Analysis of zz-www.sudokuoftheday.co.uk-20060422-absurd-base.sdk

Contents

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

level: medium

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

position: .9...73...5.3....9....45.1..73.2..5.4....92...6..71......1...........59..372..14. initial

Autosolve

position: .94..73.575.3.24.93..945.1..73.2..5.4...392...6..71......1........7..59..372..14. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 6,8 => CTR => H1: 2
* DIS # D4: 6,8 => CTR => D4: 4
* DIS # H1: 6,8 => CTR => H1: 2
* DIS # C5: 1,8 => CTR => C5: 5
* PRF # I5: 1,8 => SOL
* DIS # D4: 6,8 => CTR => D4: 4
* PRF # I4: 6,8 => SOL
* DIS # G4: 6 => CTR => G4: 8,9
* DIS # I6: 3,8 => CTR => I6: 4
* DIS # I8: 6,8 => CTR => I8: 2,3
* DIS # I7: 6,8 => CTR => I7: 2,3,7
* DIS # I8: 6,8 => CTR => I8: 2,3
* PRF # I4: 6,8 => SOL
* CNT  13 HDP CHAINS /  65 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 # H1: 6,8 => CTR => H1: 2
* DIS H1: 2 # D4: 6,8 => CTR => D4: 4
* DIS H1: 2 + D4: 4 # D5: 5 => CTR => D5: 6,8
* PRF H1: 2 + D4: 4 + D5: 6,8 # I5: 1,8 => SOL
* STA H1: 2 + D4: 4 + D5: 6,8 + I5: 1,8
* CNT   4 HDP CHAINS /  29 HYP OPENED

