Analysis of xx-top500-303-base.sdk
Contents
Original Sudoku
level: medium
position: 4.1.........8....6.............1423.56...........2.........314.67.5.............. initial
Autosolve
position: 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6..25.6314.6745.13.231.4.265. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 8,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * DIS # C4: 7,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * DIS # A3: 7 => CTR => A3: 8,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # A4: 8,9 => CTR => A4: 7 * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 8 => CTR => H1: 7,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # A4: 8,9 => CTR => A4: 7 * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * DIS # C4: 7 => CTR => C4: 8,9 * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 8 => CTR => I7: 7,9 * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * CNT 53 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 7 => CTR => A3: 8,9 * PRF A3: 8,9 # G1: 8,9 => SOL * STA A3: 8,9 + G1: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.1.........8....6.............1423.56...........2.........314.67.5.............. | initial |
| 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6..25.6314.6745.13.231.4.265. | autosolve |
| 481256973237849516956137824798614235562378491143925768825763149674591382319482657 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 8,9 C2: 7,9 F2: 7,9 F3: 7,9 G3: 8,9 B4: 8,9 E5: 7,9 D6: 7,9 H5: 7,9 I6: 8,9 A7: 8,9 C9: 8,9 D7: 7,9 E8: 8,9 H8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,A3: 7.. / C2 = 7 => 14 pairs (_) / A3 = 7 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 0 pairs (X) / F3 = 7 => 14 pairs (_) G1,H1: 7.. / G1 = 7 => 0 pairs (X) / H1 = 7 => 0 pairs (_) A4,C4: 7.. / A4 = 7 => 14 pairs (_) / C4 = 7 => 0 pairs (X) E5,D6: 7.. / E5 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) H5,G6: 7.. / H5 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) D7,E9: 7.. / D7 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) I7,I9: 7.. / I7 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) C2,F2: 7.. / C2 = 7 => 14 pairs (_) / F2 = 7 => 0 pairs (X) A3,F3: 7.. / A3 = 7 => 0 pairs (X) / F3 = 7 => 14 pairs (_) E5,H5: 7.. / E5 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) D6,G6: 7.. / D6 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) D7,I7: 7.. / D7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) E9,I9: 7.. / E9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A3,A4: 7.. / A3 = 7 => 0 pairs (X) / A4 = 7 => 14 pairs (_) C2,C4: 7.. / C2 = 7 => 14 pairs (_) / C4 = 7 => 0 pairs (X) D6,D7: 7.. / D6 = 7 => 0 pairs (X) / D7 = 7 => 0 pairs (_) E5,E9: 7.. / E5 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) G1,G6: 7.. / G1 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) H1,H5: 7.. / H1 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) B1,A3: 8.. / B1 = 8 => 0 pairs (*) / A3 = 8 => 0 pairs (X) G6,I6: 8.. / G6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) A7,C9: 8.. / A7 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) A3,G3: 8.. / A3 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) A7,I7: 8.. / A7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) E8,H8: 8.. / E8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) B1,B4: 8.. / B1 = 8 => 0 pairs (*) / B4 = 8 => 0 pairs (X) C4,C9: 8.. / C4 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) H1,H8: 8.. / H1 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) F2,F3: 9.. / F2 = 9 => 14 pairs (_) / F3 = 9 => 0 pairs (X) E5,D6: 9.. / E5 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) A7,C9: 9.. / A7 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) C2,F2: 9.. / C2 = 9 => 0 pairs (X) / F2 = 9 => 14 pairs (_) E5,H5: 9.. / E5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) E8,H8: 9.. / E8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) B1,B4: 9.. / B1 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) D6,D7: 9.. / D6 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) * DURATION: 0:01:09.684297 START: 13:19:04.293518 END: 13:20:13.977815 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B4,C2,C9,D6,D7,E5,E8,F2,F3,G3,H5,H8,I6) * 