Analysis of xx-top500-028-base.sdk
Contents
Original Sudoku
level: medium
position: .8...4.5....7..3............1..85...6.....2......4....3.26............417........ initial
Autosolve
position: .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 2,9 => CTR => B3: 3,6,7 * DIS # I1: 2,9 => CTR => I1: 6,7 * DIS # A6: 8 => CTR => A6: 2,9 * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # F3: 3,9 => CTR => F3: 1,2 * DIS # C1: 3,9 => CTR => C1: 6,7 * DIS # I1: 2,6 => CTR => I1: 7,9 * PRF # H3: 2,6 => SOL * DIS # H3: 7 => CTR => H3: 2,6 * DIS # I3: 2,6 => CTR => I3: 7,9 * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # C6: 3,7 => CTR => C6: 8,9 * DIS # I4: 3,7 => CTR => I4: 6 * PRF # C3: 3,7 => SOL * DIS # B6: 3,9 => CTR => B6: 2,7 * DIS # C6: 3,9 => CTR => C6: 7,8 * DIS # F5: 7 => CTR => F5: 3,9 * PRF # B3: 3,9 => SOL * DIS # B3: 2,6,7 => CTR => B3: 3,9 * DIS # F5: 9 => CTR => F5: 3,7 * DIS # F5: 7 => CTR => F5: 3,9 * DIS # B6: 3,9 => CTR => B6: 2,7 * DIS # C6: 3,9 => CTR => C6: 7,8 * DIS # I4: 3,7 => CTR => I4: 6 * DIS # C6: 3,7 => CTR => C6: 8,9 * DIS # C8: 6 => CTR => C8: 8,9 * DIS # A6: 8,9 => CTR => A6: 2 * DIS # C8: 8 => CTR => C8: 6,9 * DIS # B2: 6,9 => CTR => B2: 2 * DIS # B3: 6,9 => CTR => B3: 2,3,7 * CNT 30 HDP CHAINS / 69 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 2,9 => CTR => B3: 3,6,7 * DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9 * DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7 * DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9 * PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL * STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8...4.5....7..3............1..85...6.....2......4....3.26............417........ | initial |
| .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. | autosolve |
| 986324157124759368537861429413285976695173284278946513342617895869532741751498632 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,9 A2: 1,5 A3: 1,5 D1: 3,9 H2: 2,6 C4: 3,7 B5: 3,9 E5: 3,7 D6: 3,9 I6: 3,7 A8: 8,9 B8: 6,9 E7: 1,7 F7: 1,7 E8: 2,3 F8: 2,3 H9: 2,3 I9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 17 pairs (_) / A3 = 1 => 16 pairs (_) E7,F7: 1.. / E7 = 1 => 16 pairs (_) / F7 = 1 => 0 pairs (X) A6,B6: 2.. / A6 = 2 => 21 pairs (_) / B6 = 2 => 0 pairs (X) E8,F8: 2.. / E8 = 2 => 18 pairs (_) / F8 = 2 => 16 pairs (_) H9,I9: 2.. / H9 = 2 => 0 pairs (X) / I9 = 2 => 17 pairs (_) A1,A6: 2.. / A1 = 2 => 0 pairs (X) / A6 = 2 => 21 pairs (_) E8,F8: 3.. / E8 = 3 => 16 pairs (_) / F8 = 3 => 18 pairs (_) H9,I9: 3.. / H9 = 3 => 17 pairs (_) / I9 = 3 => 0 pairs (X) D1,D6: 3.. / D1 = 3 => 21 pairs (_) / D6 = 3 => 0 pairs (X) H4,H9: 3.. / H4 = 3 => 0 pairs (X) / H9 = 3 => 17 pairs (_) A2,A3: 5.. / A2 = 5 => 16 pairs (_) / A3 = 5 => 17 pairs (_) E2,E3: 5.. / E2 = 5 => 17 pairs (_) / E3 = 5 => 16 pairs (_) A2,E2: 5.. / A2 = 5 => 16 pairs (_) / E2 = 5 => 17 pairs (_) A3,E3: 5.. / A3 = 5 => 17 pairs (_) / E3 = 5 => 16 pairs (_) H4,I4: 6.. / H4 = 6 => 0 pairs (X) / I4 = 6 => 19 pairs (_) B8,C8: 6.. / B8 = 6 => 21 pairs (_) / C8 = 6 => 0 pairs (X) E5,F5: 7.. / E5 = 7 => 16 pairs (_) / F5 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 0 pairs (X) / F7 = 7 => 16 pairs (_) C1,I1: 7.. / C1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) B3,B6: 7.. / B3 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) E5,E7: 7.. / E5 = 7 => 16 pairs (_) / E7 = 7 => 0 pairs (X) F5,F7: 7.. / F5 = 7 => 0 pairs (X) / F7 = 7 => 16 pairs (_) H3,H4: 7.. / H3 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) A6,C6: 8.. / A6 = 8 => 0 pairs (X) / C6 = 8 => 19 pairs (_) A8,C8: 8.. / A8 = 8 => 19 pairs (_) / C8 = 8 => 0 pairs (X) A6,A8: 8.. / A6 = 8 => 0 pairs (X) / A8 = 8 => 19 pairs (_) C6,C8: 8.. / C6 = 8 => 19 pairs (_) / C8 = 8 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 0 pairs (X) / I3 = 9 => 18 pairs (_) F5,D6: 9.. / F5 = 9 => 0 pairs (X) / D6 = 9 => 21 pairs (_) B2,F2: 9.. / B2 = 9 => 0 pairs (X) / F2 = 9 => 21 pairs (_) B5,F5: 9.. / B5 = 9 => 21 pairs (_) / F5 = 9 => 0 pairs (X) D1,D6: 9.. / D1 = 9 => 0 pairs (X) / D6 = 9 => 21 pairs (_) * DURATION: 0:01:10.859583 START: 03:34:11.934740 END: 03:35:22.794323 2017-05-04 * CP COUNT: (32) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A8,B5,B8,C4,D1,D6,E5,E7,E8,F7,F8,H2,H9,I6,I9) * .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. * PAIR A1: 2,9 BLK 1 B2: 2,9,6 # reduction candidate for 2,9 B2: 2,9 # 21 pairs B3: 2,9,3,6,7 # reduction candidate for 2,9 B3: 2,9 => CTR * .8.3.415...47..3.8..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632 B3: 3,6,7 # 18 pairs * PAIR A1: 2,9 ROW 1 I1: 2,9,6,7 # reduction candidate for 2,9 I1: 2,9 => CTR * .87.6415...47..3.8...8..4..4132859..6951..284.789465133426..8958695..741751498632 I1: 6,7 # 18 pairs * PAIR A1: 2,9 COL A A6: 2,9,8 # reduction candidate for 2,9 A6: 8 => CTR * 28...415..947..3.8.7.8..4..41.2859766351..28482..4651.3426..8959685..7417514986.. A6: 2,9 # 19 pairs * PAIR A2: 1,5 ROW 2 E2: 1,5,2,6 # reduction candidate for 1,5 E2: 2,6 => CTR * 287..415.5947.13.81..85.4..41.2859..635179284...346517342617895.6.5..7417514986.. E2: 1,5 # 20 pairs * PAIR A3: 1,5 ROW 3 E3: 1,5,2,3,6 # reduction candidate for 1,5 E3: 1,5 # 19 pairs E3: 2,3,6 # 15 pairs * PAIR D1: 3,9 BLK 2 F3: 3,9,1,2 # reduction candidate for 3,9 F3: 3,9 => CTR * .8...415..947..3.8...8..4..41.2859..635179284...346517342617895.6.5327417514986.. F3: 1,2 # 19 pairs * PAIR D1: 3,9 ROW 1 C1: 3,9,6,7 # reduction candidate for 3,9 C1: 3,9 => CTR * 28.364157..47.93.8...8..4.94132859766951..284...9465133426..895.6.5..741751498632 C1: 6,7 # 19 pairs * PAIR H2: 2,6 BLK 3 I1: 2,6,7,9 # reduction candidate for 2,6 I1: 2,6 => CTR * 987324156.247..3.8...8..4.94132859..6951..284.789465133426..8958695..741751498632 I1: 7,9 # 19 pairs H3: 2,6,7 # reduction candidate for 2,6 H3: 2,6 => SOLVED * 986324157124759368537861429413285976695173284278946513342617895869532741751498632 H3: 7 => CTR * .873.415...47..328.238..47.41.2859..6.51..284.7..465133426..895...5..741751498632 I3: 2,6,7,9 # reduction candidate for 2,6 I3: 2,6 => CTR * .8...4159..47..3.8...8..47.41.2859..6.51..284.7.9465133426..8959685..7417514986.. I3: 7,9 # 19 pairs * PAIR H2: 2,6 ROW 2 B2: 2,6,9 # reduction candidate for 