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

Details

Positions

.9...73...5.3....9....45.1..73.2..5.4....92...6..71......1...........59..372..14. initial
.94..73.575.3.24.93..945.1..73.2..5.4...392...6..71......1........7..59..372..14. autosolve
694817325751362489328945617173428956485639271962571834849153762216784593537296148 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B3: 2,8
D1: 6,8
H2: 6,8
B5: 1,8
F4: 6,8
G6: 8,9
H6: 3,8
A9: 5,9
E7: 5,9
F7: 3,4
E8: 6,8
F8: 3,4
E9: 5,9
F9: 6,8
I9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C2: 1.. / A1 = 1  => 20 pairs (_) / C2 = 1  => 17 pairs (_)
E1,E2: 1.. / E1 = 1  => 17 pairs (_) / E2 = 1  => 20 pairs (_)
I4,I5: 1.. / I4 = 1  => 16 pairs (_) / I5 = 1  =>  0 pairs (*)
A1,E1: 1.. / A1 = 1  => 20 pairs (_) / E1 = 1  => 17 pairs (_)
C2,E2: 1.. / C2 = 1  => 17 pairs (_) / E2 = 1  => 20 pairs (_)
A4,I4: 1.. / A4 = 1  =>  0 pairs (*) / I4 = 1  =>  0 pairs (X)
B5,B8: 1.. / B5 = 1  => 16 pairs (_) / B8 = 1  => 16 pairs (_)
H1,I3: 2.. / H1 = 2  => 15 pairs (_) / I3 = 2  =>  0 pairs (X)
A6,C6: 2.. / A6 = 2  => 15 pairs (_) / C6 = 2  => 14 pairs (_)
A1,H1: 2.. / A1 = 2  =>  0 pairs (X) / H1 = 2  => 15 pairs (_)
H1,H7: 2.. / H1 = 2  => 15 pairs (_) / H7 = 2  =>  0 pairs (X)
H6,I6: 3.. / H6 = 3  => 15 pairs (_) / I6 = 3  =>  0 pairs (X)
F7,F8: 3.. / F7 = 3  => 13 pairs (_) / F8 = 3  => 15 pairs (_)
F8,I8: 3.. / F8 = 3  => 15 pairs (_) / I8 = 3  => 13 pairs (_)
H6,H7: 3.. / H6 = 3  => 15 pairs (_) / H7 = 3  =>  0 pairs (X)
D4,D6: 4.. / D4 = 4  => 15 pairs (_) / D6 = 4  =>  0 pairs (X)
I4,I6: 4.. / I4 = 4  =>  0 pairs (X) / I6 = 4  => 15 pairs (_)
B7,B8: 4.. / B7 = 4  => 13 pairs (_) / B8 = 4  => 15 pairs (_)
F7,F8: 4.. / F7 = 4  => 15 pairs (_) / F8 = 4  => 13 pairs (_)
D4,I4: 4.. / D4 = 4  => 15 pairs (_) / I4 = 4  =>  0 pairs (X)
D6,I6: 4.. / D6 = 4  =>  0 pairs (X) / I6 = 4  => 15 pairs (_)
B7,F7: 4.. / B7 = 4  => 13 pairs (_) / F7 = 4  => 15 pairs (_)
B8,F8: 4.. / B8 = 4  => 15 pairs (_) / F8 = 4  => 13 pairs (_)
D5,D6: 5.. / D5 = 5  =>  0 pairs (X) / D6 = 5  => 15 pairs (_)
E7,E9: 5.. / E7 = 5  => 12 pairs (_) / E9 = 5  => 18 pairs (_)
C5,D5: 5.. / C5 = 5  => 15 pairs (_) / D5 = 5  =>  0 pairs (X)
A9,E9: 5.. / A9 = 5  => 12 pairs (_) / E9 = 5  => 18 pairs (_)
E8,F9: 6.. / E8 = 6  =>  0 pairs (X) / F9 = 6  => 20 pairs (_)
F9,I9: 6.. / F9 = 6  => 20 pairs (_) / I9 = 6  =>  0 pairs (X)
F4,F9: 6.. / F4 = 6  =>  0 pairs (X) / F9 = 6  => 20 pairs (_)
G3,I3: 7.. / G3 = 7  => 17 pairs (_) / I3 = 7  => 16 pairs (_)
H5,I5: 7.. / H5 = 7  => 15 pairs (_) / I5 = 7  => 21 pairs (_)
G3,G7: 7.. / G3 = 7  => 17 pairs (_) / G7 = 7  => 16 pairs (_)
H5,H7: 7.. / H5 = 7  => 15 pairs (_) / H7 = 7  => 21 pairs (_)
E8,F9: 8.. / E8 = 8  => 20 pairs (_) / F9 = 8  =>  0 pairs (X)
F9,I9: 8.. / F9 = 8  =>  0 pairs (X) / I9 = 8  => 20 pairs (_)
F4,F9: 8.. / F4 = 8  => 20 pairs (_) / F9 = 8  =>  0 pairs (X)
G4,G6: 9.. / G4 = 9  => 21 pairs (_) / G6 = 9  => 13 pairs (_)
E7,E9: 9.. / E7 = 9  => 18 pairs (_) / E9 = 9  => 12 pairs (_)
A4,G4: 9.. / A4 = 9  => 13 pairs (_) / G4 = 9  => 21 pairs (_)
A9,E9: 9.. / A9 = 9  => 18 pairs (_) / E9 = 9  => 12 pairs (_)
C6,C7: 9.. / C6 = 9  => 22 pairs (_) / C7 = 9  => 12 pairs (_)
* DURATION: 0:00:44.790757  START: 22:33:41.105282  END: 22:34:25.896039 2019-04-30
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B5,D1,E7,E8,E9,F4,F7,F8,F9,G6,H2,H6,I9)
* .94..73.575.3.24.93..945.1..73.2..5.4...392...6..71......1........7..59..372..14.
* PAIR B3: 2,8 BLK 1
A1: 2,8,1,6                              # reduction candidate for 2,8
A1: 2,8                                  # 21 pairs
C3: 2,8,6                                # reduction candidate for 2,8
C3: 2,8                                  # 24 pairs
* PAIR B3: 2,8 ROW 3
I3: 2,8,6,7                              # reduction candidate for 2,8
I3: 2,8                                  # 20 pairs
I3: 6,7                                  # 16 pairs
* PAIR B3: 2,8 COL B
