Analysis of zz-www.sudokuoftheday.co.uk-20060812-absurd-base.sdk

Contents

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

level: medium

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

position: 1.9.4.8...6..9..7.........193..7..2.....5.4.9.2.......3...8..47.8..2.9.6.1.9...8. initial

Autosolve

position: 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 2,8 => CTR => C2: 3
* DIS # A3: 2,8 => CTR => A3: 7
* DIS # D1: 3,6 => CTR => D1: 2,7
* DIS # D3: 3,6 => CTR => D3: 2,5,8
* DIS # F3: 3,6 => CTR => F3: 2,5,8
* DIS # G3: 2,5 => CTR => G3: 3,6
* DIS # G3: 2,5 => CTR => G3: 3,6
* DIS # D1: 3,6 => CTR => D1: 2,7
* PRF # H5: 3,6 => SOL
* DIS # H5: 1 => CTR => H5: 3,6
* DIS # H6: 3,6 => CTR => H6: 5
* PRF # H6: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* DIS # G3: 2,3 => CTR => G3: 5,6
* DIS # D1: 2,3 => CTR => D1: 6,7
* DIS # F1: 2,3 => CTR => F1: 6,7
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # C4: 6,8 => CTR => C4: 1,4,5
* DIS # C5: 6,8 => CTR => C5: 1
* PRF # C5: 1 => SOL
* PRF # A6: 6,8 => SOL
* DIS # C6: 6,8 => CTR => C6: 4,5
* DIS # D5: 6,8 => CTR => D5: 2,3
* DIS # F5: 6,8 => CTR => F5: 2,3
* DIS # H5: 3 => CTR => H5: 1,6
* DIS # C4: 1,6 => CTR => C4: 4,5,8
* PRF # C4: 4,5,8 => SOL
* DIS # I6: 5,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* PRF # C4: 5,8 => SOL
* DIS # C4: 1,4,6 => CTR => C4: 5,8
* DIS # F9: 3,6 => CTR => F9: 4,5,7
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* DIS # G3: 2,3 => CTR => G3: 5,6
* CNT  37 HDP CHAINS /  63 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 # C2: 2,8 => CTR => C2: 3
* DIS C2: 3 # A3: 2,8 => CTR => A3: 7
* DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7
* DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8
* DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8
* PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL
* STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6
* CNT   6 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