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6..25.6314.6745.13.231.4.265. * PAIR B1: 8,9 BLK 1 A3: 8,9,7 # reduction candidate for 8,9 A3: 7 => CTR * 481256..3239847516756139824.976142355623.84.1143.25.68.25.6314.6745.13.231.4.265. A3: 8,9 # 14 pairs * PAIR B1: 8,9 ROW 1 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 G1: 7 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 H1: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR C2: 7,9 BLK 1 A3: 7,9,8 # reduction candidate for 7,9 A3: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 A3: 8 => CTR * 4.1256..32378495168561379247896142355623.84.1143.25.6.92576314867458139231849265. * PAIR C2: 7,9 COL C C4: 7,9,8 # reduction candidate for 7,9 C4: 7,9 => CTR * 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6.92576314867458139231849265. C4: 8 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR F3: 7,9 ROW 3 A3: 7,9,8 # reduction candidate for 7,9 A3: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 A3: 8 => CTR * 4.1256..32378495168561379247896142355623.84.1143.25.6.92576314867458139231849265. * PAIR G3: 8,9 BLK 3 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 G1: 7 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 H1: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR G3: 8,9 ROW 3 A3: 8,9,7 # reduction candidate for 8,9 A3: 7 => CTR * 481256..3239847516756139824.976142355623.84.1143.25.68.25.6314.6745.13.231.4.265. A3: 8,9 # 14 pairs * PAIR G3: 8,9 COL G G6: 8,9,7 # reduction candidate for 8,9 G6: 8,9 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 G6: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR B4: 8,9 BLK 4 A4: 8,9,7 # reduction candidate for 8,9 A4: 8,9 => CTR * 4.1256..323.84.516756139824..76142355623.84.1143.25.68825.6314.6745.13823194.265. A4: 7 # 14 pairs C4: 8,9,7 # reduction candidate for 8,9 C4: 8,9 # 14 pairs * PAIR E5: 7,9 COL E E9: 7,9,8 # reduction candidate for 7,9 E9: 7,9 => CTR * 4.1256.8323.84.516856137924789614235562398471143725869.25.6314.67458139231.4.265. E9: 8 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR D6: 7,9 ROW 6 G6: 7,9,8 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 G6: 8 => CTR * 49125678323784951685613.924...6142355623.8471143725869.25963147674581392319472658 * PAIR H5: 7,9 BLK 6 G6: 7,9,8 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 G6: 8 => CTR * 49125678323784951685613.924...6142355623.8471143725869.25963147674581392319472658 * PAIR H5: 7,9 COL H H1: 7,9,8 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 H1: 8 => CTR * 4.125678323.84.5168561379247896142355623.8471143725869.25.6314.6745.13.231.4.265. * PAIR I6: 8,9 BLK 6 G6: 8,9,7 # reduction candidate for 8,9 G6: 8,9 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 G6: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR I6: 8,9 COL I I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 I7: 7 => CTR * 48125697323.84.516.5613..24...6142355623.84.1143.25.6.825963147674581392319472658 I9: 8,9,7 # reduction candidate for 8,9 I9: 8,9 => CTR * 481256..323.84.516.5613..24...614235562398471143725.6.825963147674581392319472658 I9: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR A7: 8,9 ROW 7 I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 I7: 7 => CTR * 48125697323.84.516.5613..24...6142355623.84.1143.25.6.825963147674581392319472658 * PAIR A7: 8,9 COL A A3: 8,9,7 # reduction candidate for 8,9 A3: 8,9 # 14 pairs A4: 8,9,7 # reduction candidate for 8,9 A4: 8,9 => CTR * 4.1256..323.84.516756139824..76142355623.84.1143.25.68825.6314.6745.13823194.265. A4: 7 # 14 pairs * PAIR C9: 8,9 ROW 9 E9: 8,9,7 # reduction candidate for 8,9 E9: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 E9: 7 => CTR * 4.1256.8323784951685613..24...6142355623.84.1143.25.6..25.6314.674581392319472658 I9: 8,9,7 # reduction candidate for 8,9 I9: 8,9 => CTR * 481256..323.84.516.5613..24...614235562398471143725.6.825963147674581392319472658 I9: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR C9: 8,9 COL C C4: 8,9,7 # reduction candidate for 8,9 C4: 7 => CTR * 4.1256..32398475167561398248976142355623.84.1143.25.6892576314.6745.13.23184.265. C4: 8,9 # 14 pairs * PAIR D7: 7,9 BLK 8 E9: 7,9,8 # reduction candidate for 7,9 E9: 7,9 => CTR * 4.1256.8323.84.516856137924789614235562398471143725869.25.6314.67458139231.4.265. E9: 