Analysis of zz-www.sudokuoftheday.co.uk-20060907-absurd-base.sdk

Contents

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

level: medium

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

position: .1.2....5.2.49.1...4.....7.9...8....354.........9......9.5....77.....5.8...1.89.2 initial

Autosolve

position: .1.2....5.2.49.1...4.8..27.97..8....3547......869..7...985....77....95.84.51789.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 6,8 => CTR => G1: 3,4
* DIS # F4: 1,2 => CTR => F4: 4,5
* PRF # E6: 1,2 => SOL
* DIS # F6: 1,2 => CTR => F6: 3,4,5
* DIS # H6: 3 => CTR => H6: 2,5
* PRF # I6: 3 => SOL
* DIS # H5: 6,8 => CTR => H5: 2,9
* DIS # G1: 6,8 => CTR => G1: 3,4
* CNT   8 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 # G1: 6,8 => CTR => G1: 3,4
* DIS G1: 3,4 # F4: 1,2 => CTR => F4: 4,5
* PRF G1: 3,4 + F4: 4,5 # E6: 1,2 => SOL
* STA G1: 3,4 + F4: 4,5 + E6: 1,2
* CNT   3 HDP CHAINS /  37 HYP OPENED

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

Details

Positions

.1.2....5.2.49.1...4.....7.9...8....354.........9......9.5....77.....5.8...1.89.2 initial
.1.2....5.2.49.1...4.8..27.97..8....3547......869..7...985....77....95.84.51789.2 autosolve
819267345527493186643851279971385624354726891286914753198532467732649518465178932 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
A1: 6,8
C2: 3,7
A3: 5,6
C3: 3,9
E1: 3,6
I2: 3,6
C4: 1,2
A6: 1,2
D4: 3,6
G4: 3,6
H4: 2,5
I4: 1,4
G5: 6,8
A7: 1,2
B8: 3,6
C8: 1,2
B9: 3,6
D8: 3,6
E8: 2,4
H8: 1,4
H9: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E3,F3: 1.. / E3 = 1  => 22 pairs (_) / F3 = 1  => 22 pairs (_)
C4,A6: 1.. / C4 = 1  => 17 pairs (_) / A6 = 1  => 18 pairs (_)
A7,C8: 1.. / A7 = 1  => 17 pairs (_) / C8 = 1  => 18 pairs (_)
H7,H8: 1.. / H7 = 1  => 18 pairs (_) / H8 = 1  => 17 pairs (_)
A7,H7: 1.. / A7 = 1  => 17 pairs (_) / H7 = 1  => 18 pairs (_)
C8,H8: 1.. / C8 = 1  => 18 pairs (_) / H8 = 1  => 17 pairs (_)
A6,A7: 1.. / A6 = 1  => 18 pairs (_) / A7 = 1  => 17 pairs (_)
C4,C8: 1.. / C4 = 1  => 17 pairs (_) / C8 = 1  => 18 pairs (_)
C4,A6: 2.. / C4 = 2  => 18 pairs (_) / A6 = 2  => 17 pairs (_)
A7,C8: 2.. / A7 = 2  => 18 pairs (_) / C8 = 2  => 17 pairs (_)
C8,E8: 2.. / C8 = 2  => 17 pairs (_) / E8 = 2  => 18 pairs (_)
A6,A7: 2.. / A6 = 2  => 17 pairs (_) / A7 = 2  => 18 pairs (_)
C4,C8: 2.. / C4 = 2  => 18 pairs (_) / C8 = 2  => 17 pairs (_)
B8,B9: 3.. / B8 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
D4,G4: 3.. / D4 = 3  =>  0 pairs (*) / G4 = 3  =>  0 pairs (X)
B8,D8: 3.. / B8 = 3  =>  0 pairs (*) / D8 = 3  =>  0 pairs (X)
B9,H9: 3.. / B9 = 3  =>  0 pairs (X) / H9 = 3  =>  0 pairs (_)
D4,D8: 3.. / D4 = 3  =>  0 pairs (*) / D8 = 3  =>  0 pairs (X)
G1,H1: 4.. / G1 = 4  => 22 pairs (_) / H1 = 4  => 15 pairs (_)
I4,I6: 4.. / I4 = 4  => 21 pairs (_) / I6 = 4  => 19 pairs (_)
F4,I4: 4.. / F4 = 4  => 19 pairs (_) / I4 = 4  => 21 pairs (_)
E8,H8: 4.. / E8 = 4  => 17 pairs (_) / H8 = 4  => 18 pairs (_)
G1,G7: 4.. / G1 = 4  => 22 pairs (_) / G7 = 4  => 15 pairs (_)
A2,A3: 5.. / A2 = 5  => 21 pairs (_) / A3 = 5  => 22 pairs (_)
H4,H6: 5.. / H4 = 5  => 21 pairs (_) / H6 = 5  => 15 pairs (_)
A2,F2: 5.. / A2 = 5  => 21 pairs (_) / F2 = 5  => 22 pairs (_)
F4,H4: 5.. / F4 = 5  => 15 pairs (_) / H4 = 5  => 21 pairs (_)
E3,E6: 5.. / E3 = 5  => 20 pairs (_) / E6 = 5  => 21 pairs (_)
B8,B9: 6.. / B8 = 6  =>  0 pairs (X) / B9 = 6  =>  0 pairs (_)
D4,G4: 6.. / D4 = 6  =>  0 pairs (X) / G4 = 6  =>  0 pairs (_)
