Analysis of zz-www.sudokuoftheday.co.uk-20190419-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: ..28...3...3.16..8..1..5.6..7.5........73...6....687....61..5.7.....4.1.9.8...... initial

Autosolve

position: .628.9135..3.16.78..13.5.6.67.5........73...6....687....61.35.7..7..4.1.918.57... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A3: 4,7 => SOL
* DIS # A3: 8 => CTR => A3: 4,7
* DIS # B2: 4,5 => CTR => B2: 9
* DIS # E3: 4,7 => CTR => E3: 2
* PRF # E3: 2 => SOL
* PRF # E3: 2,4 => SOL
* DIS # E3: 7 => CTR => E3: 2,4
* DIS # G2: 9 => CTR => G2: 2,4
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* DIS # B3: 4,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # I6: 4,9 => SOL
* PRF # A5: 2,8 => SOL
* DIS # A5: 1 => CTR => A5: 2,8
* DIS # A6: 2,3 => CTR => A6: 1
* PRF # A6: 1 => SOL
* PRF # I4: 1,2 => SOL
* DIS # I4: 3 => CTR => I4: 1,2
* DIS # A5: 1,2 => CTR => A5: 8
* PRF # A5: 8 => SOL
* PRF # I6: 4,9 => SOL
* PRF # I6: 4,9 => SOL
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* PRF # E8: 8,9 => SOL
* DIS # E8: 2 => CTR => E8: 8,9
* PRF # D8: 2,6 => SOL
* DIS # D8: 9 => CTR => D8: 2,6
* DIS # D8: 2,9 => CTR => D8: 6
* PRF # D8: 6 => SOL
* PRF # E8: 2,9 => SOL
* DIS # E8: 8 => CTR => E8: 2,9
* DIS # I6: 2,9 => CTR => I6: 1,4
* DIS # I9: 2,4 => CTR => I9: 3
* PRF # I9: 3 => SOL
* PRF # H6: 2,4 => SOL
* CNT  41 HDP CHAINS /  56 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # A3: 4,7 => SOL
* STA A3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..28...3...3.16..8..1..5.6..7.5........73...6....687....61..5.7.....4.1.9.8...... initial
.628.9135..3.16.78..13.5.6.67.5........73...6....687....61.35.7..7..4.1.918.57... autosolve
462879135593416278781325469679542381824731956135968724246183597357694812918257643 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (26)
A1: 4,7
A2: 4,5
E1: 4,7
D2: 2,4
I3: 4,9
C4: 4,9
B5: 2,8
B6: 2,3
E4: 4,9
F4: 1,2
F5: 1,2
D6: 4,9
G4: 3,8
H4: 2,8
G5: 4,9
A7: 2,4
B7: 2,4
A8: 3,5
B8: 3,5
E7: 8,9
D9: 2,6
H7: 8,9
G8: 6,8
I8: 2,9
G9: 3,6
H9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,A6: 1.. / A5 = 1  =>  0 pairs (X) / A6 = 1  =>  0 pairs (_)
F4,F5: 1.. / F4 = 1  =>  0 pairs (X) / F5 = 1  =>  0 pairs (_)
I4,I6: 1.. / I4 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
F4,I4: 1.. / F4 = 1  =>  0 pairs (X) / I4 = 1  =>  0 pairs (_)
A5,F5: 1.. / A5 = 1  =>  0 pairs (X) / F5 = 1  =>  0 pairs (_)
A6,I6: 1.. / A6 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
D2,E3: 2.. / D2 = 2  =>  0 pairs (X) / E3 = 2  =>  0 pairs (_)
G2,G3: 2.. / G2 = 2  =>  0 pairs (*) / G3 = 2  =>  0 pairs (X)
F4,F5: 2.. / F4 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
A7,B7: 2.. / A7 = 2  => 28 pairs (_) / B7 = 2  =>  0 pairs (X)
D2,G2: 2.. / D2 = 2  =>  0 pairs (X) / G2 = 2  =>  0 pairs (_)
E3,G3: 2.. / E3 = 2  =>  0 pairs (*) / G3 = 2  =>  0 pairs (X)
E3,E8: 2.. / E3 = 2  =>  0 pairs (*) / E8 = 2  =>  0 pairs (X)
A6,B6: 3.. / A6 = 3  =>  0 pairs (X) / B6 = 3  => 24 pairs (_)
G4,I4: 3.. / G4 = 3  =>  0 pairs (*) / I4 = 3  =>  0 pairs (X)
A8,B8: 3.. / A8 = 3  => 24 pairs (_) / B8 = 3  =>  0 pairs (X)
G9,I9: 3.. / G9 = 3  =>  0 pairs (X) / I9 = 3  =>  0 pairs (_)
A6,A8: 3.. / A6 = 3  =>  0 pairs (X) / A8 = 3  => 24 pairs (_)
B6,B8: 3.. / B6 = 3  => 24 pairs (_) / B8 = 3  =>  0 pairs (X)
G4,G9: 3.. / G4 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
I4,I9: 3.. / I4 = 3  =>  0 pairs (X) / I9 = 3  =>  0 pairs (_)
E4,D6: 4.. / E4 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
A7,B7: 4.. / A7 = 4  =>  0 pairs (X) / B7 = 4  => 28 pairs (_)
H9,I9: 4.. / H9 = 4  => 28 pairs (_) / I9 = 4  =>  0 pairs (X)
A1,E1: 4.. / A1 = 4  =>  0 pairs (*) / E1 = 4  =>  0 pairs (X)
C4,E4: 4.. / C4 = 4  =>  0 pairs (X) / E4 = 4  =>  0 pairs (_)
D2,D6: 4.. / D2 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
A2,B2: 5.. / A2 = 5  => 24 pairs (_) / B2 = 5  =>  0 pairs (X)
C5,C6: 5.. / C5 = 5  => 29 pairs (_) / C6 = 5  => 27 pairs (_)
H5,H6: 5.. / H5 = 5  => 27 pairs (_) / H6 = 5  => 29 pairs (_)
A8,B8: 5.. / A8 = 5  =>  0 pairs (X) / B8 = 5  => 24 pairs (_)
C5,H5: 5.. / C5 = 5  => 29 pairs (_) / H5 = 5  => 27 pairs (_)
C6,H6: 5.. / C6 = 5  => 27 pairs (_) / H6 = 5  => 29 pairs (_)
A2,A8: 5.. / A2 = 5  => 24 pairs (_) / A8 = 5  =>  0 pairs (X)
B2,B8: 5.. / B2 = 5  =>  0 pairs (X) / B8 = 5  => 24 pairs (_)
D8,D9: 6.. / D8 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
G8,G9: 6.. / G8 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
D8,G8: 6.. / D8 = 6  =>  0 pairs (*) / G8 = 6  =>  0 pairs (X)
D9,G9: 6.. / D9 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
A1,A3: 7.. / A1 = 7  =>  0 pairs (X) / A3 = 7  =>  0 pairs (_)
E1,E3: 7.. / E1 = 7  =>  0 pairs (*) / E3 = 7  =>  0 pairs (X)
A1,E1: 7.. / A1 = 7  =>  0 pairs (X) / E1 = 7  =>  0 pairs (_)
A3,E3: 7.. / A3 = 7  =>  0 pairs (*) / E3 = 7  =>  0 pairs (X)
A3,B3: 8.. / A3 = 8  =>  0 pairs (X) / B3 = 8  =>  0 pairs (_)
A5,B5: 8.. / A5 = 8  =>  0 pairs (*) / B5 = 8  =>  0 pairs (X)
G4,H4: 8.. / G4 = 8  =>  0 pairs (X) / H4 = 8  =>  0 pairs (_)
E7,E8: 8.. / E7 = 8  =>  0 pairs (*) / E8 = 8  =>  0 pairs (X)
H7,G8: 8.. / H7 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
E7,H7: 8.. / E7 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
E8,G8: 8.. / E8 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
A3,A5: 8.. / A3 = 8  =>  0 pairs (X) / A5 = 8  =>  0 pairs (_)
B3,B5: 8.. / B3 = 8  =>  0 pairs (*) / B5 = 8  =>  0 pairs (X)
G4,G8: 8.. / G4 = 8  =>  0 pairs (X) / G8 = 8  =>  0 pairs (_)
H4,H7: 8.. / H4 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
B2,B3: 9.. / B2 = 9  => 25 pairs (_) / B3 = 9  =>  0 pairs (X)
E4,D6: 9.. / E4 = 9  =>  0 pairs (X) / D6 = 9  =>  0 pairs (_)
H7,I8: 9.. / H7 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
B2,G2: 9.. / B2 = 9  => 25 pairs (_) / G2 = 9  =>  0 pairs (X)
C4,E4: 9.. / C4 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
E7,H7: 9.. / E7 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
D6,D8: 9.. / D6 = 9  =>  0 pairs (*) / D8 = 9  =>  0 pairs (X)
* DURATION: 0:01:28.679024  START: 05:25:43.131819  END: 05:27:11.810843 2019-05-01
* CP COUNT: (61)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A7,A8,B5,B6,B7,B8,C4,D2,D6,D9,E1,E4,E7,F4,F5,G4,G5,G8,G9,H4,H7,H9,I3,I8)
* .628.9135..3.16.78..13.5.6.67.5........73...6....687....61.35.7..7..4.1.918.57...
* PAIR A1: 4,7 BLK 1
A3: 4,7,8                                # reduction candidate for 4,7
A3: 4,7 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
A3: 8 => CTR
* 762849135..3216.788.137526.67459.....8.73...6...4687....6183597..7924.1.918.57...
* PAIR A2: 4,5 BLK 1
B2: 4,5,9                                # reduction candidate for 4,5
B2: 4,5 => CTR
* .628.9135..3.16978.913.526467.5......8.73.4.6....687....61.35.7..7.24819918.57...
B2: 9                                    # 25 pairs
* PAIR E1: 4,7 BLK 2
E3: 4,7,2                                # reduction candidate for 4,7
E3: 4,7 => CTR
* .628.9135..3216.78..13.526.67.5........73...6...4687....61.35.7..7924.1.918.57...
E3: 2 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* PAIR D2: 2,4 BLK 2
E3: 2,4,7                                # reduction candidate for 2,4
E3: 2,4 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
E3: 7 => CTR
* .628.9135..3216.78..137526.67.5........73...6...4687....61.35.7..7924.1.918.57...
* PAIR D2: 2,4 ROW 2
G2: 2,4,9                                # reduction candidate for 2,4
G2: 9 => CTR
* .628.9135..3216978.913.526467.5......8.73.4.6...4687....61.35.7..7924.1.918.57...
G2: 2,4                                  # 25 pairs
* PAIR I3: 4,9 BLK 3
G2: 4,9,2                                # reduction candidate for 4,9
G2: 4,9 => CTR
* .628.9135..3216.78..13.526.67.5........73...6...4687....61.35.7..7924.1.918.57...
G2: 2 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
G3: 4,9,2                                # reduction candidate for 4,9
G3: 4,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
G3: 2 => CTR
* .628.9135..3.16.78..13.526.67.5........73...6....687....61.35.7..7.24819918.57...
* PAIR I3: 4,9 ROW 3
B3: 4,9,8                                # reduction candidate for 4,9
B3: 4,9 => CTR
* .628.9135..3.16.788.137526.67.5......8.73...6....687....61.35.7..7.24819918.57...
B3: 8 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* PAIR I3: 4,9 COL I
I6: 4,9,1,2                              # reduction candidate for 4,9
I6: 4,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
I6: 1,2                                  # 27 pairs
* PAIR C4: 4,9 BLK 4
C5: 4,9,5                                # reduction candidate for 4,9
C5: 4,9                                  # 27 pairs
C6: 4,9,5                                # reduction candidate for 4,9
C6: 4,9                                  # 29 pairs
* PAIR B5: 2,8 BLK 4
A5: 2,8,1                                # reduction candidate for 2,8
A5: 2,8 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
A5: 1 => CTR
* .628.9135..3.16.788.137526.67.5.....18.732..6....687.1..61.35.7..7.24819918.57...
* PAIR B6: 2,3 BLK 4
A6: 2,3,1                                # reduction candidate for 2,3
A6: 2,3 => CTR
* .628.9135..3.16.788.137526.67.5.1...18.732..6....687.1..61.35.7..7.24819918.57...
A6: 1 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* PAIR F4: 1,2 ROW 4
I4: 1,2,3                                # reduction candidate for 1,2
I4: 1,2 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
I4: 3 => CTR
* .628.9135..3.16.788.13.5.6.67.5.1.2318.732..6....687.1..61.3587..7.84619918657342
* PAIR F5: 1,2 ROW 5
A5: 1,2,8                                # reduction candidate for 1,2
A5: 1,2 => CTR
* .628.9135..3.16.788.137526.67.5......8.73...6....687....61.35.7..7.24819918.57...