8 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR D7: 7,9 ROW 7 I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 I7: 8 => CTR * 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6..2576314867458139231849265. * PAIR E8: 8,9 BLK 8 E9: 8,9,7 # reduction candidate for 8,9 E9: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 E9: 7 => CTR * 4.1256.8323784951685613..24...6142355623.84.1143.25.6..25.6314.674581392319472658 * PAIR H8: 8,9 BLK 9 I7: 8,9,7 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 I7: 7 => CTR * 48125697323.84.516.5613..24...6142355623.84.1143.25.6.825963147674581392319472658 I9: 8,9,7 # reduction candidate for 8,9 I9: 8,9 => CTR * 481256..323.84.516.5613..24...614235562398471143725.6.825963147674581392319472658 I9: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * PAIR H8: 8,9 COL H H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => CTR * 49125678323784951685613..24...6142355623.8471143725.6..25963147674581392319472658 H1: 7 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-303-base-pr-000.dot * REASONING * DIS # A3: 7 => CTR => A3: 8,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * DIS # C4: 7,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * DIS # A3: 7 => CTR => A3: 8,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # A4: 8,9 => CTR => A4: 7 * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 8 => CTR => H1: 7,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # A4: 8,9 => CTR => A4: 7 * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * DIS # C4: 7 => CTR => C4: 8,9 * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 8 => CTR => I7: 7,9 * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * CNT 53 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B4,C2,C9,D6,D7,E5,E8,F2,F3,G3,H5,H8,I6) * 4.1256..323.84.516.5613..24...6142355623.84.1143.25.6..25.6314.6745.13.231.4.265. * PAIR B1: 8,9 BLK 1 A3: 8,9,7 # reduction candidate for 8,9 A3: 7 => CTR * 481256..3239847516756139824.976142355623.84.1143.25.68.25.6314.6745.13.231.4.265. * PAIR B1: 8,9 ROW 1 G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 => SOLVED * 481256973237849516956137824798614235562378491143925768825763149674591382319482657 * DURATION: 0:00:03.975517 START: 13:21:23.050354 END: 13:21:27.025871 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-303-base-pr-001.dot * REASONING * DIS # A3: 7 => CTR => A3: 8,9 * PRF A3: 8,9 # G1: 8,9 => SOL * STA A3: 8,9 + G1: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 303 solution: 481256973237849516956137824798614235562378491143925768825763149674591382319482657 info: 2587 FNBWY S8.f 31247 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 481256973237849516956137824798614235562378491143925768825763149674591382319482657 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 # A3: 8,9 => UNS * DIS # A3: 7 => CTR => A3: 8,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * DIS # C4: 7,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 8 => CTR => A3: 7,9 * PRF # G1: 8,9 => SOL * DIS # G1: 7 => CTR => G1: 8,9 * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * INC # A3: 8,9 => UNS * DIS # A3: 7 => CTR => A3: 8,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # A4: 8,9 => CTR => A4: 7 * INC # A4: 7 => UNS * INC # C4: 8,9 => UNS * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # G6: 7,9 => SOL * DIS # G6: 8 => CTR => G6: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 8 => CTR => H1: 7,9 * DIS # G6: 8,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * INC # A3: 8,9 => UNS * DIS # A4: 8,9 => CTR => A4: 7 * INC # A4: 7 => UNS * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * INC # C4: 8,9 => UNS * DIS # C4: 7 => CTR => C4: 8,9 * DIS # E9: 7,9 => CTR => E9: 8 * PRF # E9: 8 => SOL * PRF # I7: 7,9 => SOL * DIS # I7: 8 => CTR => I7: 7,9 * PRF # E9: 8,9 => SOL * DIS # E9: 7 => CTR => E9: 8,9 * PRF # I7: 8,9 => SOL * DIS # I7: 7 => CTR => I7: 8,9 * DIS # I9: 8,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * DIS # H1: 8,9 => CTR => H1: 7 * PRF # H1: 7 => SOL * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 8,9 => UNS * DIS # A3: 7 => CTR => A3: 8,9 * PRF A3: 8,9 # G1: 8,9 => SOL * STA A3: 8,9 + G1: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED