAIR I7: 3,8 COL I I4: 3,8,5,7 # reduction candidate for 3,8 I4: 3,8 => CTR * 28..36..49567148323..28975617.....2.835142697692.7...1569.271.3723891465418365279 I4: 5,7 # 27 pairs I5: 3,8,7 # reduction candidate for 3,8 I5: 3,8 # 28 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-680159-base-pr-000.dot * REASONING * DIS # F3: 3,9 => CTR => F3: 4,5 * DIS # D4: 6,8 => CTR => D4: 5,9 * DIS # F3: 3,5 => CTR => F3: 4,9 * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * DIS # F3: 3,5 => CTR => F3: 4,9 * PRF # A6: 3,8 => SOL * DIS # I5: 7 => CTR => I5: 3,8 * DIS # B4: 3,7 => CTR => B4: 4,6 * PRF # I5: 8 => SOL * PRF # B3: 3,7 => SOL * DIS # I4: 3,5 => CTR => I4: 7,8 * PRF # G6: 3,5 => SOL * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * DIS # F4: 3,5 => CTR => F4: 8,9 * PRF # G8: 4 => SOL * DIS # B4: 3,6 => CTR => B4: 4,7 * DIS # I8: 3,8 => CTR => I8: 5 * DIS # C9: 1,6 => CTR => C9: 8 * PRF # C9: 8 => SOL * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * DIS # E4: 3 => CTR => E4: 5,6 * PRF # F4: 5,8 => SOL * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * DIS # I8: 3,8 => CTR => I8: 5 * DIS # I4: 3,8 => CTR => I4: 5,7 * CNT 29 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,B5,B7,B9,C2,C8,D1,D8,E1,E9,F2,F9,G1,G3,G4,H1,H3,H6,H7,I7) * 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 * PAIR C2: 4,6 COL C C4: 4,6,3,7 # reduction candidate for 4,6 C4: 4,6 # 24 pairs C4: 3,7 # 24 pairs * PAIR A3: 3,9 ROW 3 F3: 3,9,4,5 # reduction candidate for 3,9 F3: 3,9 => CTR * 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279 * PAIR RESTART * PAIR D1: 5,9 COL D D4: 5,9,6,8 # reduction candidate for 5,9 D4: 6,8 => CTR * 28.9367549567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279 * PAIR RESTART * PAIR A5: 3,8 BLK 4 A6: 3,8,6 # reduction candidate for 3,8 A6: 3,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 * DURATION: 0:00:08.643104 START: 07:50:35.596725 END: 07:50:44.239829 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-680159-base-pr-001.dot * REASONING * DIS # F3: 3,9 => CTR => F3: 4,5 * DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9 * PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL * STA F3: 4,5 + D4: 5,9 + A6: 3,8 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokus.de/680159.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 A2: 6,9 C2: 4,6 C4: 3,4,6,7 # reduction candidate for 4,6 A3: 3,9 F3: 3,4,5,9 # reduction candidate for 3,9 F3: 3,9 => CTR * 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279 D1: 5,9 D4: 5,6,8,9 # reduction candidate for 5,9 D4: 6,8 => CTR * 28.9367549567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279 F2: 4,9 G1: 7,9 H1: 1,5 G3: 7,9 H3: 1,5 A5: 3,8 A6: 3,6,8 # reduction candidate for 3,8 A6: 3,8 => SOLVED * 287536914654719832931284756146958327375142698892673541569427183723891465418365279 * SOLVED! -------------------------------------------------- -------------------------------------------------- * AUTO .. G2 = 8 # set value I3 = 6 # set value D5 = 1 # set value C6 = 2 # set value A7 = 5 # set value F7 = 7 # set value G9 = 2 # set value F5: 2.. # hidden single D3: 2.. # hidden single D3 = 2 # set value F5 = 2 # set value H5: 9.. # hidden single H5 = 9 # set value Q4: 4.. = B4,C4: 4.. => G4 != 4 Q9: 1.. = G7,H7: 1.. => B7,C7 != 1 E8: 9 # naked single Q9: 5.. = G8,I8: 5.. => D8,E8 != 5 Q7: 8.. = C7,C8,C9: 8.. => C4 != 8 Q7: 9.. = C7,C8: 9.. => C1,C2,C3 != 9 Q3: 7.. = G1,G3: 7.. => G4,G6 != 7 E6: 7.. # hidden single E6 = 7 # set value E8 = 9 # set value E2: 1 # naked single C7: 9.. # hidden single E2 = 1 # set value C7 = 9 # set value G1,G3: 7,9.. => G1,G3 != 1,5 # hidden pair H6,H7: 4,8.. => H6,H7 != 1,5 # hidden pair G7: 1.. # hidden single G7 = 1 # set value * UNSOLVED! |:step:| 00 -------------------------------------------------- * DISABLE VALUE:: D7 != 6 E9: 6.. # hidden single B7: 6.. # hidden single |:step:| 01 --------------------------------------------------
Solution
position: 287536914654719832931284756146958327375142698892673541569427183723891465418365279 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 # C4: 4,6 => UNS * INC # C4: 3,7 => UNS * DIS # F3: 3,9 => CTR => F3: 4,5 * INC # F3: 4,5 => UNS * INC # F3: 5,9 => UNS * INC # F3: 3,4 => UNS * INC # D4: 5,9 => UNS * DIS # D4: 6,8 => CTR => D4: 5,9 * DIS # F3: 3,5 => CTR => F3: 4,9 * INC # F3: 4,9 => UNS * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * INC # F3: 4,9 => UNS * DIS # F3: 3,5 => CTR => F3: 4,9 * PRF # A6: 3,8 => SOL * INC # A6: 6 => UNS * INC # I5: 3,8 => UNS * DIS # I5: 7 => CTR => I5: 3,8 * DIS # B4: 3,7 => CTR => B4: 4,6 * INC # B4: 4,6 => UNS * INC # C4: 3,7 => UNS * INC # I5: 3,7 => UNS * PRF # I5: 8 => SOL * PRF # B3: 3,7 => SOL * INC # B3: 1,4 => UNS * DIS # I4: 3,5 => CTR => I4: 7,8 * INC # I4: 7,8 => UNS * PRF # G6: 3,5 => SOL * INC # G6: 4 => UNS * PRF # E4: 3,5 => SOL * DIS # E4: 6 => CTR => E4: 3,5 * DIS # F4: 3,5 => CTR => F4: 8,9 * INC # F4: 8,9 => UNS * INC # G8: 3,5 => UNS * PRF # G8: 4 => SOL * DIS # B4: 3,6 => CTR => B4: 4,7 * INC # B4: 4,7 => UNS * DIS # I8: 3,8 => CTR => I8: 5 * INC # I8: 5 => UNS * DIS # C9: 1,6 => CTR => C9: 8 * PRF # C9: 8 => SOL * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * INC # E4: 5,6 => UNS * DIS # E4: 3 => CTR => E4: 5,6 * PRF # F4: 5,8 => SOL * INC # F4: 3,9 => UNS * INC # F6: 5,8 => UNS * PRF # D7: 4,8 => SOL * DIS # D7: 6 => CTR => D7: 4,8 * DIS # I8: 3,8 => CTR => I8: 5 * INC # I8: 5 => UNS * DIS # I4: 3,8 => CTR => I4: 5,7 * INC # I4: 5,7 => UNS * INC # I5: 3,8 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C4: 4,6 => UNS * INC # C4: 3,7 => UNS * DIS # F3: 3,9 => CTR => F3: 4,5 * INC F3: 4,5 # D4: 5,9 => UNS * DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9 * PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL * STA F3: 4,5 + D4: 5,9 + A6: 3,8 * CNT 6 HDP CHAINS / 6 HYP OPENED