1.9.4.8...6..9..7.........193..7..2.....5.4.9.2.......3...8..47.8..2.9.6.1.9...8. initial
159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8. autosolve
159746832263198574748235691935674128871352469624819753396581247587423916412967385 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
A2: 2,8
E3: 3,6
H1: 3,6
I1: 2,3
A5: 6,8
G4: 1,6
I4: 5,8
E9: 3,6
G7: 1,2
G9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,F2: 1.. / D2 = 1  => 11 pairs (_) / F2 = 1  => 11 pairs (_)
C4,C5: 1.. / C4 = 1  =>  0 pairs (X) / C5 = 1  =>  0 pairs (_)
G4,H5: 1.. / G4 = 1  =>  0 pairs (*) / H5 = 1  =>  0 pairs (X)
G7,H8: 1.. / G7 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
C4,G4: 1.. / C4 = 1  =>  0 pairs (X) / G4 = 1  =>  0 pairs (_)
C5,H5: 1.. / C5 = 1  =>  0 pairs (*) / H5 = 1  =>  0 pairs (X)
G4,G7: 1.. / G4 = 1  =>  0 pairs (*) / G7 = 1  =>  0 pairs (X)
H5,H8: 1.. / H5 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
D5,F5: 2.. / D5 = 2  => 10 pairs (_) / F5 = 2  => 10 pairs (_)
C7,G7: 2.. / C7 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
I1,I9: 2.. / I1 = 2  => 11 pairs (_) / I9 = 2  =>  0 pairs (X)
C2,C3: 3.. / C2 = 3  => 11 pairs (_) / C3 = 3  =>  0 pairs (X)
E3,E9: 3.. / E3 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  => 10 pairs (_) / G3 = 5  =>  0 pairs (X)
H8,I9: 5.. / H8 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
C4,I4: 5.. / C4 = 5  =>  0 pairs (*) / I4 = 5  =>  0 pairs (X)
H6,H8: 5.. / H6 = 5  =>  0 pairs (*) / H8 = 5  =>  0 pairs (X)
H1,G3: 6.. / H1 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
E3,E9: 6.. / E3 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
G3,G4: 6.. / G3 = 6  =>  0 pairs (*) / G4 = 6  =>  0 pairs (X)
A3,C3: 7.. / A3 = 7  => 11 pairs (_) / C3 = 7  =>  0 pairs (X)
D1,F1: 7.. / D1 = 7  => 10 pairs (_) / F1 = 7  =>  0 pairs (X)
D1,D8: 7.. / D1 = 7  => 10 pairs (_) / D8 = 7  =>  0 pairs (X)
I4,I6: 8.. / I4 = 8  =>  0 pairs (*) / I6 = 8  =>  0 pairs (X)
* DURATION: 0:00:27.060689  START: 01:44:24.317170  END: 01:44:51.377859 2019-05-01
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,E3,E9,G4,G7,G9,H1,I1,I4)
* 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8.
* PAIR A2: 2,8 BLK 1
C2: 2,8,3                                # reduction candidate for 2,8
C2: 2,8 => CTR
* 159.4.8...6..9..74.43.6..9193..7.62..7..5.419.2..197..39..8.147.8..2.9.6.1.93.285
C2: 3                                    # 11 pairs
A3: 2,8,7                                # reduction candidate for 2,8
A3: 2,8 => CTR
* 159.4.8.2.63.9.574.47....91935.7.12.67..5.4.9.2..197.339..8..47.8..2.9.6.1.9...85
A3: 7                                    # 11 pairs
C3: 2,8,3,7                              # reduction candidate for 2,8
C3: 2,8                                  # 13 pairs
* PAIR A2: 2,8 ROW 2
D2: 2,8,1,3,5                            # reduction candidate for 2,8
D2: 2,8                                  # 12 pairs
F2: 2,8,1,3,5                            # reduction candidate for 2,8
F2: 2,8                                  # 12 pairs
* PAIR E3: 3,6 BLK 2
D1: 3,6,2,7                              # reduction candidate for 3,6
D1: 3,6 => CTR
* 159.478.2.6..9..74.4.....9193547.128.71.5.469426819753392.8..4758472.9.6.1.9.4.85
D1: 2,7                                  # 11 pairs
F1: 3,6,2,7                              # reduction candidate for 3,6
F1: 3,6                                  # 12 pairs
D3: 3,6,2,5,8                            # reduction candidate for 3,6
D3: 3,6 => CTR
* 159.4.863.63.9..74.4..3..91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.96.382
D3: 2,5,8                                # 10 pairs
F3: 3,6,2,5,8                            # reduction candidate for 3,6
F3: 3,6 => CTR
* 159.4.863.63.9..74.4..36.91931.7.625.7..5.419.2..1973839268.147.8..2.956.1.9..382
F3: 2,5,8                                # 10 pairs
* PAIR E3: 3,6 ROW 3
G3: 3,6,2,5                              # reduction candidate for 3,6
G3: 2,5 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G3: 3,6                                  # 11 pairs
* PAIR H1: 3,6 BLK 3
G3: 3,6,2,5                              # reduction candidate for 3,6
G3: 2,5 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G3: 3,6                                  # 11 pairs
* PAIR H1: 3,6 ROW 1
D1: 3,6,2,7                              # reduction candidate for 3,6
D1: 3,6 => CTR
* 159.478.2.6..9..74.4.....9193547.128.71.5.469426819753392.8..4758472.9.6.1.9.4.85
D1: 2,7                                  # 11 pairs
F1: 3,6,2,7                              # reduction candidate for 3,6
F1: 3,6                                  # 12 pairs
* PAIR H1: 3,6 COL H
H5: 3,6,1                                # reduction candidate for 3,6
H5: 3,6 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
H5: 1 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
H6: 3,6,5                                # reduction candidate for 3,6
H6: 3,6 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
H6: 5 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* PAIR I1: 2,3 BLK 3
G2: 2,3,5                                # reduction candidate for 2,3
G2: 2,3 => CTR
* 159.4.86..6..9..74.4....591931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G2: 5                                    # 10 pairs
G3: 2,3,5,6                              # reduction candidate for 2,3
G3: 2,3 => CTR
* 159.4.86..6..9.574.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G3: 5,6                                  # 11 pairs
* PAIR I1: 2,3 ROW 1
D1: 2,3,6,7                              # reduction candidate for 2,3
D1: 2,3 => CTR
* 159.4786..6..9..74.4.....9193..7.62..7..5.419.2..197..39..8.147.8.721936.1.9.4285
D1: 6,7                                  # 11 pairs
F1: 2,3,6,7                              # reduction candidate for 2,3
F1: 2,3 => CTR
* 15974.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
F1: 6,7                                  # 11 pairs
* PAIR I1: 2,3 COL I
I9: 2,3,5                                # reduction candidate for 2,3
I9: 2,3 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
I9: 5 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* PAIR A5: 6,8 BLK 4
C4: 6,8,1,4,5                            # reduction candidate for 6,8
C4: 6,8 => CTR
* 159.4.8...6..9..74.4.....9193..7.125.71.5.4.9.2..197.839..8.247.8..2.9.6.1.9...8.
C4: 1,4,5                                # 10 pairs
C5: 6,8,1                                # reduction candidate for 6,8
C5: 6,8 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
C5: 1 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
A6: 6,8,4,5                              # reduction candidate for 6,8
A6: 6,8 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
A6: 4,5                                  # 11 pairs
C6: 6,8,4,5                              # reduction candidate for 6,8
C6: 6,8 => CTR
* 159.4.832.63.9.574.4..3.691935.7.128671.5.4.942..19753396.8.24758..2.916.1.96.385
C6: 4,5                                  # 11 pairs
* PAIR A5: 6,8 ROW 5
D5: 6,8,2,3                              # reduction candidate for 6,8
D5: 6,8 => CTR
* 159.4.8...6..9..74.4.....9193..7..2..7..52439.2.3197..39..8..47.8..23916.1.96..85
D5: 2,3                                  # 11 pairs
F5: 6,8,2,3                              # reduction candidate for 6,8
F5: 6,8 => CTR
* 159.4.8...6..9..74.4.....9193..7..2..7.25.439.2.3197..39..8..47.8..23916.1.96..85
F5: 2,3                                  # 11 pairs
* PAIR G4: 1,6 BLK 6
H5: 1,6,3                                # reduction candidate for 1,6
H5: 3 => CTR
* 159.4.8...6..9..74.4.....9193..7.12..71.5.439.2.31976.39..8..47.8..2.9.6.1.9...8.
H5: 1,6                                  # 14 pairs
* PAIR G4: 1,6 ROW 4
C4: 1,6,4,5,8                            # reduction candidate for 1,6
C4: 1,6 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
C4: 4,5,8 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* PAIR I4: 5,8 BLK 6
I6: 5,8,3                                # reduction candidate for 5,8
I6: 5,8 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
I6: 3 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* PAIR I4: 5,8 ROW 4
C4: 5,8,1,4,6                            # reduction candidate for 5,8
C4: 5,8 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
C4: 1,4,6 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
* PAIR E9: 3,6 BLK 8
F9: 3,6,4,5,7                            # reduction candidate for 3,6
F9: 3,6 => CTR
* 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8.
F9: 4,5,7                                # 10 pairs
* PAIR G9: 2,3 BLK 9
I9: 2,3,5                                # reduction candidate for 2,3
I9: 2,3 => CTR
* 159.4.86..6..9..74.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
I9: 5 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* PAIR G9: 2,3 COL G
G2: 2,3,5                                # reduction candidate for 2,3
G2: 2,3 => CTR
* 159.4.86..6..9..74.4....591931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G2: 5                                    # 10 pairs
G3: 2,3,5,6                              # reduction candidate for 2,3
G3: 2,3 => CTR
* 159.4.86..6..9.574.4.....91931.7.625.7..5.419.2..19738392.8.147.8..2.956.1.9...8.
G3: 5,6                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060812-absurd-base-pr-000.dot
* REASONING
* DIS # C2: 2,8 => CTR => C2: 3
* DIS # A3: 2,8 => CTR => A3: 7
* DIS # D1: 3,6 => CTR => D1: 2,7
* DIS # D3: 3,6 => CTR => D3: 2,5,8
* DIS # F3: 3,6 => CTR => F3: 2,5,8
* DIS # G3: 2,5 => CTR => G3: 3,6
* DIS # G3: 2,5 => CTR => G3: 3,6
* DIS # D1: 3,6 => CTR => D1: 2,7
* PRF # H5: 3,6 => SOL
* DIS # H5: 1 => CTR => H5: 3,6
* DIS # H6: 3,6 => CTR => H6: 5
* PRF # H6: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* DIS # G3: 2,3 => CTR => G3: 5,6
* DIS # D1: 2,3 => CTR => D1: 6,7
* DIS # F1: 2,3 => CTR => F1: 6,7
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # C4: 6,8 => CTR => C4: 1,4,5
* DIS # C5: 6,8 => CTR => C5: 1
* PRF # C5: 1 => SOL
* PRF # A6: 6,8 => SOL
* DIS # C6: 6,8 => CTR => C6: 4,5
* DIS # D5: 6,8 => CTR => D5: 2,3
* DIS # F5: 6,8 => CTR => F5: 2,3
* DIS # H5: 3 => CTR => H5: 1,6
* DIS # C4: 1,6 => CTR => C4: 4,5,8
* PRF # C4: 4,5,8 => SOL
* DIS # I6: 5,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* PRF # C4: 5,8 => SOL
* DIS # C4: 1,4,6 => CTR => C4: 5,8
* DIS # F9: 3,6 => CTR => F9: 4,5,7
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* DIS # G3: 2,3 => CTR => G3: 5,6
* CNT  37 HDP CHAINS /  63 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,E3,E9,G4,G7,G9,H1,I1,I4)
* 159.4.8...6..9..74.4.....9193..7..2..7..5.4.9.2..197..39..8..47.8..2.9.6.1.9...8.
* PAIR A2: 2,8 BLK 1
C2: 2,8,3                                # reduction candidate for 2,8
C2: 2,8 => CTR
* 159.4.8...6..9..74.43.6..9193..7.62..7..5.419.2..197..39..8.147.8..2.9.6.1.93.285
A3: 2,8,7                                # reduction candidate for 2,8
A3: 2,8 => CTR
* 159.4.8.2.63.9.574.47....91935.7.12.67..5.4.9.2..197.339..8..47.8..2.9.6.1.9...85
* RESTART
* PAIR A2: 2,8 ROW 2
D2: 2,8,1,5                              # reduction candidate for 2,8
D2: 2,8                                  # 14 pairs
F2: 2,8,1,5                              # reduction candidate for 2,8
F2: 2,8                                  # 14 pairs
* PAIR E3: 3,6 BLK 2
D1: 3,6,2,7                              # reduction candidate for 3,6
D1: 3,6 => CTR
* 159.478.2.63.9.57474.....9193547.128.71.5.469426819753392.8..4758472.9.6.179.4.85
F1: 3,6,2,7                              # reduction candidate for 3,6
F1: 3,6                                  # 14 pairs
D3: 3,6,2,5,8                            # reduction candidate for 3,6
D3: 3,6 => CTR
* 159.4.863263.9.574748.35291931.7.625.76.5.419.2.61973.392.8.147.8..2.956.1.9..382
F3: 3,6,2,5,8                            # reduction candidate for 3,6
F3: 3,6 => CTR
* 159.4.863263.9.574748536291931.7.625.76.5.419.2.61973.392.8.147.8..2.956.1.9..382
* RESTART
* PAIR H1: 3,6 COL H
H5: 3,6,1                                # reduction candidate for 3,6
H5: 3,6 => SOLVED
* 159746832263198574748235691935674128871352469624819753396581247587423916412967385
* DURATION: 0:00:07.126531  START: 01:45:29.340472  END: 01:45:36.467003 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060812-absurd-base-pr-001.dot
* REASONING
* DIS # C2: 2,8 => CTR => C2: 3
* DIS C2: 3 # A3: 2,8 => CTR => A3: 7
* DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7
* DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8
* DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8
* PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL
* STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6
* CNT   6 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060812, absurd

Solution

position: 159746832263198574748235691935674128871352469624819753396581247587423916412967385 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:

* DIS # C2: 2,8 => CTR => C2: 3
* INC # C2: 3 => UNS
* DIS # A3: 2,8 => CTR => A3: 7
* INC # A3: 7 => UNS
* INC # C3: 2,8 => UNS
* INC # D2: 2,8 => UNS
* INC # F2: 2,8 => UNS
* DIS # D1: 3,6 => CTR => D1: 2,7
* INC # D1: 2,7 => UNS
* INC # F1: 3,6 => UNS
* DIS # D3: 3,6 => CTR => D3: 2,5,8
* INC # D3: 2,5,8 => UNS
* DIS # F3: 3,6 => CTR => F3: 2,5,8
* INC # F3: 2,5,8 => UNS
* INC # G3: 3,6 => UNS
* DIS # G3: 2,5 => CTR => G3: 3,6
* INC # G3: 3,6 => UNS
* DIS # G3: 2,5 => CTR => G3: 3,6
* DIS # D1: 3,6 => CTR => D1: 2,7
* INC # D1: 2,7 => UNS
* INC # F1: 3,6 => UNS
* PRF # H5: 3,6 => SOL
* DIS # H5: 1 => CTR => H5: 3,6
* DIS # H6: 3,6 => CTR => H6: 5
* PRF # H6: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* INC # G2: 5 => UNS
* DIS # G3: 2,3 => CTR => G3: 5,6
* INC # G3: 5,6 => UNS
* DIS # D1: 2,3 => CTR => D1: 6,7
* INC # D1: 6,7 => UNS
* DIS # F1: 2,3 => CTR => F1: 6,7
* INC # F1: 6,7 => UNS
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # C4: 6,8 => CTR => C4: 1,4,5
* INC # C4: 1,4,5 => UNS
* DIS # C5: 6,8 => CTR => C5: 1
* PRF # C5: 1 => SOL
* PRF # A6: 6,8 => SOL
* INC # A6: 4,5 => UNS
* DIS # C6: 6,8 => CTR => C6: 4,5
* INC # C6: 4,5 => UNS
* DIS # D5: 6,8 => CTR => D5: 2,3
* INC # D5: 2,3 => UNS
* DIS # F5: 6,8 => CTR => F5: 2,3
* INC # F5: 2,3 => UNS
* INC # H5: 1,6 => UNS
* DIS # H5: 3 => CTR => H5: 1,6
* DIS # C4: 1,6 => CTR => C4: 4,5,8
* PRF # C4: 4,5,8 => SOL
* DIS # I6: 5,8 => CTR => I6: 3
* PRF # I6: 3 => SOL
* PRF # C4: 5,8 => SOL
* DIS # C4: 1,4,6 => CTR => C4: 5,8
* DIS # F9: 3,6 => CTR => F9: 4,5,7
* INC # F9: 4,5,7 => UNS
* DIS # I9: 2,3 => CTR => I9: 5
* PRF # I9: 5 => SOL
* DIS # G2: 2,3 => CTR => G2: 5
* INC # G2: 5 => UNS
* DIS # G3: 2,3 => CTR => G3: 5,6
* INC # G3: 5,6 => UNS
* CNT  63 HDP CHAINS /  63 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C2: 2,8 => CTR => C2: 3
* DIS C2: 3 # A3: 2,8 => CTR => A3: 7
* INC C2: 3 + A3: 7 # D2: 2,8 => UNS
* INC C2: 3 + A3: 7 # F2: 2,8 => UNS
* DIS C2: 3 + A3: 7 # D1: 3,6 => CTR => D1: 2,7
* INC C2: 3 + A3: 7 + D1: 2,7 # F1: 3,6 => UNS
* DIS C2: 3 + A3: 7 + D1: 2,7 # D3: 3,6 => CTR => D3: 2,5,8
* DIS C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 # F3: 3,6 => CTR => F3: 2,5,8
* PRF C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 # H5: 3,6 => SOL
* STA C2: 3 + A3: 7 + D1: 2,7 + D3: 2,5,8 + F3: 2,5,8 + H5: 3,6
* CNT   9 HDP CHAINS /   9 HYP OPENED