B8,D8: 6.. / B8 = 6  =>  0 pairs (X) / D8 = 6  =>  0 pairs (_)
B9,H9: 6.. / B9 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
D4,D8: 6.. / D4 = 6  =>  0 pairs (X) / D8 = 6  =>  0 pairs (_)
C1,C2: 7.. / C1 = 7  => 22 pairs (_) / C2 = 7  => 21 pairs (_)
F1,F2: 7.. / F1 = 7  => 21 pairs (_) / F2 = 7  => 22 pairs (_)
C1,F1: 7.. / C1 = 7  => 22 pairs (_) / F1 = 7  => 21 pairs (_)
C2,F2: 7.. / C2 = 7  => 21 pairs (_) / F2 = 7  => 22 pairs (_)
A1,A2: 8.. / A1 = 8  => 20 pairs (_) / A2 = 8  => 18 pairs (_)
G5,H5: 8.. / G5 = 8  => 20 pairs (_) / H5 = 8  =>  0 pairs (X)
A2,H2: 8.. / A2 = 8  => 18 pairs (_) / H2 = 8  => 20 pairs (_)
G1,G5: 8.. / G1 = 8  =>  0 pairs (X) / G5 = 8  => 20 pairs (_)
C1,C3: 9.. / C1 = 9  => 20 pairs (_) / C3 = 9  => 25 pairs (_)
H1,I3: 9.. / H1 = 9  => 25 pairs (_) / I3 = 9  => 20 pairs (_)
H5,I5: 9.. / H5 = 9  => 20 pairs (_) / I5 = 9  => 25 pairs (_)
C1,H1: 9.. / C1 = 9  => 20 pairs (_) / H1 = 9  => 25 pairs (_)
C3,I3: 9.. / C3 = 9  => 25 pairs (_) / I3 = 9  => 20 pairs (_)
H1,H5: 9.. / H1 = 9  => 25 pairs (_) / H5 = 9  => 20 pairs (_)
I3,I5: 9.. / I3 = 9  => 20 pairs (_) / I5 = 9  => 25 pairs (_)
* DURATION: 0:01:12.185766  START: 02:25:43.885012  END: 02:26:56.070778 2019-05-01
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A7,B8,B9,C2,C3,C4,C8,D4,D8,E1,E8,G4,G5,H4,H8,H9,I2,I4)
* .1.2....5.2.49.1...4.8..27.97..8....3547......869..7...985....77....95.84.51789.2
* PAIR A1: 6,8 BLK 1
A2: 6,8,5                                # reduction candidate for 6,8
A2: 6,8                                  # 22 pairs
A2: 5                                    # 21 pairs
* PAIR A1: 6,8 ROW 1
G1: 6,8,3,4                              # reduction candidate for 6,8
G1: 6,8 => CTR
* .192.7.45.2749.183.438..279971.8.3.43547..8962869.47511985.34677326495184.51789.2
G1: 3,4                                  # 21 pairs
H1: 6,8,3,4,9                            # reduction candidate for 6,8
H1: 6,8                                  # 23 pairs
* PAIR C2: 3,7 BLK 1
C1: 3,7,9                                # reduction candidate for 3,7
C1: 3,7                                  # 25 pairs
C1: 9                                    # 20 pairs
* PAIR C2: 3,7 ROW 2
F2: 3,7,5,6                              # reduction candidate for 3,7
F2: 5,6                                  # 23 pairs
F2: 3,7                                  # 23 pairs
* PAIR A3: 5,6 BLK 1
A2: 5,6,8                                # reduction candidate for 5,6
A2: 5,6                                  # 20 pairs
A2: 8                                    # 18 pairs
* PAIR A3: 5,6 ROW 3
E3: 5,6,1,3                              # reduction candidate for 5,6
E3: 5,6                                  # 24 pairs
F3: 5,6,1,3                              # reduction candidate for 5,6
F3: 5,6                                  # 24 pairs
* PAIR C3: 3,9 BLK 1
C1: 3,9,7                                # reduction candidate for 3,9
C1: 7                                    # 22 pairs
C1: 3,9                                  # 21 pairs
* PAIR C3: 3,9 ROW 3
I3: 3,9,6                                # reduction candidate for 3,9
I3: 6                                    # 22 pairs
I3: 3,9                                  # 22 pairs
* PAIR E1: 3,6 BLK 2
F1: 3,6,7                                # reduction candidate for 3,6
F1: 3,6                                  # 22 pairs
F2: 3,6,5,7                              # reduction candidate for 3,6
F2: 3,6                                  # 22 pairs
E3: 3,6,1,5                              # reduction candidate for 3,6
E3: 3,6                                  # 29 pairs
F3: 3,6,1,5                              # reduction candidate for 3,6
F3: 3,6                                  # 24 pairs
* PAIR E1: 3,6 ROW 1
G1: 3,6,4,8                              # reduction candidate for 3,6
G1: 3,6                                  # 15 pairs
H1: 3,6,4,8,9                            # reduction candidate for 3,6
H1: 3,6                                  # 23 pairs
* PAIR E1: 3,6 COL E
E7: 3,6,2,4                              # reduction candidate for 3,6
E7: 3,6                                  # 25 pairs
E7: 2,4                                  # 24 pairs
* PAIR I2: 3,6 BLK 3
G1: 3,6,4,8                              # reduction candidate for 3,6
G1: 3,6                                  # 15 pairs
H1: 3,6,4,8,9                            # reduction candidate for 3,6
H1: 3,6                                  # 23 pairs
H2: 3,6,8                                # reduction candidate for 3,6
H2: 3,6                                  # 18 pairs
I3: 3,6,9                                # reduction candidate for 3,6
I3: 3,6                                  # 25 pairs
* PAIR I2: 3,6 ROW 2
F2: 3,6,5,7                              # reduction candidate for 3,6
F2: 5,7                                  # 22 pairs
F2: 3,6                                  # 22 pairs
* PAIR C4: 1,2 ROW 4
F4: 1,2,4,5                              # reduction candidate for 1,2
F4: 1,2 => CTR
* .1.2..345.2.49.186.4.8..27997.38.6543547..8911869..72..985....773.6.95.8465178932
F4: 4,5                                  # 22 pairs
* PAIR A6: 1,2 ROW 6
E6: 1,2,3,4,5                            # reduction candidate for 1,2
E6: 1,2 => SOLVED
* 819267345527493186643851279971385624354726891286914753198532467732649518465178932
E6: 3,4,5                                # 21 pairs
F6: 1,2,3,4,5                            # reduction candidate for 1,2
F6: 1,2 => CTR
* .1.2..345.2.49.186.4.8..27997.38.6..3547..891.869.17531985..4677326495.8465178932
F6: 3,4,5                                # 21 pairs
* PAIR G4: 3,6 COL G
G1: 3,6,4,8                              # reduction candidate for 3,6
G1: 3,6                                  # 15 pairs
G7: 3,6,4                                # reduction candidate for 3,6
G7: 3,6                                  # 22 pairs
* PAIR H4: 2,5 BLK 6
H6: 2,5,3                                # reduction candidate for 2,5
H6: 3 => CTR
* .1.2....5.2.49.1...4.8..27.97..8..5.3547...29.869..73..985..3.77..3.95.8435178962
H6: 2,5                                  # 22 pairs
* PAIR H4: 2,5 ROW 4
F4: 2,5,1,4                              # reduction candidate for 2,5
F4: 1,4                                  # 18 pairs
F4: 2,5                                  # 17 pairs
* PAIR I4: 1,4 BLK 6
I6: 1,4,3                                # reduction candidate for 1,4
I6: 3 => SOLVED
* 819267345527493186643851279971385624354726891286914753198532467732649518465178932
I6: 1,4                                  # 24 pairs
* PAIR I4: 1,4 ROW 4
F4: 1,4,2,5                              # reduction candidate for 1,4
F4: 1,4                                  # 18 pairs
F4: 2,5                                  # 17 pairs
* PAIR G5: 6,8 BLK 6
H5: 6,8,2,9                              # reduction candidate for 6,8
H5: 6,8 => CTR
* .1.2..495.2.49.18..498..27.97..8....3547..869.869..7...985..6.77..6.95.8465178932
H5: 2,9                                  # 21 pairs
* PAIR G5: 6,8 COL G
G1: 6,8,3,4                              # reduction candidate for 6,8
G1: 6,8 => CTR
* .192.7.45.2749.183.438..279971.8.3.43547..8962869.47511985.34677326495184.51789.2
G1: 3,4                                  # 21 pairs
* PAIR D8: 3,6 BLK 8
E7: 3,6,2,4                              # reduction candidate for 3,6
E7: 3,6                                  # 25 pairs
F7: 3,6,2,4                              # reduction candidate for 3,6
F7: 3,6                                  # 24 pairs
* PAIR E8: 2,4 BLK 8
E7: 2,4,3,6                              # reduction candidate for 2,4
E7: 2,4                                  # 24 pairs
F7: 2,4,3,6                              # reduction candidate for 2,4
F7: 2,4                                  # 25 pairs
* PAIR E8: 2,4 COL E
E6: 2,4,1,3,5                            # reduction candidate for 2,4
E6: 2,4                                  # 28 pairs
E6: 1,3,5                                # 21 pairs
* PAIR H8: 1,4 BLK 9
H7: 1,4,3,6                              # reduction candidate for 1,4
H7: 1,4                                  # 22 pairs
H7: 3,6                                  # 15 pairs
* PAIR H9: 3,6 BLK 9
G7: 3,6,4                                # reduction candidate for 3,6
G7: 3,6                                  # 22 pairs
H7: 3,6,1,4                              # reduction candidate for 3,6
H7: 3,6                                  # 15 pairs
* PAIR H9: 3,6 COL H
H1: 3,6,4,8,9                            # reduction candidate for 3,6
H1: 3,6                                  # 23 pairs
H2: 3,6,8                                # reduction candidate for 3,6
H2: 3,6                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060907-absurd-base-pr-000.dot
* REASONING
* DIS # G1: 6,8 => CTR => G1: 3,4
* DIS # F4: 1,2 => CTR => F4: 4,5
* PRF # E6: 1,2 => SOL
* DIS # F6: 1,2 => CTR => F6: 3,4,5
* DIS # H6: 3 => CTR => H6: 2,5
* PRF # I6: 3 => SOL
* DIS # H5: 6,8 => CTR => H5: 2,9
* DIS # G1: 6,8 => CTR => G1: 3,4
* CNT   8 HDP CHAINS /  63 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,A7,B8,B9,C2,C3,C4,C8,D4,D8,E1,E8,G4,G5,H4,H8,H9,I2,I4)
* .1.2....5.2.49.1...4.8..27.97..8....3547......869..7...985....77....95.84.51789.2
* PAIR A1: 6,8 BLK 1
A2: 6,8,5                                # reduction candidate for 6,8
A2: 6,8                                  # 22 pairs
A2: 5                                    # 21 pairs
* PAIR A1: 6,8 ROW 1
G1: 6,8,3,4                              # reduction candidate for 6,8
G1: 6,8 => CTR
* .192.7.45.2749.183.438..279971.8.3.43547..8962869.47511985.34677326495184.51789.2
H1: 6,8,3,4,9                            # reduction candidate for 6,8
H1: 6,8                                  # 23 pairs
* RESTART
* PAIR A1: 6,8 ROW 1
H1: 6,8,3,4,9                            # reduction candidate for 6,8
H1: 6,8                                  # 23 pairs
H1: 3,4,9                                # 22 pairs
* PAIR RESTART
* PAIR A1: 6,8 BLK 1
A2: 6,8,5                                # reduction candidate for 6,8
A2: 6,8                                  # 23 pairs
A2: 5                                    # 22 pairs
* PAIR A1: 6,8 ROW 1
H1: 6,8,3,4,9                            # reduction candidate for 6,8
H1: 6,8                                  # 23 pairs
H1: 3,4,9                                # 22 pairs
* PAIR C2: 3,7 BLK 1
C1: 3,7,9                                # reduction candidate for 3,7
C1: 3,7                                  # 25 pairs
C1: 9                                    # 21 pairs
* PAIR C2: 3,7 ROW 2
F2: 3,7,5,6                              # reduction candidate for 3,7
F2: 5,6                                  # 24 pairs
F2: 3,7                                  # 23 pairs
* PAIR A3: 5,6 BLK 1
A2: 5,6,8                                # reduction candidate for 5,6
A2: 5,6                                  # 21 pairs
A2: 8                                    # 18 pairs
* PAIR A3: 5,6 ROW 3
E3: 5,6,1,3                              # reduction candidate for 5,6
E3: 5,6                                  # 24 pairs
F3: 5,6,1,3                              # reduction candidate for 5,6
F3: 5,6                                  # 24 pairs
* PAIR C3: 3,9 BLK 1
C1: 3,9,7                                # reduction candidate for 3,9
C1: 7                                    # 22 pairs
C1: 3,9                                  # 21 pairs
* PAIR C3: 3,9 ROW 3
I3: 3,9,6                                # reduction candidate for 3,9
I3: 6                                    # 22 pairs
I3: 3,9                                  # 22 pairs
* PAIR E1: 3,6 BLK 2
F1: 3,6,7                                # reduction candidate for 3,6
F1: 3,6                                  # 22 pairs
F2: 3,6,5,7                              # reduction candidate for 3,6
F2: 3,6                                  # 23 pairs
E3: 3,6,1,5                              # reduction candidate for 3,6
E3: 3,6                                  # 30 pairs
F3: 3,6,1,5                              # reduction candidate for 3,6
F3: 3,6                                  # 25 pairs
* PAIR E1: 3,6 ROW 1
H1: 3,6,4,8,9                            # reduction candidate for 3,6
H1: 3,6                                  # 23 pairs
H1: 4,8,9                                # 21 pairs
* PAIR E1: 3,6 COL E
E7: 3,6,2,4                              # reduction candidate for 3,6
E7: 3,6                                  # 25 pairs
E7: 2,4                                  # 24 pairs
* PAIR I2: 3,6 BLK 3
H1: 3,6,4,8,9                            # reduction candidate for 3,6
H1: 3,6                                  # 23 pairs
H2: 3,6,8                                # reduction candidate for 3,6
H2: 3,6                                  # 18 pairs
I3: 3,6,9                                # reduction candidate for 3,6
I3: 3,6                                  # 25 pairs
* PAIR I2: 3,6 ROW 2
F2: 3,6,5,7                              # reduction candidate for 3,6
F2: 3,6                                  # 23 pairs
F2: 5,7                                  # 22 pairs
* PAIR C4: 1,2 ROW 4
F4: 1,2,4,5                              # reduction candidate for 1,2
F4: 1,2 => CTR
* .1.2..345.2.49.186.4.8..27997.38.6543547..8911869..72..985....773.6.95.8465178932
* PAIR RESTART
* PAIR A6: 1,2 ROW 6
E6: 1,2,3,4,5                            # reduction candidate for 1,2
E6: 1,2 => SOLVED
* 819267345527493186643851279971385624354726891286914753198532467732649518465178932
* DURATION: 0:00:31.927920  START: 02:27:47.147721  END: 02:28:19.075641 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060907-absurd-base-pr-001.dot
* REASONING
* DIS # G1: 6,8 => CTR => G1: 3,4
* DIS G1: 3,4 # F4: 1,2 => CTR => F4: 4,5
* PRF G1: 3,4 + F4: 4,5 # E6: 1,2 => SOL
* STA G1: 3,4 + F4: 4,5 + E6: 1,2
* CNT   3 HDP CHAINS /  37 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060907, absurd