B7: 2,8,4                                # reduction candidate for 2,8
B7: 2,8                                  # 15 pairs
B8: 2,8,1,4                              # reduction candidate for 2,8
B8: 2,8                                  # 15 pairs
* PAIR D1: 6,8 BLK 2
E1: 6,8,1                                # reduction candidate for 6,8
E1: 6,8                                  # 20 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 17 pairs
* PAIR D1: 6,8 ROW 1
A1: 6,8,1,2                              # reduction candidate for 6,8
A1: 6,8                                  # 18 pairs
H1: 6,8,2                                # reduction candidate for 6,8
H1: 6,8 => CTR
* 2946173857513.24.9386945712.73.2..5.41..392...62.71.....915..27128764593537298146
H1: 2                                    # 15 pairs
* PAIR D1: 6,8 COL D
D4: 6,8,4                                # reduction candidate for 6,8
D4: 6,8 => CTR
* .94..73.57513.24.93..945.1.173.2.95448..392.1.6.471......1......1.7.4593.372..14.
D4: 4                                    # 15 pairs
D5: 6,8,5                                # reduction candidate for 6,8
D5: 6,8                                  # 15 pairs
* PAIR H2: 6,8 BLK 3
H1: 6,8,2                                # reduction candidate for 6,8
H1: 6,8 => CTR
* 2946173857513.24.9386945712.73.2..5.41..392...62.71.....915..27128764593537298146
H1: 2                                    # 15 pairs
G3: 6,8,7                                # reduction candidate for 6,8
G3: 6,8                                  # 16 pairs
I3: 6,8,2,7                              # reduction candidate for 6,8
I3: 6,8                                  # 22 pairs
* PAIR H2: 6,8 ROW 2
C2: 6,8,1                                # reduction candidate for 6,8
C2: 6,8                                  # 20 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 17 pairs
* PAIR H2: 6,8 COL H
H5: 6,8,7                                # reduction candidate for 6,8
H5: 6,8                                  # 21 pairs
H7: 6,8,2,3,7                            # reduction candidate for 6,8
H7: 6,8                                  # 19 pairs
* PAIR B5: 1,8 BLK 4
A4: 1,8,9                                # reduction candidate for 1,8
A4: 1,8                                  # 21 pairs
C5: 1,8,5                                # reduction candidate for 1,8
C5: 1,8 => CTR
* .946.732575.3.24.93..9456179734268514..5392..265871934..915.......76.59.537298146
C5: 5                                    # 15 pairs
* PAIR B5: 1,8 ROW 5
I5: 1,8,6,7                              # reduction candidate for 1,8
I5: 1,8 => SOLVED
* 694817325751362489328945617173428956485639271962571834849153762216784593537296148
I5: 6,7                                  # 17 pairs
* PAIR B5: 1,8 COL B
B8: 1,8,2,4                              # reduction candidate for 1,8
B8: 2,4                                  # 17 pairs
B8: 1,8                                  # 14 pairs
* PAIR F4: 6,8 BLK 5
D4: 6,8,4                                # reduction candidate for 6,8
D4: 6,8 => CTR
* .94..73.57513.24.93..945.1.173.2.95448..392.1.6.471......1......1.7.4593.372..14.
D4: 4                                    # 15 pairs
D5: 6,8,5                                # reduction candidate for 6,8
D5: 6,8                                  # 15 pairs
* PAIR F4: 6,8 ROW 4
G4: 6,8,9                                # reduction candidate for 6,8
G4: 6,8                                  # 13 pairs
I4: 6,8,1,4                              # reduction candidate for 6,8
I4: 6,8 => SOLVED
* 694817325751362489328945617173428956485639271962571834849153762216784593537296148
I4: 1,4                                  # 16 pairs
* PAIR G6: 8,9 BLK 6
G4: 8,9,6                                # reduction candidate for 8,9
G4: 6 => CTR
* .948.73.575.3.24.93..945817973.2.6514..6392...6.5719.4..915.......7..59.537296148
G4: 8,9                                  # 20 pairs
* PAIR G6: 8,9 ROW 6
A6: 8,9,2,5                              # reduction candidate for 8,9