2,6 B2: 2,6 # 21 pairs E2: 2,6,1,5 # reduction candidate for 2,6 E2: 2,6 => CTR * 287..415.5947.13.81..85.4..41.2859..635179284...346517342617895.6.5..7417514986.. E2: 1,5 # 20 pairs * PAIR C4: 3,7 BLK 4 B6: 3,7,2,9 # reduction candidate for 3,7 B6: 3,7 # 21 pairs C6: 3,7,8,9 # reduction candidate for 3,7 C6: 3,7 => CTR * 28.36415..947..368.7.8..4..41.2859..6.51..28482.94651.3426..8959685..7417514986.. C6: 8,9 # 19 pairs * PAIR C4: 3,7 ROW 4 H4: 3,7,6 # reduction candidate for 3,7 H4: 3,7 # 19 pairs I4: 3,7,6 # reduction candidate for 3,7 I4: 3,7 => CTR * .873.415...47..328.238..47.41.28596.6.51..284.7..465133426..895...5..741751498632 I4: 6 # 19 pairs * PAIR C4: 3,7 COL C C1: 3,7,6,9 # reduction candidate for 3,7 C1: 3,7 # 22 pairs C3: 3,7,6,9 # reduction candidate for 3,7 C3: 3,7 => SOLVED * 986324157124759368537861429413285976695173284278946513342617895869532741751498632 C3: 6,9 # 22 pairs * PAIR B5: 3,9 BLK 4 B6: 3,9,2,7 # reduction candidate for 3,9 B6: 3,9 => CTR * .8...415...47..3.8.7.8..4..41.2859766.51..2842...4651.3426..895...5..7417514986.. B6: 2,7 # 19 pairs C6: 3,9,7,8 # reduction candidate for 3,9 C6: 3,9 => CTR * 287..415..947..3.8.3.8..4..41.2859..6.51..28482..465173426..8959685..7417514986.. C6: 7,8 # 19 pairs * PAIR B5: 3,9 ROW 5 F5: 3,9,7 # reduction candidate for 3,9 F5: 7 => CTR * .8.36415..247.9368..68.247941.28593669513728427.94651.342671895.6.5237417514986.. F5: 3,9 # 16 pairs * PAIR B5: 3,9 COL B B3: 3,9,2,6,7 # reduction candidate for 3,9 B3: 3,9 => SOLVED * 986324157124759368537861429413285976695173284278946513342617895869532741751498632 B3: 2,6,7 => CTR * .8...415...47..3.8...8..4..4172859..6.51..284....465173426..895...5..7417514986.. * PAIR E5: 3,7 BLK 5 F5: 3,7,9 # reduction candidate for 3,7 F5: 9 => CTR * .87934156.9476.328...8524794132859..6.5179284...346517342617895...5..7417514986.. F5: 3,7 # 21 pairs * PAIR D6: 3,9 BLK 5 F5: 3,9,7 # reduction candidate for 3,9 F5: 7 => CTR * .8.36415..247.9368..68.247941.28593669513728427.94651.342671895.6.5237417514986.. F5: 3,9 # 16 pairs * PAIR D6: 3,9 ROW 6 B6: 3,9,2,7 # reduction candidate for 3,9 B6: 3,9 => CTR * .8...415...47..3.8.7.8..4..41.2859766.51..2842...4651.3426..895...5..7417514986.. B6: 2,7 # 19 pairs C6: 3,9,7,8 # reduction candidate for 3,9 C6: 3,9 => CTR * 287..415..947..3.8.3.8..4..41.2859..6.51..28482..465173426..8959685..7417514986.. C6: 7,8 # 19 pairs * PAIR I6: 3,7 BLK 6 H4: 3,7,6 # reduction candidate for 3,7 H4: 3,7 # 19 pairs I4: 3,7,6 # reduction candidate for 3,7 I4: 3,7 => CTR * .873.415...47..328.238..47.41.28596.6.51..284.7..465133426..895...5..741751498632 I4: 6 # 19 pairs * PAIR I6: 3,7 ROW 6 B6: 3,7,2,9 # reduction candidate for 3,7 B6: 3,7 # 21 pairs C6: 3,7,8,9 # reduction candidate for 3,7 C6: 3,7 => CTR * 28.36415..947..368.7.8..4..41.2859..6.51..28482.94651.3426..8959685..7417514986.. C6: 8,9 # 19 pairs * PAIR A8: 8,9 BLK 7 C8: 8,9,6 # reduction candidate for 8,9 C8: 6 => CTR * .8...415...47.93.8...8..4..41.2859..63517.284..8.4651.3426..8958965..7417514986.. C8: 8,9 # 21 pairs * PAIR A8: 8,9 COL A A6: 8,9,2 # reduction candidate for 8,9 A6: 8,9 => CTR * 28...415...47..3.8.7.8..4..41.2859766351..284.2..4651.3426..895...5..7417514986.. A6: 2 # 21 pairs * PAIR B8: 6,9 BLK 7 C8: 6,9,8 # reduction candidate for 6,9 C8: 8 => CTR * 28...415..947..3.8.7.8..4..41.2859766351..28482..4651.3426..8959685..7417514986.. C8: 6,9 # 19 pairs * PAIR B8: 6,9 COL B B2: 6,9,2 # reduction candidate for 6,9 B2: 6,9 => CTR * .87..415...47..3.8...8..4..41.2859..635179284...346517342617895...5..7417514986.. B2: 2 # 21 pairs B3: 6,9,2,3,7 # reduction candidate for 6,9 B3: 6,9 => CTR * .8.3.415..247.9368..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632 B3: 2,3,7 # 18 pairs * PAIR E8: 2,3 COL E E1: 2,3,6 # reduction candidate for 2,3 E1: 2,3 # 24 pairs E3: 2,3,1,5,6 # reduction candidate for 2,3 E3: 2,3 # 16 pairs * PAIR F8: 2,3 COL F F3: 2,3,1,9 # reduction candidate for 2,3 F3: 2,3 # 22 pairs F3: 1,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-028-base-pr-000.dot * REASONING * DIS # B3: 2,9 => CTR => B3: 3,6,7 * DIS # I1: 2,9 => CTR => I1: 6,7 * DIS # A6: 8 => CTR => A6: 2,9 * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # F3: 3,9 => CTR => F3: 1,2 * DIS # C1: 3,9 => CTR => C1: 6,7 * DIS # I1: 2,6 => CTR => I1: 7,9 * PRF # H3: 2,6 => SOL * DIS # H3: 7 => CTR => H3: 2,6 * DIS # I3: 2,6 => CTR => I3: 7,9 * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # C6: 3,7 => CTR => C6: 8,9 * DIS # I4: 3,7 => CTR => I4: 6 * PRF # C3: 3,7 => SOL * DIS # B6: 3,9 => CTR => B6: 2,7 * DIS # C6: 3,9 => CTR => C6: 7,8 * DIS # F5: 7 => CTR => F5: 3,9 * PRF # B3: 3,9 => SOL * DIS # B3: 2,6,7 => CTR => B3: 3,9 * DIS # F5: 9 => CTR => F5: 3,7 * DIS # F5: 7 => CTR => F5: 3,9 * DIS # B6: 3,9 => CTR => B6: 2,7 * DIS # C6: 3,9 => CTR => C6: 7,8 * DIS # I4: 3,7 => CTR => I4: 6 * DIS # C6: 3,7 => CTR => C6: 8,9 * DIS # C8: 6 => CTR => C8: 8,9 * DIS # A6: 8,9 => CTR => A6: 2 * DIS # C8: 8 => CTR => C8: 6,9 * DIS # B2: 6,9 => CTR => B2: 2 * DIS # B3: 6,9 => CTR => B3: 2,3,7 * CNT 30 HDP CHAINS / 69 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A8,B5,B8,C4,D1,D6,E5,E7,E8,F7,F8,H2,H9,I6,I9) * .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. * PAIR A1: 2,9 BLK 1 B2: 2,9,6 # reduction candidate for 2,9 B2: 2,9 # 21 pairs B3: 2,9,3,6,7 # reduction candidate for 2,9 B3: 2,9 => CTR * .8.3.415...47..3.8..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632 * RESTART * PAIR A1: 2,9 BLK 1 B2: 2,9,6 # reduction candidate for 2,9 B2: 6 => CTR * 28...415..647.9328...8..4..41.2859..6951..284....4651.3426..895...5..7417514986.. * PAIR A1: 2,9 ROW 1 I1: 2,9,6,7 # reduction candidate for 2,9 I1: 2,9 => CTR * .87.6415...47..368.368..4..4132859766951..284.789465133426..8958695..741751498632 * PAIR A1: 2,9 COL A A6: 2,9,8 # reduction candidate for 2,9 A6: 8 => CTR * 2879.415..947..3.8...8..4.941.2859..6351792848293465173426178959685..741751498632 * PAIR RESTART * PAIR A2: 1,5 ROW 2 E2: 1,5,2,6 # reduction candidate for 1,5 E2: 1,5 => SOLVED * 986324157124759368537861429413285976695173284278946513342617895869532741751498632 * DURATION: 0:00:12.518720 START: 03:36:43.469372 END: 03:36:55.988092 