Solution

position: 819267345527493186643851279971385624354726891286914753198532467732649518465178932 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 # A2: 6,8 => UNS
* INC # A2: 5 => UNS
* DIS # G1: 6,8 => CTR => G1: 3,4
* INC # G1: 3,4 => UNS
* INC # H1: 6,8 => UNS
* INC # C1: 3,7 => UNS
* INC # C1: 9 => UNS
* INC # F2: 3,7 => UNS
* INC # F2: 5,6 => UNS
* INC # A2: 5,6 => UNS
* INC # A2: 8 => UNS
* INC # E3: 5,6 => UNS
* INC # F3: 5,6 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 7 => UNS
* INC # I3: 3,9 => UNS
* INC # I3: 6 => UNS
* INC # F1: 3,6 => UNS
* INC # F2: 3,6 => UNS
* INC # E3: 3,6 => UNS
* INC # F3: 3,6 => UNS
* INC # G1: 3,6 => UNS
* INC # H1: 3,6 => UNS
* INC # E7: 3,6 => UNS
* INC # E7: 2,4 => UNS
* INC # G1: 3,6 => UNS
* INC # H1: 3,6 => UNS
* INC # H2: 3,6 => UNS
* INC # I3: 3,6 => UNS
* INC # F2: 3,6 => UNS
* INC # F2: 5,7 => UNS
* DIS # F4: 1,2 => CTR => F4: 4,5
* INC # F4: 4,5 => UNS
* PRF # E6: 1,2 => SOL
* INC # E6: 3,4,5 => UNS
* DIS # F6: 1,2 => CTR => F6: 3,4,5
* INC # F6: 3,4,5 => UNS
* INC # G1: 3,6 => UNS
* INC # G7: 3,6 => UNS
* INC # H6: 2,5 => UNS
* DIS # H6: 3 => CTR => H6: 2,5
* INC # F4: 2,5 => UNS
* INC # F4: 1,4 => UNS
* INC # I6: 1,4 => UNS
* PRF # I6: 3 => SOL
* INC # F4: 1,4 => UNS
* INC # F4: 2,5 => UNS
* DIS # H5: 6,8 => CTR => H5: 2,9
* INC # H5: 2,9 => UNS
* DIS # G1: 6,8 => CTR => G1: 3,4
* INC # G1: 3,4 => UNS
* INC # E7: 3,6 => UNS
* INC # F7: 3,6 => UNS
* INC # E7: 2,4 => UNS
* INC # F7: 2,4 => UNS
* INC # E6: 2,4 => UNS
* INC # E6: 1,3,5 => UNS
* INC # H7: 1,4 => UNS
* INC # H7: 3,6 => UNS
* INC # G7: 3,6 => UNS
* INC # H7: 3,6 => UNS
* INC # H1: 3,6 => UNS
* INC # H2: 3,6 => UNS
* CNT  63 HDP CHAINS /  63 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 6,8 => UNS
* INC # A2: 5 => UNS
* DIS # G1: 6,8 => CTR => G1: 3,4
* INC G1: 3,4 # H1: 6,8 => UNS
* INC G1: 3,4 # H1: 6,8 => UNS
* INC G1: 3,4 # H1: 3,4,9 => UNS
* INC G1: 3,4 # A2: 6,8 => UNS
* INC G1: 3,4 # A2: 5 => UNS
* INC G1: 3,4 # H1: 6,8 => UNS
* INC G1: 3,4 # H1: 3,4,9 => UNS
* INC G1: 3,4 # C1: 3,7 => UNS
* INC G1: 3,4 # C1: 9 => UNS
* INC G1: 3,4 # F2: 3,7 => UNS
* INC G1: 3,4 # F2: 5,6 => UNS
* INC G1: 3,4 # A2: 5,6 => UNS
* INC G1: 3,4 # A2: 8 => UNS
* INC G1: 3,4 # E3: 5,6 => UNS
* INC G1: 3,4 # F3: 5,6 => UNS
* INC G1: 3,4 # C1: 3,9 => UNS
* INC G1: 3,4 # C1: 7 => UNS
* INC G1: 3,4 # I3: 3,9 => UNS
* INC G1: 3,4 # I3: 6 => UNS
* INC G1: 3,4 # F1: 3,6 => UNS
* INC G1: 3,4 # F2: 3,6 => UNS
* INC G1: 3,4 # E3: 3,6 => UNS
* INC G1: 3,4 # F3: 3,6 => UNS
* INC G1: 3,4 # H1: 3,6 => UNS
* INC G1: 3,4 # H1: 4,8,9 => UNS
* INC G1: 3,4 # E7: 3,6 => UNS
* INC G1: 3,4 # E7: 2,4 => UNS
* INC G1: 3,4 # H1: 3,6 => UNS
* INC G1: 3,4 # H2: 3,6 => UNS
* INC G1: 3,4 # I3: 3,6 => UNS
* INC G1: 3,4 # F2: 3,6 => UNS
* INC G1: 3,4 # F2: 5,7 => UNS
* DIS G1: 3,4 # F4: 1,2 => CTR => F4: 4,5
* PRF G1: 3,4 + F4: 4,5 # E6: 1,2 => SOL
* STA G1: 3,4 + F4: 4,5 + E6: 1,2
* CNT  37 HDP CHAINS /  37 HYP OPENED