A6: 8,9                                  # 14 pairs
C6: 8,9,2,5                              # reduction candidate for 8,9
C6: 8,9                                  # 18 pairs
* PAIR H6: 3,8 BLK 6
I6: 3,8,4                                # reduction candidate for 3,8
I6: 3,8 => CTR
* .94..73.57513.24.93..945.1.173.2.95448..392.1.6.471......1......1.7.4593.372..14.
I6: 4                                    # 15 pairs
* PAIR H6: 3,8 COL H
H7: 3,8,2,6,7                            # reduction candidate for 3,8
H7: 3,8                                  # 20 pairs
H7: 2,6,7                                # 15 pairs
* PAIR A9: 5,9 BLK 7
A7: 5,9,2,6,8                            # reduction candidate for 5,9
A7: 5,9                                  # 22 pairs
C7: 5,9,2,6,8                            # reduction candidate for 5,9
C7: 5,9                                  # 16 pairs
* PAIR A9: 5,9 COL A
A6: 5,9,2,8                              # reduction candidate for 5,9
A6: 5,9                                  # 17 pairs
A6: 2,8                                  # 16 pairs
* PAIR E7: 5,9 ROW 7
A7: 5,9,2,6,8                            # reduction candidate for 5,9
A7: 5,9                                  # 22 pairs
C7: 5,9,2,6,8                            # reduction candidate for 5,9
C7: 5,9                                  # 16 pairs
* PAIR E8: 6,8 ROW 8
A8: 6,8,1,2                              # reduction candidate for 6,8
A8: 6,8                                  # 18 pairs
C8: 6,8,1,2                              # reduction candidate for 6,8
C8: 6,8                                  # 18 pairs
I8: 6,8,2,3                              # reduction candidate for 6,8
I8: 6,8 => CTR
* .94..73.575.3.24.93..945.12.7342..5141..392.7.6..71.34...1.4..3.4.7.359..372..14.
I8: 2,3                                  # 16 pairs
* PAIR E8: 6,8 COL E
E1: 6,8,1                                # reduction candidate for 6,8
E1: 6,8                                  # 20 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 17 pairs
* PAIR I9: 6,8 BLK 9
G7: 6,8,7                                # reduction candidate for 6,8
G7: 6,8                                  # 17 pairs
H7: 6,8,2,3,7                            # reduction candidate for 6,8
H7: 6,8                                  # 19 pairs
I7: 6,8,2,3,7                            # reduction candidate for 6,8
I7: 6,8 => CTR
* .94..73.575.3.24.93..945.1..73.2..5.4...39271.6..71......1..7...1.7.4593.372..14.
I7: 2,3,7                                # 15 pairs
I8: 6,8,2,3                              # reduction candidate for 6,8
I8: 6,8 => CTR
* .94..73.575.3.24.93..945.12.7342..5141..392.7.6..71.34...1.4..3.4.7.359..372..14.
I8: 2,3                                  # 16 pairs
* PAIR I9: 6,8 COL I
I3: 6,8,2,7                              # reduction candidate for 6,8
I3: 6,8                                  # 22 pairs
I4: 6,8,1,4                              # reduction candidate for 6,8
I4: 6,8 => SOLVED
* 694817325751362489328945617173428956485639271962571834849153762216784593537296148
I4: 1,4                                  # 16 pairs
I5: 6,8,1,7                              # reduction candidate for 6,8
I5: 6,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060422-absurd-base-pr-000.dot
* REASONING
* DIS # H1: 6,8 => CTR => H1: 2
* DIS # D4: 6,8 => CTR => D4: 4
* DIS # H1: 6,8 => CTR => H1: 2
* DIS # C5: 1,8 => CTR => C5: 5
* PRF # I5: 1,8 => SOL
* DIS # D4: 6,8 => CTR => D4: 4
* PRF # I4: 6,8 => SOL
* DIS # G4: 6 => CTR => G4: 8,9
* DIS # I6: 3,8 => CTR => I6: 4
* DIS # I8: 6,8 => CTR => I8: 2,3
* DIS # I7: 6,8 => CTR => I7: 2,3,7
* DIS # I8: 6,8 => CTR => I8: 2,3
* PRF # I4: 6,8 => SOL
* CNT  13 HDP CHAINS /  65 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B5,D1,E7,E8,E9,F4,F7,F8,F9,G6,H2,H6,I9)
* .94..73.575.3.24.93..945.1..73.2..5.4...392...6..71......1........7..59..372..14.
* PAIR B3: 2,8 BLK 1
A1: 2,8,1,6                              # reduction candidate for 2,8
