Analysis of zz-www.sudokuoftheday.co.uk-20060718-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: .......4.94..8...5.52..139..98....6.7...........9.75....143....3....9.24....756.. initial

Autosolve

position: ..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS # F2: 3,6 => CTR => F2: 2
* DIS # A1: 6,8 => CTR => A1: 1
* DIS # B1: 6,8 => CTR => B1: 1,3
* PRF # A7: 6,8 => SOL
* DIS # F2: 3,6 => CTR => F2: 2
* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS # I1: 6 => CTR => I1: 2,8
* DIS # I1: 2 => CTR => I1: 6,8
* PRF # B5: 3,6 => SOL
* DIS # D5: 3,6 => CTR => D5: 1,8
* DIS # D5: 1,3 => CTR => D5: 6,8
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # E6: 1,2 => CTR => E6: 6
* DIS # I4: 1,2 => CTR => I4: 3,7
* PRF # F5: 3,4 => SOL
* DIS # F5: 6,8 => CTR => F5: 3,4
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # I5: 1,3 => CTR => I5: 2,9
* DIS # B5: 1,3 => CTR => B5: 2,6
* DIS # D5: 1,3 => CTR => D5: 6,8
* PRF # B7: 2,8 => SOL
* DIS # D8: 8 => CTR => D8: 1,6
* DIS # E6: 2 => CTR => E6: 1,6
* DIS # F7: 6 => CTR => F7: 2,8
* PRF # G7: 7,8 => SOL
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # I5: 1,3 => CTR => I5: 2,9
* CNT  29 HDP CHAINS /  66 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2
* DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8
* PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL
* STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6
* CNT   4 HDP CHAINS /   6 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.......4.94..8...5.52..139..98....6.7...........9.75....143....3....9.24....756.. initial
..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756.. autosolve
137596248946382175852741396598123467763854912214967583621438759375619824489275631 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
C2: 3,6
A3: 6,8
F1: 3,6
G1: 2,8
I3: 6,8
C5: 3,6
D4: 1,3
E4: 1,2
F4: 3,4
H5: 1,3
B9: 2,8
E8: 1,6
D9: 2,8
G8: 7,8
H9: 1,3
I9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  => 17 pairs (_) / B1 = 1  =>  0 pairs (X)
D8,E8: 1.. / D8 = 1  =>  0 pairs (X) / E8 = 1  => 17 pairs (_)
H9,I9: 1.. / H9 = 1  =>  0 pairs (X) / I9 = 1  => 15 pairs (_)
A1,A6: 1.. / A1 = 1  => 17 pairs (_) / A6 = 1  =>  0 pairs (X)
H5,H9: 1.. / H5 = 1  => 15 pairs (_) / H9 = 1  =>  0 pairs (X)
D2,F2: 2.. / D2 = 2  =>  0 pairs (X) / F2 = 2  => 18 pairs (_)
G1,I1: 2.. / G1 = 2  => 19 pairs (_) / I1 = 2  =>  0 pairs (X)
E4,E6: 2.. / E4 = 2  => 17 pairs (_) / E6 = 2  =>  0 pairs (X)
F7,D9: 2.. / F7 = 2  =>  0 pairs (X) / D9 = 2  => 18 pairs (_)
B9,D9: 2.. / B9 = 2  =>  0 pairs (X) / D9 = 2  => 18 pairs (_)
A6,A7: 2.. / A6 = 2  =>  0 pairs (*) / A7 = 2  =>  0 pairs (X)
D2,D9: 2.. / D2 = 2  =>  0 pairs (X) / D9 = 2  => 18 pairs (_)
F2,F7: 2.. / F2 = 2  => 18 pairs (_) / F7 = 2  =>  0 pairs (X)
B1,C2: 3.. / B1 = 3  => 22 pairs (_) / C2 = 3  =>  0 pairs (X)
H9,I9: 3.. / H9 = 3  => 15 pairs (_) / I9 = 3  =>  0 pairs (X)
B1,F1: 3.. / B1 = 3  => 22 pairs (_) / F1 = 3  =>  0 pairs (X)
B6,I6: 3.. / B6 = 3  =>  0 pairs (X) / I6 = 3  => 17 pairs (_)
C2,C5: 3.. / C2 = 3  =>  0 pairs (X) / C5 = 3  => 22 pairs (_)
H5,H9: 3.. / H5 = 3  =>  0 pairs (X) / H9 = 3  => 15 pairs (_)
F4,F5: 4.. / F4 = 4  => 24 pairs (_) / F5 = 4  =>  0 pairs (*)
G4,G5: 4.. / G4 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
F4,G4: 4.. / F4 = 4  => 24 pairs (_) / G4 = 4  =>  0 pairs (*)
F5,G5: 4.. / F5 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
I1,I3: 6.. / I1 = 6  =>  0 pairs (X) / I3 = 6  => 17 pairs (_)
A3,I3: 6.. / A3 = 6  =>  0 pairs (X) / I3 = 6  => 17 pairs (_)
C2,C5: 6.. / C2 = 6  => 22 pairs (_) / C5 = 6  =>  0 pairs (X)
E6,E8: 6.. / E6 = 6  => 17 pairs (_) / E8 = 6  =>  0 pairs (X)
G4,I4: 7.. / G4 = 7  => 18 pairs (_) / I4 = 7  => 20 pairs (_)
B7,B8: 7.. / B7 = 7  =>  0 pairs (X) / B8 = 7  => 21 pairs (_)
B8,G8: 7.. / B8 = 7  => 21 pairs (_) / G8 = 7  =>  0 pairs (X)
I4,I7: 7.. / I4 = 7  => 20 pairs (_) / I7 = 7  => 18 pairs (_)
D5,F5: 8.. / D5 = 8  => 21 pairs (_) / F5 = 8  =>  0 pairs (X)
A3,I3: 8.. / A3 = 8  => 17 pairs (_) / I3 = 8  =>  0 pairs (X)
B9,D9: 8.. / B9 = 8  => 18 pairs (_) / D9 = 8  =>  0 pairs (X)
F5,F7: 8.. / F5 = 8  =>  0 pairs (X) / F7 = 8  => 21 pairs (_)
G5,I5: 9.. / G5 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
G7,I7: 9.. / G7 = 9  => 18 pairs (_) / I7 = 9  =>  0 pairs (*)
G5,G7: 9.. / G5 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
I5,I7: 9.. / I5 = 9  => 18 pairs (_) / I7 = 9  =>  0 pairs (*)
* DURATION: 0:00:49.738430  START: 00:46:32.995432  END: 00:47:22.733862 2019-05-01
* CP COUNT: (39)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B9,C2,C5,D4,D9,E4,E8,F1,F4,G1,G8,H5,H9,I3,I9)
* ..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756..
* PAIR C2: 3,6 BLK 1
B1: 3,6,1,8                              # reduction candidate for 3,6
B1: 1,8 => CTR
* ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756..
B1: 3,6                                  # 18 pairs
* PAIR C2: 3,6 ROW 2
D2: 3,6,2                                # reduction candidate for 3,6
D2: 3,6                                  # 18 pairs
F2: 3,6,2                                # reduction candidate for 3,6
F2: 3,6 => CTR
* ..759..4.94.28.175.5274139.598....6.7...584....49.758...1432.5.3.5..9.244298756..
F2: 2                                    # 18 pairs
* PAIR A3: 6,8 BLK 1
A1: 6,8,1                                # reduction candidate for 6,8
A1: 6,8 => CTR
* .17593.4.943.8.175.5274139.598..4.6.7.6.584.91.496758.2.143695.365.197244892756..
A1: 1                                    # 17 pairs
B1: 6,8,1,3                              # reduction candidate for 6,8
B1: 6,8 => CTR
* 1.7593.4.943.8.175.5274139.598..4.6.7.6.584.92.496758...143.95.3.5.19.244.9.756..
B1: 1,3                                  # 18 pairs
* PAIR A3: 6,8 COL A
A7: 6,8,2                                # reduction candidate for 6,8
A7: 6,8 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
A7: 2                                    # 20 pairs
* PAIR F1: 3,6 BLK 2
D2: 3,6,2                                # reduction candidate for 3,6
D2: 3,6                                  # 18 pairs
F2: 3,6,2                                # reduction candidate for 3,6
F2: 3,6 => CTR
* ..759..4.94.28.175.5274139.598....6.7...584....49.758...1432.5.3.5..9.244298756..
F2: 2                                    # 18 pairs
* PAIR F1: 3,6 ROW 1
B1: 3,6,1,8                              # reduction candidate for 3,6
B1: 1,8 => CTR
* ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756..
B1: 3,6                                  # 18 pairs
* PAIR F1: 3,6 COL F
F5: 3,6,4,8                              # reduction candidate for 3,6
F5: 3,6                                  # 18 pairs
F5: 4,8                                  # 17 pairs
* PAIR G1: 2,8 BLK 3
I1: 2,8,6                                # reduction candidate for 2,8
I1: 6 => CTR
* ..7593246943.8.175652741398598.2476.7.6.584.9..49675822.14369573.5.19.244.9.756..
I1: 2,8                                  # 17 pairs
* PAIR I3: 6,8 BLK 3
I1: 6,8,2                                # reduction candidate for 6,8
I1: 2 => CTR
* ..759.84294..8.175852741396598..426772..584.9..492758.2714369583658197244.9.756..
I1: 6,8                                  # 19 pairs
* PAIR C5: 3,6 BLK 4
B5: 3,6,1,2                              # reduction candidate for 3,6
B5: 3,6 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
B5: 1,2                                  # 17 pairs
B6: 3,6,1,2                              # reduction candidate for 3,6
B6: 3,6                                  # 19 pairs
* PAIR C5: 3,6 ROW 5
D5: 3,6,1,8                              # reduction candidate for 3,6
D5: 3,6 => CTR
* ..759..4.94..8.175.5274139.598..4.6.72..58419..49.758.2.143695.365.19724489275631
D5: 1,8                                  # 17 pairs
F5: 3,6,4,8                              # reduction candidate for 3,6
F5: 3,6                                  # 18 pairs
* PAIR D4: 1,3 BLK 5
D5: 1,3,6,8                              # reduction candidate for 1,3
D5: 1,3 => CTR
* ..759..4.94..8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756..
D5: 6,8                                  # 17 pairs
* PAIR D4: 1,3 ROW 4
I4: 1,3,2,7                              # reduction candidate for 1,3
I4: 1,3 => CTR
* .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631
I4: 2,7                                  # 19 pairs
* PAIR E4: 1,2 BLK 5
E6: 1,2,6                                # reduction candidate for 1,2
E6: 1,2 => CTR
* .37596.4.94..8.175.5274139.5983.4.6.72..5.419..49.7583261438957375169824489275631
E6: 6                                    # 17 pairs
* PAIR E4: 1,2 ROW 4
I4: 1,2,3,7                              # reduction candidate for 1,2
I4: 1,2 => CTR
* ..759.24.94..82175.5274139.5983.476.72.856419614927583261438957375169824489275631
I4: 3,7                                  # 18 pairs
* PAIR F4: 3,4 BLK 5
F5: 3,4,6,8                              # reduction candidate for 3,4
F5: 3,4 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
F5: 6,8 => CTR
* ..7593.4.943682175.5274139.598..4.6.726.584.91349675822.14369583658197244892756..
* PAIR H5: 1,3 BLK 6
I4: 1,3,2,7                              # reduction candidate for 1,3
I4: 1,3 => CTR
* .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631
I4: 2,7                                  # 19 pairs
I5: 1,3,2,9                              # reduction candidate for 1,3
I5: 1,3 => CTR
* ..759.24.94..82175.5274139.598.2346772.8549...349675822614387593756198244892756..
I5: 2,9                                  # 17 pairs
I6: 1,3,2                                # reduction candidate for 1,3
I6: 1,3                                  # 21 pairs
* PAIR H5: 1,3 ROW 5
B5: 1,3,2,6                              # reduction candidate for 1,3
B5: 1,3 => CTR
* ..759..4.943.8.175.5274139.598.2..6.7...5......49.758...143..5.3.5..9.244.9.756..
B5: 2,6                                  # 22 pairs
D5: 1,3,6,8                              # reduction candidate for 1,3
D5: 1,3 => CTR
* ..759..4.94..8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756..
D5: 6,8                                  # 17 pairs
* PAIR B9: 2,8 BLK 7
A7: 2,8,6                                # reduction candidate for 2,8
A7: 2,8                                  # 19 pairs
B7: 2,8,6,7                              # reduction candidate for 2,8
B7: 2,8 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
B7: 6,7                                  # 17 pairs
* PAIR E8: 1,6 BLK 8
D8: 1,6,8                                # reduction candidate for 1,6
D8: 8 => CTR
* ..759..4.94..82175.5274139.598.2.4677...5......49.758...143..5.3.58197244892756..
