Analysis of zz-www.sudokuoftheday.co.uk-20060505-absurd-base.sdk

Contents

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

level: medium

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

position: 4.62..9......56...8....4........8..3........5.2.....7..9..1.53.23......41.74...6. initial

Autosolve

position: 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 2 => SOL
* DIS # A6: 3,9 => CTR => A6: 5
* DIS # B1: 1,7 => CTR => B1: 5
* DIS # D2: 1,7 => CTR => D2: 8
* PRF # D2: 8 => SOL
* DIS # G2: 1,7 => CTR => G2: 3,8
* PRF # G2: 3,8 => SOL
* PRF # I2: 1,7 => SOL
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* DIS # D3: 7,9 => CTR => D3: 1
* DIS # E4: 7,9 => CTR => E4: 2,4,6
* DIS # E5: 7,9 => CTR => E5: 2,4,6
* DIS # E8: 7,9 => CTR => E8: 6,8
* DIS # H1: 1,5 => CTR => H1: 8
* PRF # H1: 8 => SOL
* DIS # B3: 1,5 => CTR => B3: 7
* DIS # E4: 4,6 => CTR => E4: 2,7,9
* PRF # C6: 1,9 => SOL
* DIS # G5: 4,6 => CTR => G5: 1,8
* DIS # F5: 1,9 => CTR => F5: 7
* PRF # F5: 7 => SOL
* PRF # C6: 1,9 => SOL
* DIS # D8: 7,8 => CTR => D8: 6,9
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # D8: 7,9 => CTR => D8: 6,8
* DIS # E8: 7,9 => CTR => E8: 6,8
* PRF # F5: 7,9 => SOL
* DIS # F5: 1 => CTR => F5: 7,9
* PRF # G8: 7,8 => SOL
* DIS # G8: 1 => CTR => G8: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # I2: 7,8 => SOL
* DIS # G8: 1,8 => CTR => G8: 7
* PRF # G8: 7 => SOL
* DIS # H1: 5 => CTR => H1: 1,8
* CNT  42 HDP CHAINS /  73 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 # C2: 2 => SOL
* STA C2: 2
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

4.62..9......56...8....4........8..3........5.2.....7..9..1.53.23......41.74...6. initial
4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269 autosolve
456273981912856347873194652761528493348967125529341876694712538235689714187435269 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A2: 3,9
B2: 1,7
C3: 2,3
E1: 7,8
E3: 7,9
G3: 3,6
H3: 1,5
I3: 2,6
B4: 4,6
C4: 1,9
B5: 4,6
F6: 1,9
H4: 2,9
H5: 2,9
D7: 7,8
F8: 7,9
I7: 7,8
H8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  0 pairs (X) / D3 = 1  => 19 pairs (_)
F5,F6: 1.. / F5 = 1  =>  0 pairs (X) / F6 = 1  =>  0 pairs (_)
G8,H8: 1.. / G8 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
C4,G4: 1.. / C4 = 1  => 18 pairs (_) / G4 = 1  =>  0 pairs (X)
C2,C3: 2.. / C2 = 2  =>  0 pairs (*) / C3 = 2  =>  0 pairs (X)
I2,I3: 2.. / I2 = 2  => 17 pairs (_) / I3 = 2  =>  0 pairs (*)
E4,E5: 2.. / E4 = 2  => 18 pairs (_) / E5 = 2  => 18 pairs (_)
H4,H5: 2.. / H4 = 2  => 18 pairs (_) / H5 = 2  => 18 pairs (_)
C2,I2: 2.. / C2 = 2  =>  0 pairs (*) / I2 = 2  =>  0 pairs (X)
C3,I3: 2.. / C3 = 2  => 17 pairs (_) / I3 = 2  =>  0 pairs (*)
E4,H4: 2.. / E4 = 2  => 18 pairs (_) / H4 = 2  => 18 pairs (_)
E5,H5: 2.. / E5 = 2  => 18 pairs (_) / H5 = 2  => 18 pairs (_)
G2,G3: 3.. / G2 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
D5,D6: 3.. / D5 = 3  => 19 pairs (_) / D6 = 3  => 19 pairs (_)
C3,G3: 3.. / C3 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
B4,B5: 4.. / B4 = 4  => 17 pairs (_) / B5 = 4  => 17 pairs (_)
E6,G6: 4.. / E6 = 4  => 18 pairs (_) / G6 = 4  => 24 pairs (_)
B1,B3: 5.. / B1 = 5  => 19 pairs (_) / B3 = 5  =>  0 pairs (X)
H1,H3: 5.. / H1 = 5  =>  0 pairs (X) / H3 = 5  => 19 pairs (_)
A4,A6: 5.. / A4 = 5  =>  0 pairs (X) / A6 = 5  => 19 pairs (_)
D4,D6: 5.. / D4 = 5  => 19 pairs (_) / D6 = 5  =>  0 pairs (X)
B1,H1: 5.. / B1 = 5  => 19 pairs (_) / H1 = 5  =>  0 pairs (X)
B3,H3: 5.. / B3 = 5  =>  0 pairs (X) / H3 = 5  => 19 pairs (_)
A4,D4: 5.. / A4 = 5  =>  0 pairs (X) / D4 = 5  => 19 pairs (_)
A6,D6: 5.. / A6 = 5  => 19 pairs (_) / D6 = 5  =>  0 pairs (X)
G3,I3: 6.. / G3 = 6  =>  0 pairs (*) / I3 = 6  =>  0 pairs (X)
B4,B5: 6.. / B4 = 6  => 17 pairs (_) / B5 = 6  => 17 pairs (_)
D8,E8: 6.. / D8 = 6  => 21 pairs (_) / E8 = 6  =>  0 pairs (X)
I3,I6: 6.. / I3 = 6  => 17 pairs (_) / I6 = 6  =>  0 pairs (*)
A4,A5: 7.. / A4 = 7  => 19 pairs (_) / A5 = 7  =>  0 pairs (X)
I7,G8: 7.. / I7 = 7  =>  0 pairs (X) / G8 = 7  =>  0 pairs (_)
D7,I7: 7.. / D7 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
F5,F8: 7.. / F5 = 7  =>  0 pairs (*) / F8 = 7  =>  0 pairs (X)
G2,G8: 7.. / G2 = 7  =>  0 pairs (X) / G8 = 7  =>  0 pairs (_)
E1,D2: 8.. / E1 = 8  =>  0 pairs (X) / D2 = 8  =>  0 pairs (_)
C5,C6: 8.. / C5 = 8  => 18 pairs (_) / C6 = 8  => 23 pairs (_)
C5,G5: 8.. / C5 = 8  => 18 pairs (_) / G5 = 8  => 23 pairs (_)
D7,I7: 8.. / D7 = 8  =>  0 pairs (X) / I7 = 8  =>  0 pairs (_)
E1,E8: 8.. / E1 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
H1,H8: 8.. / H1 = 8  =>  0 pairs (*) / H8 = 8  =>  0 pairs (X)
A2,C2: 9.. / A2 = 9  => 22 pairs (_) / C2 = 9  => 19 pairs (_)
D3,E3: 9.. / D3 = 9  =>  0 pairs (X) / E3 = 9  => 20 pairs (_)
H4,H5: 9.. / H4 = 9  => 18 pairs (_) / H5 = 9  => 18 pairs (_)
* DURATION: 0:00:59.574732  START: 22:54:57.415902  END: 22:55:56.990634 2019-04-30
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B4,B5,C3,C4,D7,E1,E3,F6,F8,G3,H3,H4,H5,H8,I3,I7)
* 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269
* PAIR A2: 3,9 BLK 1
C2: 3,9,2                                # reduction candidate for 3,9
C2: 2 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
C2: 3,9                                  # 17 pairs
* PAIR A2: 3,9 COL A
A5: 3,9,7                                # reduction candidate for 3,9
A5: 3,9                                  # 19 pairs
A6: 3,9,5                                # reduction candidate for 3,9
A6: 3,9 => CTR
* 4.62.39......5674.8....43.65....8..37..3....5.2.5...7.694812537235..7..4187435269
A6: 5                                    # 19 pairs
* PAIR B2: 1,7 BLK 1
B1: 1,7,5                                # reduction candidate for 1,7
B1: 1,7 => CTR
* 416283957....56.4.85...4.1......8..3........5.2.....71694.1253.235...184187435269
B1: 5                                    # 19 pairs
B3: 1,7,5                                # reduction candidate for 1,7
B3: 1,7                                  # 19 pairs
* PAIR B2: 1,7 ROW 2
D2: 1,7,8                                # reduction candidate for 1,7
D2: 1,7 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269
D2: 8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
G2: 1,7,3,8                              # reduction candidate for 1,7
G2: 1,7 => CTR
* 4.62.39.....856.428.2194356.....8..3........5.2.....7.694712538235.89714187435269
G2: 3,8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
I2: 1,7,2,8                              # reduction candidate for 1,7
I2: 1,7 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
I2: 2,8                                  # 19 pairs
* PAIR C3: 2,3 BLK 1
C2: 2,3,9                                # reduction candidate for 2,3
C2: 2,3                                  # 22 pairs
C2: 9                                    # 19 pairs
* PAIR E1: 7,8 BLK 2
D2: 7,8,1                                # reduction candidate for 7,8
D2: 1 => CTR
* 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269
D2: 7,8                                  # 19 pairs
* PAIR E1: 7,8 ROW 1
I1: 7,8,1                                # reduction candidate for 7,8
I1: 7,8 => CTR
* 4.62839.7....56.4.8....4........8..3........5.2.....7.694.1253.235...184187435269
I1: 1 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
* PAIR E1: 7,8 COL E
E8: 7,8,6,9                              # reduction candidate for 7,8
E8: 7,8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
E8: 6,9 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269
* PAIR E3: 7,9 BLK 2
D3: 7,9,1                                # reduction candidate for 7,9
D3: 7,9 => CTR
* 4.62839...7.156.4.8....4........8..3........5.2.....7.694.1253.235...7.4187435269
D3: 1                                    # 19 pairs
* PAIR E3: 7,9 COL E
E4: 7,9,2,4,6                            # reduction candidate for 7,9
E4: 7,9 => CTR
* 476283951....56.4.8....4........8.23....2..95.2..4..7.694812537235.6.184187435269
E4: 2,4,6                                # 20 pairs
E5: 7,9,2,4,6                            # reduction candidate for 7,9
E5: 7,9 => CTR
* 476283951....56.4.8....4.....1.28.93.......25.2..4..7.694812537235.6.184187435269
E5: 2,4,6                                # 18 pairs
E8: 7,9,6,8                              # reduction candidate for 7,9
E8: 7,9 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.6948125372356..184187435269
E8: 6,8                                  # 19 pairs
* PAIR H3: 1,5 BLK 3
H1: 1,5,8                                # reduction candidate for 1,5
H1: 1,5 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269
H1: 8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
* PAIR H3: 1,5 ROW 3
B3: 1,5,7                                # reduction candidate for 1,5
B3: 1,5 => CTR
* 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269
B3: 7                                    # 19 pairs
* PAIR B4: 4,6 ROW 4
E4: 4,6,2,7,9                            # reduction candidate for 4,6
E4: 4,6 => CTR
* 45627398191.8563478731946527.95.81233..62..95.2.....7.694712538235.89714187435269
E4: 2,7,9                                # 18 pairs
G4: 4,6,1                                # reduction candidate for 4,6
G4: 4,6                                  # 18 pairs
* PAIR C4: 1,9 BLK 4
C5: 1,9,3,8                              # reduction candidate for 1,9
C5: 1,9                                  # 26 pairs
C6: 1,9,3,8                              # reduction candidate for 1,9
C6: 1,9 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
C6: 3,8                                  # 19 pairs
* PAIR B5: 4,6 ROW 5
E5: 4,6,2,7,9                            # reduction candidate for 4,6
E5: 4,6                                  # 20 pairs
G5: 4,6,1,8                              # reduction candidate for 4,6
G5: 4,6 => CTR
* 4.62.39......5674.8....43.6.....8..3..8..1..5.2...9.7.694812537235..7..4187435269
G5: 1,8                                  # 19 pairs
* PAIR F6: 1,9 BLK 5
F5: 1,9,7                                # reduction candidate for 1,9
F5: 1,9 => CTR
* 4.62.39......5674.8....43.6.....8..3........5.2.....7.694812537235..7..4187435269
F5: 7 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
* PAIR F6: 1,9 ROW 6
C6: 1,9,3,8                              # reduction candidate for 1,9
C6: 1,9 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
C6: 3,8                                  # 19 pairs
* PAIR H4: 2,9 ROW 4
E4: 2,9,4,6,7                            # reduction candidate for 2,9
E4: 2,9                                  # 21 pairs
E4: 4,6,7                                # 18 pairs
* PAIR H5: 2,9 ROW 5
E5: 2,9,4,6,7                            # reduction candidate for 2,9
E5: 2,9                                  # 21 pairs
E5: 4,6,7                                # 18 pairs
* PAIR D7: 7,8 BLK 8
D8: 7,8,6,9                              # reduction candidate for 7,8
D8: 7,8 => CTR
* 4.62839......56.4.8...74...7..5.8..3.....7..552...1.7.694812537235769184187435269
D8: 6,9                                  # 19 pairs
E8: 7,8,6,9                              # reduction candidate for 7,8
E8: 7,8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
E8: 6,9 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.694812537235...184187435269
* PAIR D7: 7,8 COL D
D2: 7,8,1                                # reduction candidate for 7,8
D2: 1 => CTR
* 4.62839...7.156.4.8....4........8..3........5.2.....7.694812537235....84187435269
D2: 7,8                                  # 19 pairs
* PAIR F8: 7,9 BLK 8
D8: 7,9,6,8                              # reduction candidate for 7,9
D8: 7,9 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.694812537235.6..84187435269
D8: 6,8                                  # 19 pairs
E8: 7,9,6,8                              # reduction candidate for 7,9
E8: 7,9 => CTR
* 476283951....56.4.8....4........8..3........5.2.....7.6948125372356..184187435269
E8: 6,8                                  # 19 pairs
* PAIR F8: 7,9 COL F
F5: 7,9,1                                # reduction candidate for 7,9
F5: 7,9 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
F5: 1 => CTR
* 4.62.39......5674.8....43.6.....8..3.....1..5.2...9.7.694812537235..7..4187435269
* PAIR I7: 7,8 BLK 9
G8: 7,8,1                                # reduction candidate for 7,8
G8: 7,8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
G8: 1 => CTR
* 4.62839.1....5674.8....43.6.....8..3........5.2.....7.694.12537235...184187435269
* PAIR I7: 7,8 COL I
I1: 7,8,1                                # reduction candidate for 7,8
I1: 7,8 => CTR
* 4.62839.7....56.4.8....4........8..3........5.2.....7.694.1253.235...184187435269
I1: 1 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
I2: 7,8,1,2                              # reduction candidate for 7,8
I2: 7,8 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
I2: 1,2                                  # 19 pairs
* PAIR H8: 1,8 BLK 9
G8: 1,8,7                                # reduction candidate for 1,8
G8: 1,8 => CTR
* 4.62.39...1.85674.8....43.6.....8..3........5.2.....7.694.12537235.....4187435269
G8: 7 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
* PAIR H8: 1,8 COL H
H1: 1,8,5                                # reduction candidate for 1,8
H1: 5 => CTR
* 416283957....56.4.85...4.1......8..3........5.2.....71694.1253.235...184187435269
H1: 1,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060505-absurd-base-pr-000.dot
* REASONING
* PRF # C2: 2 => SOL
* DIS # A6: 3,9 => CTR => A6: 5
* DIS # B1: 1,7 => CTR => B1: 5
* DIS # D2: 1,7 => CTR => D2: 8
* PRF # D2: 8 => SOL
* DIS # G2: 1,7 => CTR => G2: 3,8
* PRF # G2: 3,8 => SOL
* PRF # I2: 1,7 => SOL
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* DIS # D3: 7,9 => CTR => D3: 1
* DIS # E4: 7,9 => CTR => E4: 2,4,6
* DIS # E5: 7,9 => CTR => E5: 2,4,6
* DIS # E8: 7,9 => CTR => E8: 6,8
* DIS # H1: 1,5 => CTR => H1: 8
* PRF # H1: 8 => SOL
* DIS # B3: 1,5 => CTR => B3: 7
* DIS # E4: 4,6 => CTR => E4: 2,7,9
* PRF # C6: 1,9 => SOL
* DIS # G5: 4,6 => CTR => G5: 1,8
* DIS # F5: 1,9 => CTR => F5: 7
* PRF # F5: 7 => SOL
* PRF # C6: 1,9 => SOL
* DIS # D8: 7,8 => CTR => D8: 6,9
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # D8: 7,9 => CTR => D8: 6,8
* DIS # E8: 7,9 => CTR => E8: 6,8
* PRF # F5: 7,9 => SOL
* DIS # F5: 1 => CTR => F5: 7,9
* PRF # G8: 7,8 => SOL
* DIS # G8: 1 => CTR => G8: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # I2: 7,8 => SOL
* DIS # G8: 1,8 => CTR => G8: 7
* PRF # G8: 7 => SOL
* DIS # H1: 5 => CTR => H1: 1,8
* CNT  42 HDP CHAINS /  73 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B2,B4,B5,C3,C4,D7,E1,E3,F6,F8,G3,H3,H4,H5,H8,I3,I7)
* 4.62.39......56.4.8....4........8..3........5.2.....7.694.1253.235.....4187435269
* PAIR A2: 3,9 BLK 1
C2: 3,9,2                                # reduction candidate for 3,9
C2: 2 => SOLVED
* 456273981912856347873194652761528493348967125529341876694712538235689714187435269
* DURATION: 0:00:02.598470  START: 22:56:56.057284  END: 22:56:58.655754 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060505-absurd-base-pr-001.dot
* REASONING
* PRF # C2: 2 => SOL
* STA C2: 2
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060505, absurd

Solution

position: 456273981912856347873194652761528493348967125529341876694712538235689714187435269 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 # C2: 3,9 => UNS
* PRF # C2: 2 => SOL
* INC # A5: 3,9 => UNS
* DIS # A6: 3,9 => CTR => A6: 5
* INC # A6: 5 => UNS
* DIS # B1: 1,7 => CTR => B1: 5
* INC # B1: 5 => UNS
* INC # B3: 1,7 => UNS
* DIS # D2: 1,7 => CTR => D2: 8
* PRF # D2: 8 => SOL
* DIS # G2: 1,7 => CTR => G2: 3,8
* PRF # G2: 3,8 => SOL
* PRF # I2: 1,7 => SOL
* INC # I2: 2,8 => UNS
* INC # C2: 2,3 => UNS
* INC # C2: 9 => UNS
* INC # D2: 7,8 => UNS
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* DIS # D3: 7,9 => CTR => D3: 1
* INC # D3: 1 => UNS
* DIS # E4: 7,9 => CTR => E4: 2,4,6
* INC # E4: 2,4,6 => UNS
* DIS # E5: 7,9 => CTR => E5: 2,4,6
* INC # E5: 2,4,6 => UNS
* DIS # E8: 7,9 => CTR => E8: 6,8
* INC # E8: 6,8 => UNS
* DIS # H1: 1,5 => CTR => H1: 8
* PRF # H1: 8 => SOL
* DIS # B3: 1,5 => CTR => B3: 7
* INC # B3: 7 => UNS
* DIS # E4: 4,6 => CTR => E4: 2,7,9
* INC # E4: 2,7,9 => UNS
* INC # G4: 4,6 => UNS
* INC # C5: 1,9 => UNS
* PRF # C6: 1,9 => SOL
* INC # C6: 3,8 => UNS
* INC # E5: 4,6 => UNS
* DIS # G5: 4,6 => CTR => G5: 1,8
* INC # G5: 1,8 => UNS
* DIS # F5: 1,9 => CTR => F5: 7
* PRF # F5: 7 => SOL
* PRF # C6: 1,9 => SOL
* INC # C6: 3,8 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 4,6,7 => UNS
* INC # E5: 2,9 => UNS
* INC # E5: 4,6,7 => UNS
* DIS # D8: 7,8 => CTR => D8: 6,9
* INC # D8: 6,9 => UNS
* PRF # E8: 7,8 => SOL
* DIS # E8: 6,9 => CTR => E8: 7,8
* INC # D2: 7,8 => UNS
* DIS # D2: 1 => CTR => D2: 7,8
* DIS # D8: 7,9 => CTR => D8: 6,8
* INC # D8: 6,8 => UNS
* DIS # E8: 7,9 => CTR => E8: 6,8
* INC # E8: 6,8 => UNS
* PRF # F5: 7,9 => SOL
* DIS # F5: 1 => CTR => F5: 7,9
* PRF # G8: 7,8 => SOL
* DIS # G8: 1 => CTR => G8: 7,8
* DIS # I1: 7,8 => CTR => I1: 1
* PRF # I1: 1 => SOL
* PRF # I2: 7,8 => SOL
* INC # I2: 1,2 => UNS
* DIS # G8: 1,8 => CTR => G8: 7
* PRF # G8: 7 => SOL
* INC # H1: 1,8 => UNS
* DIS # H1: 5 => CTR => H1: 1,8
* CNT  73 HDP CHAINS /  73 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 3,9 => UNS
* PRF # C2: 2 => SOL
* STA C2: 2
* CNT   2 HDP CHAINS /   2 HYP OPENED