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-028-base-pr-001.dot * REASONING * DIS # B3: 2,9 => CTR => B3: 3,6,7 * DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9 * DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7 * DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9 * PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL * STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 028 solution: 986324157124759368537861429413285976695173284278946513342617895869532741751498632 info: 1324 FNBTHWX S8.f 23501 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 986324157124759368537861429413285976695173284278946513342617895869532741751498632 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 # B2: 2,9 => UNS * DIS # B3: 2,9 => CTR => B3: 3,6,7 * INC # B3: 3,6,7 => UNS * DIS # I1: 2,9 => CTR => I1: 6,7 * INC # I1: 6,7 => UNS * INC # A6: 2,9 => UNS * DIS # A6: 8 => CTR => A6: 2,9 * INC # E2: 1,5 => UNS * DIS # E2: 2,6 => CTR => E2: 1,5 * INC # E3: 1,5 => UNS * INC # E3: 2,3,6 => UNS * DIS # F3: 3,9 => CTR => F3: 1,2 * INC # F3: 1,2 => UNS * DIS # C1: 3,9 => CTR => C1: 6,7 * INC # C1: 6,7 => UNS * DIS # I1: 2,6 => CTR => I1: 7,9 * INC # I1: 7,9 => UNS * PRF # H3: 2,6 => SOL * DIS # H3: 7 => CTR => H3: 2,6 * DIS # I3: 2,6 => CTR => I3: 7,9 * INC # I3: 7,9 => UNS * INC # B2: 2,6 => UNS * DIS # E2: 2,6 => CTR => E2: 1,5 * INC # E2: 1,5 => UNS * INC # B6: 3,7 => UNS * DIS # C6: 3,7 => CTR => C6: 8,9 * INC # C6: 8,9 => UNS * INC # H4: 3,7 => UNS * DIS # I4: 3,7 => CTR => I4: 6 * INC # I4: 6 => UNS * INC # C1: 3,7 => UNS * PRF # C3: 3,7 => SOL * INC # C3: 6,9 => UNS * DIS # B6: 3,9 => CTR => B6: 2,7 * INC # B6: 2,7 => UNS * DIS # C6: 3,9 => CTR => C6: 7,8 * INC # C6: 7,8 => UNS * INC # F5: 3,9 => UNS * DIS # F5: 7 => CTR => F5: 3,9 * PRF # B3: 3,9 => SOL * DIS # B3: 2,6,7 => CTR => B3: 3,9 * INC # F5: 3,7 => UNS * DIS # F5: 9 => CTR => F5: 3,7 * INC # F5: 3,9 => UNS * DIS # F5: 7 => CTR => F5: 3,9 * DIS # B6: 3,9 => CTR => B6: 2,7 * INC # B6: 2,7 => UNS * DIS # C6: 3,9 => CTR => C6: 7,8 * INC # C6: 7,8 => UNS * INC # H4: 3,7 => UNS * DIS # I4: 3,7 => CTR => I4: 6 * INC # I4: 6 => UNS * INC # B6: 3,7 => UNS * DIS # C6: 3,7 => CTR => C6: 8,9 * INC # C6: 8,9 => UNS * INC # C8: 8,9 => UNS * DIS # C8: 6 => CTR => C8: 8,9 * DIS # A6: 8,9 => CTR => A6: 2 * INC # A6: 2 => UNS * INC # C8: 6,9 => UNS * DIS # C8: 8 => CTR => C8: 6,9 * DIS # B2: 6,9 => CTR => B2: 2 * INC # B2: 2 => UNS * DIS # B3: 6,9 => CTR => B3: 2,3,7 * INC # B3: 2,3,7 => UNS * INC # E1: 2,3 => UNS * INC # E3: 2,3 => UNS * INC # F3: 2,3 => UNS * INC # F3: 1,9 => UNS * CNT 69 HDP CHAINS / 69 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 2,9 => UNS * DIS # B3: 2,9 => CTR => B3: 3,6,7 * INC B3: 3,6,7 # B2: 2,9 => UNS * DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9 * DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7 * INC B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 2,9 => UNS * DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9 * PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL * STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5 * CNT 8 HDP CHAINS / 8 HYP OPENED