D8: 1,6                                  # 19 pairs
* PAIR E8: 1,6 COL E
E6: 1,6,2                                # reduction candidate for 1,6
E6: 2 => CTR
* ..759.24.94..82175.5274139.59831476272.8564.9614927583261438957375169824489275631
E6: 1,6                                  # 17 pairs
* PAIR D9: 2,8 BLK 8
F7: 2,8,6                                # reduction candidate for 2,8
F7: 6 => CTR
* ..759..4.94..82175.5274139.598....6.7...584.9..49.758...143695.365.197244.92756..
F7: 2,8                                  # 19 pairs
* PAIR G8: 7,8 BLK 9
G7: 7,8,9                                # reduction candidate for 7,8
G7: 7,8 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
G7: 9                                    # 18 pairs
I7: 7,8,9                                # reduction candidate for 7,8
I7: 7,8                                  # 18 pairs
* PAIR G8: 7,8 ROW 8
B8: 7,8,6                                # reduction candidate for 7,8
B8: 6 => CTR
* ..759..4.94..8.175.5274139.598.2.4677...54.....496758..7143..5.365.197244.9.756..
B8: 7,8                                  # 19 pairs
* PAIR I9: 1,3 COL I
I4: 1,3,2,7                              # reduction candidate for 1,3
I4: 1,3 => CTR
* .1759324.943682175.5274139.598.2476.72.85.419.349.7582261438957375..9824489275631
I4: 2,7                                  # 19 pairs
I5: 1,3,2,9                              # reduction candidate for 1,3
I5: 1,3 => CTR
* ..759.24.94..82175.5274139.598.2346772.8549...349675822614387593756198244892756..
I5: 2,9                                  # 17 pairs
I6: 1,3,2                                # reduction candidate for 1,3
I6: 1,3                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060718-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS # F2: 3,6 => CTR => F2: 2
* DIS # A1: 6,8 => CTR => A1: 1
* DIS # B1: 6,8 => CTR => B1: 1,3
* PRF # A7: 6,8 => SOL
* DIS # F2: 3,6 => CTR => F2: 2
* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS # I1: 6 => CTR => I1: 2,8
* DIS # I1: 2 => CTR => I1: 6,8
* PRF # B5: 3,6 => SOL
* DIS # D5: 3,6 => CTR => D5: 1,8
* DIS # D5: 1,3 => CTR => D5: 6,8
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # E6: 1,2 => CTR => E6: 6
* DIS # I4: 1,2 => CTR => I4: 3,7
* PRF # F5: 3,4 => SOL
* DIS # F5: 6,8 => CTR => F5: 3,4
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # I5: 1,3 => CTR => I5: 2,9
* DIS # B5: 1,3 => CTR => B5: 2,6
* DIS # D5: 1,3 => CTR => D5: 6,8
* PRF # B7: 2,8 => SOL
* DIS # D8: 8 => CTR => D8: 1,6
* DIS # E6: 2 => CTR => E6: 1,6
* DIS # F7: 6 => CTR => F7: 2,8
* PRF # G7: 7,8 => SOL
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I4: 1,3 => CTR => I4: 2,7
* DIS # I5: 1,3 => CTR => I5: 2,9
* CNT  29 HDP CHAINS /  66 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B9,C2,C5,D4,D9,E4,E8,F1,F4,G1,G8,H5,H9,I3,I9)
* ..759..4.94..8.175.5274139.598....6.7...5......49.758...143..5.3.5..9.244.9.756..
* PAIR C2: 3,6 BLK 1
B1: 3,6,1,8                              # reduction candidate for 3,6
B1: 1,8 => CTR
* ..7593.4.943.8.175.5274139.598.2476.726.584.91349675822.14369573.5.19.244.9.756..
* PAIR C2: 3,6 ROW 2
D2: 3,6,2                                # reduction candidate for 3,6
D2: 3,6                                  # 19 pairs
F2: 3,6,2                                # reduction candidate for 3,6
F2: 3,6 => CTR
* 1.759..4.94.28.175852741396598....6.7...584....49.758...1432.5.3.5..9.244298756..
* RESTART
* PAIR RESTART
* PAIR F1: 3,6 COL F
F5: 3,6,4,8                              # reduction candidate for 3,6
F5: 3,6 => CTR
* 13759624894..82175852741396598..476.72.85.419614927583261438957375.69824489275631
* PAIR RESTART
* PAIR C5: 3,6 BLK 4
B5: 3,6,1,2                              # reduction candidate for 3,6
B5: 3,6 => SOLVED
* 137596248946382175852741396598123467763854912214967583621438759375619824489275631
* DURATION: 0:00:06.443487  START: 00:48:09.067178  END: 00:48:15.510665 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060718-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 1,8 => CTR => B1: 3,6
* DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2
* DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8
* PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL
* STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060718, absurd

Solution

position: 137596248946382175852741396598123467763854912214967583621438759375619824489275631 solved
Solution

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 # B1: 3,6 => UNS
* DIS # B1: 1,8 => CTR => B1: 3,6
* INC # D2: 3,6 => UNS
* DIS # F2: 3,6 => CTR => F2: 2
* INC # F2: 2 => UNS
* DIS # A1: 6,8 => CTR => A1: 1
* INC # A1: 1 => UNS
* DIS # B1: 6,8 => CTR => B1: 1,3
* INC # B1: 1,3 => UNS
* PRF # A7: 6,8 => SOL
* INC # A7: 2 => UNS
* INC # D2: 3,6 => UNS
* DIS # F2: 3,6 => CTR => F2: 2
* INC # F2: 2 => UNS
* INC # B1: 3,6 => UNS
* DIS # B1: 1,8 => CTR => B1: 3,6
* INC # F5: 3,6 => UNS
* INC # F5: 4,8 => UNS
* INC # I1: 2,8 => UNS
* DIS # I1: 6 => CTR => I1: 2,8
* INC # I1: 6,8 => UNS
* DIS # I1: 2 => CTR => I1: 6,8
* PRF # B5: 3,6 => SOL
* INC # B5: 1,2 => UNS
* INC # B6: 3,6 => UNS
* DIS # D5: 3,6 => CTR => D5: 1,8
* INC # D5: 1,8 => UNS
* INC # F5: 3,6 => UNS
* DIS # D5: 1,3 => CTR => D5: 6,8
* INC # D5: 6,8 => UNS
* DIS # I4: 1,3 => CTR => I4: 2,7
* INC # I4: 2,7 => UNS
* DIS # E6: 1,2 => CTR => E6: 6
* INC # E6: 6 => UNS
* DIS # I4: 1,2 => CTR => I4: 3,7
* INC # I4: 3,7 => UNS
* PRF # F5: 3,4 => SOL
* DIS # F5: 6,8 => CTR => F5: 3,4
* DIS # I4: 1,3 => CTR => I4: 2,7
* INC # I4: 2,7 => UNS
* DIS # I5: 1,3 => CTR => I5: 2,9
* INC # I5: 2,9 => UNS
* INC # I6: 1,3 => UNS
* DIS # B5: 1,3 => CTR => B5: 2,6
* INC # B5: 2,6 => UNS
* DIS # D5: 1,3 => CTR => D5: 6,8
* INC # D5: 6,8 => UNS
* INC # A7: 2,8 => UNS
* PRF # B7: 2,8 => SOL
* INC # B7: 6,7 => UNS
* INC # D8: 1,6 => UNS
* DIS # D8: 8 => CTR => D8: 1,6
* INC # E6: 1,6 => UNS
* DIS # E6: 2 => CTR => E6: 1,6
* INC # F7: 2,8 => UNS
* DIS # F7: 6 => CTR => F7: 2,8
* PRF # G7: 7,8 => SOL
* INC # G7: 9 => UNS
* INC # I7: 7,8 => UNS
* INC # B8: 7,8 => UNS
* DIS # B8: 6 => CTR => B8: 7,8
* DIS # I4: 1,3 => CTR => I4: 2,7
* INC # I4: 2,7 => UNS
* DIS # I5: 1,3 => CTR => I5: 2,9
* INC # I5: 2,9 => UNS
* INC # I6: 1,3 => UNS
* CNT  66 HDP CHAINS /  66 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 3,6 => UNS
* DIS # B1: 1,8 => CTR => B1: 3,6
* INC B1: 3,6 # D2: 3,6 => UNS
* DIS B1: 3,6 # F2: 3,6 => CTR => F2: 2
* DIS B1: 3,6 + F2: 2 # F5: 3,6 => CTR => F5: 4,8
* PRF B1: 3,6 + F2: 2 + F5: 4,8 # B5: 3,6 => SOL
* STA B1: 3,6 + F2: 2 + F5: 4,8 + B5: 3,6
* CNT   6 HDP CHAINS /   6 HYP OPENED