A1: 2,8                                  # 21 pairs
C3: 2,8,6                                # reduction candidate for 2,8
C3: 2,8                                  # 24 pairs
* PAIR B3: 2,8 ROW 3
I3: 2,8,6,7                              # reduction candidate for 2,8
I3: 2,8                                  # 20 pairs
I3: 6,7                                  # 16 pairs
* PAIR B3: 2,8 COL B
B7: 2,8,4                                # reduction candidate for 2,8
B7: 2,8                                  # 15 pairs
B8: 2,8,1,4                              # reduction candidate for 2,8
B8: 2,8                                  # 15 pairs
* PAIR D1: 6,8 BLK 2
E1: 6,8,1                                # reduction candidate for 6,8
E1: 6,8                                  # 20 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 17 pairs
* PAIR D1: 6,8 ROW 1
A1: 6,8,1,2                              # reduction candidate for 6,8
A1: 6,8                                  # 18 pairs
H1: 6,8,2                                # reduction candidate for 6,8
H1: 6,8 => CTR
* 2946173857513.24.9386945712.73.2..5.41..392...62.71.....915..27128764593537298146
* RESTART
* PAIR D1: 6,8 ROW 1
A1: 6,8,1                                # reduction candidate for 6,8
A1: 1                                    # 20 pairs
A1: 6,8                                  # 18 pairs
* PAIR D1: 6,8 COL D
D4: 6,8,4                                # reduction candidate for 6,8
D4: 6,8 => CTR
* .94..73257513.24.93..945.1.173.2.95448..392.1.6.471......1......1.7.4593.372..14.
D5: 6,8,5                                # reduction candidate for 6,8
D5: 6,8                                  # 17 pairs
* RESTART
* PAIR D1: 6,8 COL D
D5: 6,8,5                                # reduction candidate for 6,8
D5: 5 => CTR
* .946.732575.3.24.93..94561797342685.4..5392...6.871934..915.......76.59.537298146
* PAIR RESTART
* PAIR D1: 6,8 BLK 2
E1: 6,8,1                                # reduction candidate for 6,8
E1: 6,8                                  # 19 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 19 pairs
* PAIR D1: 6,8 ROW 1
A1: 6,8,1                                # reduction candidate for 6,8
A1: 6,8                                  # 19 pairs
A1: 1                                    # 19 pairs
* PAIR H2: 6,8 BLK 3
G3: 6,8,7                                # reduction candidate for 6,8
G3: 6,8                                  # 19 pairs
I3: 6,8,7                                # reduction candidate for 6,8
I3: 6,8                                  # 20 pairs
* PAIR H2: 6,8 ROW 2
C2: 6,8,1                                # reduction candidate for 6,8
C2: 6,8                                  # 19 pairs
E2: 6,8,1                                # reduction candidate for 6,8
E2: 6,8                                  # 19 pairs
* PAIR H2: 6,8 COL H
H5: 6,8,7                                # reduction candidate for 6,8
H5: 6,8                                  # 20 pairs
H7: 6,8,7                                # reduction candidate for 6,8
H7: 6,8                                  # 19 pairs
* PAIR B5: 1,8 BLK 4
A4: 1,8,9                                # reduction candidate for 1,8
A4: 1,8                                  # 23 pairs
A4: 9                                    # 15 pairs
* PAIR B5: 1,8 ROW 5
I5: 1,8,6,7                              # reduction candidate for 1,8
I5: 1,8 => SOLVED
* 694817325751362489328945617173428956485639271962571834849153762216784593537296148
* DURATION: 0:00:19.471009  START: 22:35:04.274639  END: 22:35:23.745648 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060422-absurd-base-pr-001.dot
* REASONING
* DIS # H1: 6,8 => CTR => H1: 2
* DIS H1: 2 # D4: 6,8 => CTR => D4: 4
* DIS H1: 2 + D4: 4 # D5: 5 => CTR => D5: 6,8
* PRF H1: 2 + D4: 4 + D5: 6,8 # I5: 1,8 => SOL
* STA H1: 2 + D4: 4 + D5: 6,8 + I5: 1,8
* CNT   4 HDP CHAINS /  29 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060422, absurd