A5: 8 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* PAIR D6: 4,9 ROW 6
C6: 4,9,5                                # reduction candidate for 4,9
C6: 4,9                                  # 29 pairs
H6: 4,9,2,5                              # reduction candidate for 4,9
H6: 4,9                                  # 29 pairs
I6: 4,9,1,2                              # reduction candidate for 4,9
I6: 4,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
I6: 1,2                                  # 27 pairs
* PAIR G5: 4,9 BLK 6
H5: 4,9,5                                # reduction candidate for 4,9
H5: 4,9                                  # 29 pairs
H6: 4,9,2,5                              # reduction candidate for 4,9
H6: 4,9                                  # 29 pairs
I6: 4,9,1,2                              # reduction candidate for 4,9
I6: 4,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
I6: 1,2                                  # 27 pairs
* PAIR G5: 4,9 ROW 5
C5: 4,9,5                                # reduction candidate for 4,9
C5: 5                                    # 29 pairs
C5: 4,9                                  # 27 pairs
* PAIR G5: 4,9 COL G
G2: 4,9,2                                # reduction candidate for 4,9
G2: 4,9 => CTR
* .628.9135..3216.78..13.526.67.5........73...6...4687....61.35.7..7924.1.918.57...
G2: 2 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
G3: 4,9,2                                # reduction candidate for 4,9
G3: 4,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
G3: 2 => CTR
* .628.9135..3.16.78..13.526.67.5........73...6....687....61.35.7..7.24819918.57...
* PAIR E7: 8,9 BLK 8
E8: 8,9,2                                # reduction candidate for 8,9
E8: 8,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
E8: 2 => CTR
* .628.9135..3.16.78..13.5.6.67.5........73...6....687....6183597..7924.1.918.57...
* PAIR D9: 2,6 BLK 8
D8: 2,6,9                                # reduction candidate for 2,6
D8: 2,6 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
D8: 9 => CTR
* .628.9135..3.16.78..13.5.6.67.5........73...6....687....61.35.7..79.4612918.57...
* PAIR I8: 2,9 ROW 8
D8: 2,9,6                                # reduction candidate for 2,9
D8: 2,9 => CTR
* .628.9135..3.16.78..1325.6467.5.182318.7324.6...968751..6193587..7284619918657342
D8: 6 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
E8: 2,9,8                                # reduction candidate for 2,9
E8: 2,9 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
E8: 8 => CTR
* .62879135..3416278781325.6.67.54.82382.73...6....687....61.35.7..7.8461.9186573..
* PAIR I8: 2,9 COL I
I6: 2,9,1,4                              # reduction candidate for 2,9
I6: 2,9 => CTR
* .628.91355.3416278..132596467.542381..97314.613..687....6183597357..4812918257643
I6: 1,4                                  # 27 pairs
* PAIR H9: 2,4 BLK 9
I9: 2,4,3                                # reduction candidate for 2,4
I9: 2,4 => CTR
* .628.9135..3.16.788.13.5.6.67.5.182318.732..6....687.1..61.3587..7.84619918657342
I9: 3 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* PAIR H9: 2,4 COL H
H6: 2,4,5,9                              # reduction candidate for 2,4
H6: 2,4 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
H6: 5,9                                  # 29 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190419-absurd-base-pr-000.dot
* REASONING
* PRF # A3: 4,7 => SOL
* DIS # A3: 8 => CTR => A3: 4,7
* DIS # B2: 4,5 => CTR => B2: 9
* DIS # E3: 4,7 => CTR => E3: 2
* PRF # E3: 2 => SOL
* PRF # E3: 2,4 => SOL
* DIS # E3: 7 => CTR => E3: 2,4
* DIS # G2: 9 => CTR => G2: 2,4
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* DIS # B3: 4,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # I6: 4,9 => SOL
* PRF # A5: 2,8 => SOL
* DIS # A5: 1 => CTR => A5: 2,8
* DIS # A6: 2,3 => CTR => A6: 1
* PRF # A6: 1 => SOL
* PRF # I4: 1,2 => SOL
* DIS # I4: 3 => CTR => I4: 1,2
* DIS # A5: 1,2 => CTR => A5: 8
* PRF # A5: 8 => SOL
* PRF # I6: 4,9 => SOL
* PRF # I6: 4,9 => SOL
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* PRF # E8: 8,9 => SOL
* DIS # E8: 2 => CTR => E8: 8,9
* PRF # D8: 2,6 => SOL
* DIS # D8: 9 => CTR => D8: 2,6
* DIS # D8: 2,9 => CTR => D8: 6
* PRF # D8: 6 => SOL
* PRF # E8: 2,9 => SOL
* DIS # E8: 8 => CTR => E8: 2,9
* DIS # I6: 2,9 => CTR => I6: 1,4
* DIS # I9: 2,4 => CTR => I9: 3
* PRF # I9: 3 => SOL
* PRF # H6: 2,4 => SOL
* CNT  41 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A7,A8,B5,B6,B7,B8,C4,D2,D6,D9,E1,E4,E7,F4,F5,G4,G5,G8,G9,H4,H7,H9,I3,I8)
* .628.9135..3.16.78..13.5.6.67.5........73...6....687....61.35.7..7..4.1.918.57...
