Analysis of zz-www.sudokuoftheday.co.uk-20060409-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: 1...67.4.5..........3158...9....5...........1.8.9.4..........6...2.7..18.6..4.93. initial

Autosolve

position: 1...67.4.5..4..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I1: 2,9 => CTR => I1: 3,5
* DIS # A3: 2,7 => CTR => A3: 4,6
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # B5: 2,7 => CTR => B5: 3,4,5
* DIS # E2: 2,3 => CTR => E2: 9
* DIS # I1: 2,3 => CTR => I1: 5,9
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # I3: 2,7 => CTR => I3: 6,9
* DIS # A3: 2,7 => CTR => A3: 4,6
* DIS # H4: 8 => CTR => H4: 2,7
* CNT  10 HDP CHAINS /  46 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 # I1: 2,9 => CTR => I1: 3,5
* DIS I1: 3,5 # A3: 2,7 => CTR => A3: 4,6
* DIS I1: 3,5 + A3: 4,6 # H2: 2,7 => CTR => H2: 8
* DIS I1: 3,5 + A3: 4,6 + H2: 8 # G1: 5 => CTR => G1: 2,3
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 # D7: 2,3 => CTR => D7: 5,8
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B8: 5 => CTR => B8: 3,4
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 # F7: 3 => CTR => F7: 1,2
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 2 => CTR => I2: 6,7
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 # C4: 6,7 => CTR => C4: 1,4
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 # C6: 1 => CTR => C6: 6,7
* PRF I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 # G3: 2,7 => SOL
* STA I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 + G3: 2,7
* CNT  11 HDP CHAINS /  41 HYP OPENED

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

Details

Positions

1...67.4.5..........3158...9....5...........1.8.9.4..........6...2.7..18.6..4.93. initial
1...67.4.5..4..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93. autosolve
198267345527493186643158279971385624354726891286914753819532467432679518765841932 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B1: 2,9
C1: 8,9
B2: 2,7
D1: 2,3
H3: 2,7
A8: 3,4
A9: 7,8
F9: 1,2
G8: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E6: 1.. / E4 = 1  => 10 pairs (_) / E6 = 1  => 10 pairs (_)
F7,F9: 1.. / F7 = 1  => 13 pairs (_) / F9 = 1  =>  9 pairs (_)
C6,E6: 1.. / C6 = 1  => 10 pairs (_) / E6 = 1  => 10 pairs (_)
C9,F9: 1.. / C9 = 1  => 13 pairs (_) / F9 = 1  =>  9 pairs (_)
B4,B7: 1.. / B4 = 1  => 10 pairs (_) / B7 = 1  =>  9 pairs (_)
A3,B3: 4.. / A3 = 4  => 19 pairs (_) / B3 = 4  =>  9 pairs (_)
I4,I7: 4.. / I4 = 4  =>  9 pairs (_) / I7 = 4  => 11 pairs (_)
G1,I1: 5.. / G1 = 5  =>  0 pairs (X) / I1 = 5  => 10 pairs (_)
B5,C5: 5.. / B5 = 5  =>  9 pairs (_) / C5 = 5  => 10 pairs (_)
C2,A3: 6.. / C2 = 6  => 14 pairs (_) / A3 = 6  => 16 pairs (_)
D8,F8: 6.. / D8 = 6  => 10 pairs (_) / F8 = 6  =>  0 pairs (X)
C2,I2: 6.. / C2 = 6  => 14 pairs (_) / I2 = 6  => 16 pairs (_)
F5,F8: 6.. / F5 = 6  => 10 pairs (_) / F8 = 6  =>  0 pairs (X)
D4,D5: 7.. / D4 = 7  => 11 pairs (_) / D5 = 7  =>  9 pairs (_)
C1,C2: 8.. / C1 = 8  => 11 pairs (_) / C2 = 8  =>  0 pairs (X)
G1,H2: 8.. / G1 = 8  =>  0 pairs (X) / H2 = 8  => 11 pairs (_)
A7,A9: 8.. / A7 = 8  => 10 pairs (_) / A9 = 8  =>  9 pairs (_)
C1,G1: 8.. / C1 = 8  => 11 pairs (_) / G1 = 8  =>  0 pairs (X)
C2,H2: 8.. / C2 = 8  =>  0 pairs (X) / H2 = 8  => 11 pairs (_)
A9,D9: 8.. / A9 = 8  =>  9 pairs (_) / D9 = 8  => 10 pairs (_)
H2,H4: 8.. / H2 = 8  => 11 pairs (_) / H4 = 8  =>  0 pairs (X)
E2,F2: 9.. / E2 = 9  => 10 pairs (_) / F2 = 9  =>  0 pairs (X)
I1,I3: 9.. / I1 = 9  =>  0 pairs (X) / I3 = 9  =>  9 pairs (_)
B3,I3: 9.. / B3 = 9  =>  0 pairs (X) / I3 = 9  =>  9 pairs (_)
B8,F8: 9.. / B8 = 9  =>  0 pairs (X) / F8 = 9  => 10 pairs (_)
C1,C7: 9.. / C1 = 9  =>  0 pairs (X) / C7 = 9  => 11 pairs (_)
E2,E7: 9.. / E2 = 9  => 10 pairs (_) / E7 = 9  =>  0 pairs (X)
* DURATION: 0:00:21.703300  START: 22:15:30.261935  END: 22:15:51.965235 2019-04-30
* CP COUNT: (27)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B1,B2,C1,D1,F9,G8,H3)
* 1...67.4.5..4..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93.
* PAIR B1: 2,9 BLK 1
B3: 2,9,4,7                              # reduction candidate for 2,9
B3: 2,9                                  # 20 pairs
B3: 4,7                                  # 10 pairs
* PAIR B1: 2,9 ROW 1
I1: 2,9,3,5                              # reduction candidate for 2,9
I1: 2,9 => CTR
* 1.836754.5.64..183..3158...9....5..4.......91.8.9.4.5...9....6.352679418.6..4.93.
I1: 3,5                                  # 10 pairs
* PAIR B2: 2,7 BLK 1
A3: 2,7,4,6                              # reduction candidate for 2,7
A3: 2,7 => CTR
* 198.67.455.649.18.2431586799....5.26325.8649168.924.5..59.31.64432679518.61542937
A3: 4,6                                  # 10 pairs
B3: 2,7,4,9                              # reduction candidate for 2,7
B3: 2,7                                  # 21 pairs
* PAIR B2: 2,7 ROW 2
H2: 2,7,8                                # reduction candidate for 2,7
H2: 2,7 => CTR
* 1...678455.84..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93.
H2: 8                                    # 11 pairs
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 23 pairs
* PAIR B2: 2,7 COL B
B4: 2,7,1,3,4                            # reduction candidate for 2,7
B4: 2,7                                  # 18 pairs
B5: 2,7,3,4,5                            # reduction candidate for 2,7
B5: 2,7 => CTR
* 1982673455.64931822431586799147358263.5..6491.8.9.4.5..59..1.64432679518861542937
B5: 3,4,5                                #  9 pairs
* PAIR D1: 2,3 BLK 2
E2: 2,3,9                                # reduction candidate for 2,3
E2: 2,3 => CTR
* 1293678455784291....3158...9....5..........91.8.9.4.5.....9..6..92.7..18.6..4.93.
E2: 9                                    # 10 pairs
F2: 2,3,9                                # reduction candidate for 2,3
F2: 2,3                                  # 10 pairs
* PAIR D1: 2,3 ROW 1
G1: 2,3,5,8                              # reduction candidate for 2,3
G1: 2,3                                  # 12 pairs
I1: 2,3,5,9                              # reduction candidate for 2,3
I1: 2,3 => CTR
* 1.8.6754.5..4..18...3158..99....5..4.......91.8.9.4.5...9....6.352679418.6..4.93.
I1: 5,9                                  # 10 pairs
* PAIR D1: 2,3 COL D
D4: 2,3,6,7,8                            # reduction candidate for 2,3
D4: 2,3                                  # 14 pairs
D5: 2,3,6,7,8                            # reduction candidate for 2,3
D5: 2,3                                  # 15 pairs
D7: 2,3,5,8                              # reduction candidate for 2,3
D7: 2,3                                  # 12 pairs
* PAIR H3: 2,7 BLK 3
H2: 2,7,8                                # reduction candidate for 2,7
H2: 2,7 => CTR
* 1...678455.84..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93.
H2: 8                                    # 11 pairs
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 23 pairs
G3: 2,7,6                                # reduction candidate for 2,7
G3: 2,7                                  # 17 pairs
I3: 2,7,6,9                              # reduction candidate for 2,7
I3: 2,7 => CTR
* 1283675495764921834931586..9....5........6.9168.9.4.5...9..3.6.3.2679418.6..4193.
I3: 6,9                                  # 10 pairs
* PAIR H3: 2,7 ROW 3
A3: 2,7,4,6                              # reduction candidate for 2,7
A3: 2,7 => CTR
* 198.67.455.649.18.2431586799....5.26325.8649168.924.5..59.31.64432679518.61542937
A3: 4,6                                  # 10 pairs
B3: 2,7,4,9                              # reduction candidate for 2,7
B3: 2,7                                  # 21 pairs
* PAIR H3: 2,7 COL H
H4: 2,7,8                                # reduction candidate for 2,7
H4: 8 => CTR
* 1...678455.84..1....3158...9....5.8........91.8.9.4.5........6...2.7..18.6..4.93.
H4: 2,7                                  # 11 pairs
* PAIR A8: 3,4 BLK 7
A7: 3,4,7,8                              # reduction candidate for 3,4
A7: 3,4                                  # 11 pairs
B7: 3,4,1,5,7,9                          # reduction candidate for 3,4
B7: 3,4                                  # 14 pairs
B8: 3,4,5,9                              # reduction candidate for 3,4
B8: 3,4                                  # 14 pairs
* PAIR A8: 3,4 COL A
A5: 3,4,2,6,7                            # reduction candidate for 3,4
A5: 3,4                                  # 15 pairs
A5: 2,6,7                                #  9 pairs
* PAIR A9: 7,8 BLK 7
A7: 7,8,3,4                              # reduction candidate for 7,8
A7: 7,8                                  # 11 pairs
A7: 3,4                                  # 11 pairs
* PAIR F9: 1,2 BLK 8
F7: 1,2,3,9                              # reduction candidate for 1,2
F7: 1,2                                  # 13 pairs
F7: 3,9                                  # 10 pairs
* PAIR G8: 4,5 BLK 9
G7: 4,5,2,7                              # reduction candidate for 4,5
G7: 4,5                                  # 14 pairs
I7: 4,5,2,7                              # reduction candidate for 4,5
I7: 4,5                                  # 12 pairs
* PAIR G8: 4,5 ROW 8
B8: 4,5,3,9                              # reduction candidate for 4,5
B8: 4,5                                  # 10 pairs
B8: 3,9                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060409-absurd-base-pr-000.dot
* REASONING
* DIS # I1: 2,9 => CTR => I1: 3,5
* DIS # A3: 2,7 => CTR => A3: 4,6
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # B5: 2,7 => CTR => B5: 3,4,5
* DIS # E2: 2,3 => CTR => E2: 9
* DIS # I1: 2,3 => CTR => I1: 5,9
* DIS # H2: 2,7 => CTR => H2: 8
* DIS # I3: 2,7 => CTR => I3: 6,9
* DIS # A3: 2,7 => CTR => A3: 4,6
* DIS # H4: 8 => CTR => H4: 2,7
* CNT  10 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B1,B2,C1,D1,F9,G8,H3)
* 1...67.4.5..4..1....3158...9....5..........91.8.9.4.5........6...2.7..18.6..4.93.
* PAIR B1: 2,9 BLK 1
B3: 2,9,4,7                              # reduction candidate for 2,9
B3: 2,9                                  # 20 pairs
B3: 4,7                                  # 10 pairs
* PAIR B1: 2,9 ROW 1
I1: 2,9,3,5                              # reduction candidate for 2,9
I1: 2,9 => CTR
* 1.836754.5.64..183..3158...9....5..4.......91.8.9.4.5...9....6.352679418.6..4.93.
* PAIR RESTART
* PAIR B2: 2,7 BLK 1
A3: 2,7,4,6                              # reduction candidate for 2,7
A3: 2,7 => CTR
* 198.67.455.649.18.2431586799....5.26325.8649168.924.5..59.31.64432679518.61542937
B3: 2,7,4                                # reduction candidate for 2,7
B3: 2,7                                  # 21 pairs
* RESTART
* PAIR B2: 2,7 BLK 1
B3: 2,7,4                                # reduction candidate for 2,7
B3: 2,7                                  # 21 pairs
B3: 4                                    # 16 pairs
* PAIR B2: 2,7 ROW 2
H2: 2,7,8                                # reduction candidate for 2,7
H2: 2,7 => CTR
* 1...678455.84..1....3158..99....5..........91.8.9.4.5........6...2.7..18.6..4.93.
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 24 pairs
* RESTART
* PAIR B2: 2,7 ROW 2
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 24 pairs
I2: 3,6                                  # 14 pairs
* PAIR RESTART
* PAIR B2: 2,7 BLK 1
B3: 2,7,4                                # reduction candidate for 2,7
B3: 2,7                                  # 21 pairs
B3: 4                                    # 16 pairs
* PAIR B2: 2,7 ROW 2
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 24 pairs
I2: 3,6                                  # 14 pairs
* PAIR D1: 2,3 ROW 1
G1: 2,3,5                                # reduction candidate for 2,3
G1: 5 => CTR
* 1982675435..49318...3158..99....5........6.91.8.9.4.5...9....6..52679418.6..4.93.
* PAIR D1: 2,3 COL D
D4: 2,3,7,8                              # reduction candidate for 2,3
D4: 2,3                                  # 20 pairs
D5: 2,3,7,8                              # reduction candidate for 2,3
D5: 2,3                                  # 18 pairs
D7: 2,3,5,8                              # reduction candidate for 2,3
D7: 2,3 => CTR
* 1982673455.6493182423158679914735826.758.6491.8.9.4.5.759.81264..2679518861542937
* PAIR RESTART
* PAIR D1: 2,3 COL D
D4: 2,3,7,8                              # reduction candidate for 2,3
D4: 2,3                                  # 20 pairs
D5: 2,3,7,8                              # reduction candidate for 2,3
D5: 2,3                                  # 18 pairs
* PAIR H3: 2,7 BLK 3
I2: 2,7,3,6                              # reduction candidate for 2,7
I2: 2,7                                  # 24 pairs
G3: 2,7,6                                # reduction candidate for 2,7
G3: 2,7                                  # 19 pairs
* PAIR H3: 2,7 ROW 3
B3: 2,7,4                                # reduction candidate for 2,7
B3: 2,7                                  # 22 pairs
B3: 4                                    # 19 pairs
* PAIR A8: 3,4 BLK 7
B8: 3,4,5                                # reduction candidate for 3,4
B8: 5 => CTR
* 198.67.455..49.18...3158..99....5........6.91.8.9.4.5...9....6.352679418.6.54.93.
* PAIR F9: 1,2 BLK 8
F7: 1,2,3                                # reduction candidate for 1,2
F7: 3 => CTR
* 1983672455..492183.231586799....5.2..5...6.9168.924357.1958376...2679518.65.4193.

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A5,A7,A8,A9,B2,B7,B8,C2,C9,D4,D5,D7,D9,E5,E6,F7,F9,H3,H4,I9)
* 1982673455..49318...3158..99....5........6.91.8.9.4.5...9.3..6...2679518.6..4.93.
* PAIR B2: 2,7 BLK 1
B3: 2,7,4                                # reduction candidate for 2,7
B3: 4                                    # 25 pairs
B3: 2,7                                  # 24 pairs
* PAIR B2: 2,7 ROW 2
I2: 2,7,6                                # reduction candidate for 2,7
I2: 6                                    # 25 pairs
I2: 2,7                                  # 24 pairs
* PAIR C2: 6,7 ROW 2
I2: 6,7,2                                # reduction candidate for 6,7
I2: 2 => CTR
* 1982673455764931824231586799...158262...86491681924753719.3.264342679518.6..42937
* PAIR C2: 6,7 COL C
C4: 6,7,1,4                              # reduction candidate for 6,7
C4: 6,7 => CTR
* 19826734552.49318...3158..99...15824254386791.81924653819532.6...2679518765841932
C6: 6,7,1                                # reduction candidate for 6,7
C6: 6,7                                  # 30 pairs
* RESTART
* PAIR C2: 6,7 COL C
C6: 6,7,1                                # reduction candidate for 6,7
C6: 1 => CTR
* 1982673455264931874731586299...258.......6.91.8.9.4.53..9.3..6...2679518.6..4.93.
* PAIR RESTART
* PAIR H3: 2,7 BLK 3
G3: 2,7,6                                # reduction candidate for 2,7
G3: 2,7 => SOLVED
* 198267345527493186643158279971385624354726891286914753819532467432679518765841932
* DURATION: 0:00:31.846009  START: 22:16:14.901159  END: 22:16:46.747168 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060409-absurd-base-pr-001.dot
* REASONING
* DIS # I1: 2,9 => CTR => I1: 3,5
* DIS I1: 3,5 # A3: 2,7 => CTR => A3: 4,6
* DIS I1: 3,5 + A3: 4,6 # H2: 2,7 => CTR => H2: 8
* DIS I1: 3,5 + A3: 4,6 + H2: 8 # G1: 5 => CTR => G1: 2,3
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 # D7: 2,3 => CTR => D7: 5,8
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B8: 5 => CTR => B8: 3,4
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 # F7: 3 => CTR => F7: 1,2
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 2 => CTR => I2: 6,7
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 # C4: 6,7 => CTR => C4: 1,4
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 # C6: 1 => CTR => C6: 6,7
* PRF I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 # G3: 2,7 => SOL
* STA I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 + G3: 2,7
* CNT  11 HDP CHAINS /  41 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060409, absurd

Solution

position: 198267345527493186643158279971385624354726891286914753819532467432679518765841932 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 # B3: 2,9 => UNS
* INC # B3: 4,7 => UNS
* DIS # I1: 2,9 => CTR => I1: 3,5
* INC # I1: 3,5 => UNS
* DIS # A3: 2,7 => CTR => A3: 4,6
* INC # A3: 4,6 => UNS
* INC # B3: 2,7 => UNS
* DIS # H2: 2,7 => CTR => H2: 8
* INC # H2: 8 => UNS
* INC # I2: 2,7 => UNS
* INC # B4: 2,7 => UNS
* DIS # B5: 2,7 => CTR => B5: 3,4,5
* INC # B5: 3,4,5 => UNS
* DIS # E2: 2,3 => CTR => E2: 9
* INC # E2: 9 => UNS
* INC # F2: 2,3 => UNS
* INC # G1: 2,3 => UNS
* DIS # I1: 2,3 => CTR => I1: 5,9
* INC # I1: 5,9 => UNS
* INC # D4: 2,3 => UNS
* INC # D5: 2,3 => UNS
* INC # D7: 2,3 => UNS
* DIS # H2: 2,7 => CTR => H2: 8
* INC # H2: 8 => UNS
* INC # I2: 2,7 => UNS
* INC # G3: 2,7 => UNS
* DIS # I3: 2,7 => CTR => I3: 6,9
* INC # I3: 6,9 => UNS
* DIS # A3: 2,7 => CTR => A3: 4,6
* INC # A3: 4,6 => UNS
* INC # B3: 2,7 => UNS
* INC # H4: 2,7 => UNS
* DIS # H4: 8 => CTR => H4: 2,7
* INC # A7: 3,4 => UNS
* INC # B7: 3,4 => UNS
* INC # B8: 3,4 => UNS
* INC # A5: 3,4 => UNS
* INC # A5: 2,6,7 => UNS
* INC # A7: 7,8 => UNS
* INC # A7: 3,4 => UNS
* INC # F7: 1,2 => UNS
* INC # F7: 3,9 => UNS
* INC # G7: 4,5 => UNS
* INC # I7: 4,5 => UNS
* INC # B8: 4,5 => UNS
* INC # B8: 3,9 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 2,9 => UNS
* INC # B3: 4,7 => UNS
* DIS # I1: 2,9 => CTR => I1: 3,5
* DIS I1: 3,5 # A3: 2,7 => CTR => A3: 4,6
* INC I1: 3,5 + A3: 4,6 # B3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 # B3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 # B3: 4 => UNS
* DIS I1: 3,5 + A3: 4,6 # H2: 2,7 => CTR => H2: 8
* INC I1: 3,5 + A3: 4,6 + H2: 8 # I2: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # I2: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # I2: 3,6 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # B3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # B3: 4 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # I2: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # I2: 3,6 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 # G1: 2,3 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 # G1: 5 => CTR => G1: 2,3
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 # D4: 2,3 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 # D5: 2,3 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 # D7: 2,3 => CTR => D7: 5,8
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # D4: 2,3 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # D5: 2,3 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # I2: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # G3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B3: 4 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B8: 3,4 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 # B8: 5 => CTR => B8: 3,4
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 # F7: 1,2 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 # F7: 3 => CTR => F7: 1,2
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # B3: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # B3: 4 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 2,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 6 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 6,7 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 # I2: 2 => CTR => I2: 6,7
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 # C4: 6,7 => CTR => C4: 1,4
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 # C6: 6,7 => UNS
* INC I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 # C6: 6,7 => UNS
* DIS I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 # C6: 1 => CTR => C6: 6,7
* PRF I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 # G3: 2,7 => SOL
* STA I1: 3,5 + A3: 4,6 + H2: 8 + G1: 2,3 + D7: 5,8 + B8: 3,4 + F7: 1,2 + I2: 6,7 + C4: 1,4 + C6: 6,7 + G3: 2,7
* CNT  41 HDP CHAINS /  41 HYP OPENED