Solution

position: 694817325751362489328945617173428956485639271962571834849153762216784593537296148 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 # A1: 2,8 => UNS
* INC # C3: 2,8 => UNS
* INC # I3: 2,8 => UNS
* INC # I3: 6,7 => UNS
* INC # B7: 2,8 => UNS
* INC # B8: 2,8 => UNS
* INC # E1: 6,8 => UNS
* INC # E2: 6,8 => UNS
* INC # A1: 6,8 => UNS
* DIS # H1: 6,8 => CTR => H1: 2
* INC # H1: 2 => UNS
* DIS # D4: 6,8 => CTR => D4: 4
* INC # D4: 4 => UNS
* INC # D5: 6,8 => UNS
* DIS # H1: 6,8 => CTR => H1: 2
* INC # H1: 2 => UNS
* INC # G3: 6,8 => UNS
* INC # I3: 6,8 => UNS
* INC # C2: 6,8 => UNS
* INC # E2: 6,8 => UNS
* INC # H5: 6,8 => UNS
* INC # H7: 6,8 => UNS
* INC # A4: 1,8 => UNS
* DIS # C5: 1,8 => CTR => C5: 5
* INC # C5: 5 => UNS
* PRF # I5: 1,8 => SOL
* INC # I5: 6,7 => UNS
* INC # B8: 1,8 => UNS
* INC # B8: 2,4 => UNS
* DIS # D4: 6,8 => CTR => D4: 4
* INC # D4: 4 => UNS
* INC # D5: 6,8 => UNS
* INC # G4: 6,8 => UNS
* PRF # I4: 6,8 => SOL
* INC # I4: 1,4 => UNS
* INC # G4: 8,9 => UNS
* DIS # G4: 6 => CTR => G4: 8,9
* INC # A6: 8,9 => UNS
* INC # C6: 8,9 => UNS
* DIS # I6: 3,8 => CTR => I6: 4
* INC # I6: 4 => UNS
* INC # H7: 3,8 => UNS
* INC # H7: 2,6,7 => UNS
* INC # A7: 5,9 => UNS
* INC # C7: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A6: 2,8 => UNS
* INC # A7: 5,9 => UNS
* INC # C7: 5,9 => UNS
* INC # A8: 6,8 => UNS
* INC # C8: 6,8 => UNS
* DIS # I8: 6,8 => CTR => I8: 2,3
* INC # I8: 2,3 => UNS
* INC # E1: 6,8 => UNS
* INC # E2: 6,8 => UNS
* INC # G7: 6,8 => UNS
* INC # H7: 6,8 => UNS
* DIS # I7: 6,8 => CTR => I7: 2,3,7
* INC # I7: 2,3,7 => UNS
* DIS # I8: 6,8 => CTR => I8: 2,3
* INC # I8: 2,3 => UNS
* INC # I3: 6,8 => UNS
* PRF # I4: 6,8 => SOL
* INC # I4: 1,4 => UNS
* INC # I5: 6,8 => UNS
* CNT  65 HDP CHAINS /  65 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 2,8 => UNS
* INC # C3: 2,8 => UNS
* INC # I3: 2,8 => UNS
* INC # I3: 6,7 => UNS
* INC # B7: 2,8 => UNS
* INC # B8: 2,8 => UNS
* INC # E1: 6,8 => UNS
* INC # E2: 6,8 => UNS
* INC # A1: 6,8 => UNS
* DIS # H1: 6,8 => CTR => H1: 2
* INC H1: 2 # A1: 6,8 => UNS
* INC H1: 2 # A1: 1 => UNS
* DIS H1: 2 # D4: 6,8 => CTR => D4: 4
* INC H1: 2 + D4: 4 # D5: 6,8 => UNS
* INC H1: 2 + D4: 4 # D5: 6,8 => UNS
* DIS H1: 2 + D4: 4 # D5: 5 => CTR => D5: 6,8
* INC H1: 2 + D4: 4 + D5: 6,8 # E1: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # E2: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # A1: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # A1: 1 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # G3: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # I3: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # C2: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # E2: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # H5: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # H7: 6,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # A4: 1,8 => UNS
* INC H1: 2 + D4: 4 + D5: 6,8 # A4: 9 => UNS
* PRF H1: 2 + D4: 4 + D5: 6,8 # I5: 1,8 => SOL
* STA H1: 2 + D4: 4 + D5: 6,8 + I5: 1,8
* CNT  29 HDP CHAINS /  29 HYP OPENED