* PAIR A1: 4,7 BLK 1
A3: 4,7,8                                # reduction candidate for 4,7
A3: 4,7 => SOLVED
* 462879135593416278781325469679542381824731956135968724246183597357694812918257643
* DURATION: 0:00:01.832783  START: 05:28:01.942940  END: 05:28:03.775723 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190419-absurd-base-pr-001.dot
* REASONING
* PRF # A3: 4,7 => SOL
* STA A3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190419, absurd

Solution

position: 462879135593416278781325469679542381824731956135968724246183597357694812918257643 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:

* PRF # A3: 4,7 => SOL
* DIS # A3: 8 => CTR => A3: 4,7
* DIS # B2: 4,5 => CTR => B2: 9
* INC # B2: 9 => UNS
* DIS # E3: 4,7 => CTR => E3: 2
* PRF # E3: 2 => SOL
* PRF # E3: 2,4 => SOL
* DIS # E3: 7 => CTR => E3: 2,4
* INC # G2: 2,4 => UNS
* DIS # G2: 9 => CTR => G2: 2,4
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* DIS # B3: 4,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # I6: 4,9 => SOL
* INC # I6: 1,2 => UNS
* INC # C5: 4,9 => UNS
* INC # C6: 4,9 => UNS
* PRF # A5: 2,8 => SOL
* DIS # A5: 1 => CTR => A5: 2,8
* DIS # A6: 2,3 => CTR => A6: 1
* PRF # A6: 1 => SOL
* PRF # I4: 1,2 => SOL
* DIS # I4: 3 => CTR => I4: 1,2
* DIS # A5: 1,2 => CTR => A5: 8
* PRF # A5: 8 => SOL
* INC # C6: 4,9 => UNS
* INC # H6: 4,9 => UNS
* PRF # I6: 4,9 => SOL
* INC # I6: 1,2 => UNS
* INC # H5: 4,9 => UNS
* INC # H6: 4,9 => UNS
* PRF # I6: 4,9 => SOL
* INC # I6: 1,2 => UNS
* INC # C5: 4,9 => UNS
* INC # C5: 5 => UNS
* DIS # G2: 4,9 => CTR => G2: 2
* PRF # G2: 2 => SOL
* PRF # G3: 4,9 => SOL
* DIS # G3: 2 => CTR => G3: 4,9
* PRF # E8: 8,9 => SOL
* DIS # E8: 2 => CTR => E8: 8,9
* PRF # D8: 2,6 => SOL
* DIS # D8: 9 => CTR => D8: 2,6
* DIS # D8: 2,9 => CTR => D8: 6
* PRF # D8: 6 => SOL
* PRF # E8: 2,9 => SOL
* DIS # E8: 8 => CTR => E8: 2,9
* DIS # I6: 2,9 => CTR => I6: 1,4
* INC # I6: 1,4 => UNS
* DIS # I9: 2,4 => CTR => I9: 3
* PRF # I9: 3 => SOL
* PRF # H6: 2,4 => SOL
* INC # H6: 5,9 => UNS
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A3: 4,7 => SOL
* STA A3: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED