Analysis of zz-www.sudokuoftheday.co.uk-20060423-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: .37...8..6........9..1...562.1...47...3..56.9.......1....2.4...4.6.3.1....27..... initial

Autosolve

position: .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 2,4,8 => CTR => B2: 1,5
* PRF # A7: 3,8 => SOL
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* DIS # B3: 4,8 => CTR => B3: 2
* DIS # F1: 6,9 => CTR => F1: 2
* DIS # D4: 6,9 => CTR => D4: 3,8
* DIS # D6: 6,9 => CTR => D6: 4
* PRF # E2: 4,7 => SOL
* DIS # H2: 4,9 => CTR => H2: 3
* DIS # H9: 3,6,8 => CTR => H9: 4,9
* PRF # I2: 1,4 => SOL
* DIS # I2: 3,7 => CTR => I2: 1,4
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* DIS # B3: 4,8 => CTR => B3: 2
* DIS # B4: 6,9 => CTR => B4: 5,8
* DIS # A7: 5,8 => CTR => A7: 1,3
* PRF # A9: 5,8 => SOL
* DIS # B6: 4,9 => CTR => B6: 6
* DIS # D6: 6 => CTR => D6: 4,9
* DIS # D4: 8,9 => CTR => D4: 3,6
* DIS # F4: 8,9 => CTR => F4: 3,6
* PRF # B4: 8,9 => SOL
* DIS # E9: 8,9 => CTR => E9: 6
* DIS # B4: 6,9 => CTR => B4: 5,8
* PRF # I6: 8 => SOL
* DIS # E9: 8,9 => CTR => E9: 6
* DIS # F4: 8,9 => CTR => F4: 3,6
* DIS # H7: 8,9 => CTR => H7: 3,6
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* CNT  29 HDP CHAINS /  66 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 # B2: 2,4,8 => CTR => B2: 1,5
* PRF B2: 1,5 # E2: 4,7 => SOL
* STA B2: 1,5 + E2: 4,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.37...8..6........9..1...562.1...47...3..56.9.......1....2.4...4.6.3.1....27..... initial
.37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1... autosolve
137652894654978231928143756281396475743815629569427318315284967476539182892761543 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
A1: 1,5
C3: 4,8
D1: 6,9
E3: 4,7
H1: 4,9
I1: 1,4
B5: 4,8
A6: 5,8
C6: 4,9
E4: 8,9
D5: 4,8
E6: 2,7
F6: 2,7
I4: 5,8
G6: 3,5
F8: 8,9
H8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B2: 1.. / A1 = 1  =>  0 pairs (*) / B2 = 1  =>  0 pairs (X)
I1,I2: 1.. / I1 = 1  => 24 pairs (_) / I2 = 1  =>  0 pairs (*)
A7,B7: 1.. / A7 = 1  => 24 pairs (_) / B7 = 1  =>  0 pairs (*)
A1,I1: 1.. / A1 = 1  =>  0 pairs (*) / I1 = 1  =>  0 pairs (X)
B2,I2: 1.. / B2 = 1  => 24 pairs (_) / I2 = 1  =>  0 pairs (*)
A1,A7: 1.. / A1 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
B2,B7: 1.. / B2 = 1  => 24 pairs (_) / B7 = 1  =>  0 pairs (*)
B2,B3: 2.. / B2 = 2  =>  0 pairs (X) / B3 = 2  => 20 pairs (_)
E1,F1: 2.. / E1 = 2  =>  0 pairs (X) / F1 = 2  => 17 pairs (_)
G2,G3: 2.. / G2 = 2  => 20 pairs (_) / G3 = 2  =>  0 pairs (X)
E6,F6: 2.. / E6 = 2  => 17 pairs (_) / F6 = 2  =>  0 pairs (X)
B2,G2: 2.. / B2 = 2  =>  0 pairs (X) / G2 = 2  => 20 pairs (_)
B3,G3: 2.. / B3 = 2  => 20 pairs (_) / G3 = 2  =>  0 pairs (X)
E1,E6: 2.. / E1 = 2  =>  0 pairs (X) / E6 = 2  => 17 pairs (_)
F1,F6: 2.. / F1 = 2  => 17 pairs (_) / F6 = 2  =>  0 pairs (X)
D4,F4: 3.. / D4 = 3  => 18 pairs (_) / F4 = 3  =>  0 pairs (X)
G6,I6: 3.. / G6 = 3  => 23 pairs (_) / I6 = 3  => 21 pairs (_)
A7,A9: 3.. / A7 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
F3,G3: 3.. / F3 = 3  => 20 pairs (_) / G3 = 3  =>  0 pairs (X)
D2,D4: 3.. / D2 = 3  =>  0 pairs (X) / D4 = 3  => 18 pairs (_)
D5,D6: 4.. / D5 = 4  =>  0 pairs (X) / D6 = 4  => 20 pairs (_)
H9,I9: 4.. / H9 = 4  =>  0 pairs (*) / I9 = 4  =>  0 pairs (X)
B5,D5: 4.. / B5 = 4  => 20 pairs (_) / D5 = 4  =>  0 pairs (X)
E1,E2: 5.. / E1 = 5  =>  0 pairs (*) / E2 = 5  =>  0 pairs (X)
B4,A6: 5.. / B4 = 5  => 20 pairs (_) / A6 = 5  =>  0 pairs (*)
A1,E1: 5.. / A1 = 5  => 24 pairs (_) / E1 = 5  =>  0 pairs (*)
B4,I4: 5.. / B4 = 5  => 20 pairs (_) / I4 = 5  =>  0 pairs (*)
C2,C7: 5.. / C2 = 5  =>  0 pairs (X) / C7 = 5  => 25 pairs (_)
D1,F1: 6.. / D1 = 6  => 19 pairs (_) / F1 = 6  =>  0 pairs (X)
B4,B6: 6.. / B4 = 6  =>  0 pairs (X) / B6 = 6  => 20 pairs (_)
E7,E9: 6.. / E7 = 6  =>  0 pairs (X) / E9 = 6  => 18 pairs (_)
H7,H9: 6.. / H7 = 6  => 18 pairs (_) / H9 = 6  =>  0 pairs (X)
B6,D6: 6.. / B6 = 6  => 20 pairs (_) / D6 = 6  =>  0 pairs (X)
E7,H7: 6.. / E7 = 6  =>  0 pairs (X) / H7 = 6  => 18 pairs (_)
E9,H9: 6.. / E9 = 6  => 18 pairs (_) / H9 = 6  =>  0 pairs (X)
F1,F4: 6.. / F1 = 6  =>  0 pairs (X) / F4 = 6  => 19 pairs (_)
E6,F6: 7.. / E6 = 7  =>  0 pairs (X) / F6 = 7  => 17 pairs (_)
G7,I7: 7.. / G7 = 7  =>  0 pairs (X) / I7 = 7  => 25 pairs (_)
I2,I7: 7.. / I2 = 7  =>  0 pairs (X) / I7 = 7  => 25 pairs (_)
I4,I6: 8.. / I4 = 8  => 20 pairs (_) / I6 = 8  =>  0 pairs (*)
B5,D5: 8.. / B5 = 8  =>  0 pairs (X) / D5 = 8  => 20 pairs (_)
A6,I6: 8.. / A6 = 8  => 20 pairs (_) / I6 = 8  =>  0 pairs (*)
F8,H8: 8.. / F8 = 8  =>  0 pairs (X) / H8 = 8  => 18 pairs (_)
F8,H8: 9.. / F8 = 9  => 18 pairs (_) / H8 = 9  =>  0 pairs (X)
C6,C7: 9.. / C6 = 9  => 20 pairs (_) / C7 = 9  =>  0 pairs (X)
* DURATION: 0:01:04.154153  START: 22:35:32.653967  END: 22:36:36.808120 2019-04-30
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,C3,C6,D1,D5,E3,E4,E6,F6,F8,G6,H1,H8,I1,I4)
* .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1...
* PAIR A1: 1,5 BLK 1
B2: 1,5,2,4,8                            # reduction candidate for 1,5
B2: 2,4,8 => CTR
* 1376528946.59.8.319..1.3.562.139647.7.3815629.69427.1..182.4.67476539182..2761.4.
B2: 1,5                                  # 25 pairs
* PAIR A1: 1,5 COL A
A7: 1,5,3,8                              # reduction candidate for 1,5
A7: 3,8 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
A7: 1,5                                  # 23 pairs
* PAIR C3: 4,8 BLK 1
B2: 4,8,1,2,5                            # reduction candidate for 4,8
B2: 4,8 => CTR
* 1376528946.5.7.23192.1437562.13.647.7.3.15629.64927.1..192.4.674765391.2..27.1.4.
B2: 1,2,5                                # 17 pairs
C2: 4,8,5                                # reduction candidate for 4,8
C2: 4,8                                  # 25 pairs
B3: 4,8,2                                # reduction candidate for 4,8
B3: 4,8 => CTR
* 1376528946259487319..1732562.139647.7.3815629.69427.1..182.4.67476539182..2761.4.
B3: 2                                    # 20 pairs
* PAIR D1: 6,9 BLK 2
F1: 6,9,2                                # reduction candidate for 6,9
F1: 6,9 => CTR
* 537.2.841614.58297928147356251.9347874381562986947251.1.52.4...47653.1.23.27.1..4
F1: 2                                    # 17 pairs
* PAIR D1: 6,9 COL D
D4: 6,9,3,8                              # reduction candidate for 6,9
D4: 6,9 => CTR
* .37..68..6..3..2.792.1..3562516934787438156298694.2513.9.2.47.54765391825827.19..
D4: 3,8                                  # 18 pairs
D6: 6,9,4                                # reduction candidate for 6,9
D6: 6,9 => CTR
* 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791...
D6: 4                                    # 20 pairs
* PAIR E3: 4,7 BLK 2
E2: 4,7,5                                # reduction candidate for 4,7
E2: 4,7 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
E2: 5                                    # 24 pairs
* PAIR H1: 4,9 BLK 3
H2: 4,9,3                                # reduction candidate for 4,9
H2: 4,9 => CTR
* 537...8.161..572.392.14..56251.9.4787.38156298694...1.1.5264.374765391823.2781564
H2: 3                                    # 20 pairs
* PAIR H1: 4,9 COL H
H9: 4,9,3,6,8                            # reduction candidate for 4,9
H9: 3,6,8 => CTR
* 537...8.161..572.392.14..56251.9.4787438156298694..3151.52.49.7476539182392781564
H9: 4,9                                  # 23 pairs
* PAIR I1: 1,4 BLK 3
I2: 1,4,3,7                              # reduction candidate for 1,4
I2: 1,4 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
I2: 3,7 => CTR
* 537...8.161..572.392.14..56251.9.4787438156298694..3151.52.49.7476539182392781564
* PAIR B5: 4,8 COL B
B2: 4,8,1,2,5                            # reduction candidate for 4,8
B2: 4,8 => CTR
* 1376528946.5.7.23192.1437562.13.647.7.3.15629.64927.1..192.4.674765391.2..27.1.4.
B2: 1,2,5                                # 17 pairs
B3: 4,8,2                                # reduction candidate for 4,8
B3: 4,8 => CTR
* 1376528946259487319..1732562.139647.7.3815629.69427.1..182.4.67476539182..2761.4.
B3: 2                                    # 20 pairs
* PAIR A6: 5,8 BLK 4
B4: 5,8,6,9                              # reduction candidate for 5,8
B4: 6,9 => CTR
* 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791...
B4: 5,8                                  # 20 pairs
* PAIR A6: 5,8 ROW 6
I6: 5,8,3                                # reduction candidate for 5,8
I6: 5,8                                  # 23 pairs
I6: 3                                    # 21 pairs
* PAIR A6: 5,8 COL A
A7: 5,8,1,3                              # reduction candidate for 5,8
A7: 5,8 => CTR
* 1376528946......319..1.3.562513964787.381562986942751..1.2.4..747653.1.23.27.1.45
A7: 1,3                                  # 18 pairs
A9: 5,8,3                                # reduction candidate for 5,8
A9: 5,8 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
A9: 3                                    # 19 pairs
* PAIR C6: 4,9 BLK 4
B6: 4,9,6                                # reduction candidate for 4,9
B6: 4,9 => CTR
* 13795.8..6........9..1...56261...4757.3.156295..6..318...2.4...47653.1.2..27.1...
B6: 6                                    # 20 pairs
* PAIR C6: 4,9 ROW 6
D6: 4,9,6                                # reduction candidate for 4,9
D6: 6 => CTR
* .379.684161....29.92.1...56261...4757834156295..6...1....2.4...47653.1.2..27.1...
D6: 4,9                                  # 20 pairs
* PAIR E4: 8,9 BLK 5
D4: 8,9,3,6                              # reduction candidate for 8,9
D4: 8,9 => CTR
* .37...8..6..3.....9..1..3562.1..347.7.3.15629...6..513...2.4...47653.1.2..27.19..
D4: 3,6                                  # 18 pairs
F4: 8,9,3,6                              # reduction candidate for 8,9
F4: 8,9 => CTR
* .3792684161.85.29.92814..562613..4757834156295..6.2.1....2.4...47653.1.2..27.1...
F4: 3,6                                  # 18 pairs
* PAIR E4: 8,9 ROW 4
B4: 8,9,5,6                              # reduction candidate for 8,9
B4: 8,9 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
B4: 5,6                                  # 19 pairs
* PAIR E4: 8,9 COL E
E7: 8,9,6                                # reduction candidate for 8,9
E7: 8,9                                  # 18 pairs
E9: 8,9,6                                # reduction candidate for 8,9
E9: 8,9 => CTR
* 537...8.161..572.392.14..56251.9.4787438156298694..315185264937476539182392781564
E9: 6                                    # 18 pairs
* PAIR I4: 5,8 BLK 6
I6: 5,8,3                                # reduction candidate for 5,8
I6: 5,8                                  # 23 pairs
I6: 3                                    # 21 pairs
* PAIR I4: 5,8 ROW 4
B4: 5,8,6,9                              # reduction candidate for 5,8
B4: 6,9 => CTR
* 137.528.46.......19..1.3.562.13.6475783415629564927318.192.45.747653.1.2.52791...
B4: 5,8                                  # 20 pairs
* PAIR G6: 3,5 BLK 6
I6: 3,5,8                                # reduction candidate for 3,5
I6: 8 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
I6: 3,5                                  # 20 pairs
* PAIR G6: 3,5 COL G
G7: 3,5,7,9                              # reduction candidate for 3,5
G7: 3,5                                  # 27 pairs
G9: 3,5,9                                # reduction candidate for 3,5
G9: 3,5                                  # 22 pairs
* PAIR F8: 8,9 BLK 8
E7: 8,9,6                                # reduction candidate for 8,9
E7: 8,9                                  # 18 pairs
E9: 8,9,6                                # reduction candidate for 8,9
E9: 8,9 => CTR
* 537...8.161..572.392.14..56251.9.4787438156298694..315185264937476539182392781564
E9: 6                                    # 18 pairs
* PAIR F8: 8,9 COL F
F2: 8,9,3,7                              # reduction candidate for 8,9
F2: 8,9                                  # 22 pairs
F4: 8,9,3,6                              # reduction candidate for 8,9
F4: 8,9 => CTR
* .3792684161.85.29.92814..562613..4757834156295..6.2.1....2.4...47653.1.2..27.1...
F4: 3,6                                  # 18 pairs
* PAIR H8: 8,9 BLK 9
H7: 8,9,3,6                              # reduction candidate for 8,9
H7: 8,9 => CTR
* .37...8.161....2379..1...562.1...47.7.3.15629.......1....264...47653.1.2..27.1.64
H7: 3,6                                  # 18 pairs
H9: 8,9,3,4,6                            # reduction candidate for 8,9
H9: 8,9 => CTR
* .37...8.161....2379..1...562.1...47.7.3.15629.......1....2.4.6.47653.1.2..2761..4
H9: 3,4,6                                # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060423-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 2,4,8 => CTR => B2: 1,5
* PRF # A7: 3,8 => SOL
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* DIS # B3: 4,8 => CTR => B3: 2
* DIS # F1: 6,9 => CTR => F1: 2
* DIS # D4: 6,9 => CTR => D4: 3,8
* DIS # D6: 6,9 => CTR => D6: 4
* PRF # E2: 4,7 => SOL
* DIS # H2: 4,9 => CTR => H2: 3
* DIS # H9: 3,6,8 => CTR => H9: 4,9
* PRF # I2: 1,4 => SOL
* DIS # I2: 3,7 => CTR => I2: 1,4
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* DIS # B3: 4,8 => CTR => B3: 2
* DIS # B4: 6,9 => CTR => B4: 5,8
* DIS # A7: 5,8 => CTR => A7: 1,3
* PRF # A9: 5,8 => SOL
* DIS # B6: 4,9 => CTR => B6: 6
* DIS # D6: 6 => CTR => D6: 4,9
* DIS # D4: 8,9 => CTR => D4: 3,6
* DIS # F4: 8,9 => CTR => F4: 3,6
* PRF # B4: 8,9 => SOL
* DIS # E9: 8,9 => CTR => E9: 6
* DIS # B4: 6,9 => CTR => B4: 5,8
* PRF # I6: 8 => SOL
* DIS # E9: 8,9 => CTR => E9: 6
* DIS # F4: 8,9 => CTR => F4: 3,6
* DIS # H7: 8,9 => CTR => H7: 3,6
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* CNT  29 HDP CHAINS /  66 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,C3,C6,D1,D5,E3,E4,E6,F6,F8,G6,H1,H8,I1,I4)
* .37...8..6........9..1...562.1...47.7.3.15629.......1....2.4...47653.1.2..27.1...
* PAIR A1: 1,5 BLK 1
B2: 1,5,2,4,8                            # reduction candidate for 1,5
B2: 2,4,8 => CTR
* 1376528946.59.8.319..1.3.562.139647.7.3815629.69427.1..182.4.67476539182..2761.4.
* PAIR E3: 4,7 BLK 2
E2: 4,7,5                                # reduction candidate for 4,7
E2: 4,7 => SOLVED
* 137652894654978231928143756281396475743815629569427318315284967476539182892761543
* DURATION: 0:00:03.560617  START: 22:37:25.114358  END: 22:37:28.674975 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060423-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 2,4,8 => CTR => B2: 1,5
* PRF B2: 1,5 # E2: 4,7 => SOL
* STA B2: 1,5 + E2: 4,7
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060423, absurd

Solution

position: 137652894654978231928143756281396475743815629569427318315284967476539182892761543 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 # B2: 1,5 => UNS
* DIS # B2: 2,4,8 => CTR => B2: 1,5
* INC # A7: 1,5 => UNS
* PRF # A7: 3,8 => SOL
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* INC # B2: 1,2,5 => UNS
* INC # C2: 4,8 => UNS
* DIS # B3: 4,8 => CTR => B3: 2
* INC # B3: 2 => UNS
* DIS # F1: 6,9 => CTR => F1: 2
* INC # F1: 2 => UNS
* DIS # D4: 6,9 => CTR => D4: 3,8
* INC # D4: 3,8 => UNS
* DIS # D6: 6,9 => CTR => D6: 4
* INC # D6: 4 => UNS
* PRF # E2: 4,7 => SOL
* INC # E2: 5 => UNS
* DIS # H2: 4,9 => CTR => H2: 3
* INC # H2: 3 => UNS
* INC # H9: 4,9 => UNS
* DIS # H9: 3,6,8 => CTR => H9: 4,9
* PRF # I2: 1,4 => SOL
* DIS # I2: 3,7 => CTR => I2: 1,4
* DIS # B2: 4,8 => CTR => B2: 1,2,5
* INC # B2: 1,2,5 => UNS
* DIS # B3: 4,8 => CTR => B3: 2
* INC # B3: 2 => UNS
* INC # B4: 5,8 => UNS
* DIS # B4: 6,9 => CTR => B4: 5,8
* INC # I6: 5,8 => UNS
* INC # I6: 3 => UNS
* DIS # A7: 5,8 => CTR => A7: 1,3
* INC # A7: 1,3 => UNS
* PRF # A9: 5,8 => SOL
* INC # A9: 3 => UNS
* DIS # B6: 4,9 => CTR => B6: 6
* INC # B6: 6 => UNS
* INC # D6: 4,9 => UNS
* DIS # D6: 6 => CTR => D6: 4,9
* DIS # D4: 8,9 => CTR => D4: 3,6
* INC # D4: 3,6 => UNS
* DIS # F4: 8,9 => CTR => F4: 3,6
* INC # F4: 3,6 => UNS
* PRF # B4: 8,9 => SOL
* INC # B4: 5,6 => UNS
* INC # E7: 8,9 => UNS
* DIS # E9: 8,9 => CTR => E9: 6
* INC # E9: 6 => UNS
* INC # I6: 5,8 => UNS
* INC # I6: 3 => UNS
* INC # B4: 5,8 => UNS
* DIS # B4: 6,9 => CTR => B4: 5,8
* INC # I6: 3,5 => UNS
* PRF # I6: 8 => SOL
* INC # G7: 3,5 => UNS
* INC # G9: 3,5 => UNS
* INC # E7: 8,9 => UNS
* DIS # E9: 8,9 => CTR => E9: 6
* INC # E9: 6 => UNS
* INC # F2: 8,9 => UNS
* DIS # F4: 8,9 => CTR => F4: 3,6
* INC # F4: 3,6 => UNS
* DIS # H7: 8,9 => CTR => H7: 3,6
* INC # H7: 3,6 => UNS
* DIS # H9: 8,9 => CTR => H9: 3,4,6
* INC # H9: 3,4,6 => UNS
* CNT  66 HDP CHAINS /  66 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,5 => UNS
* DIS # B2: 2,4,8 => CTR => B2: 1,5
* PRF B2: 1,5 # E2: 4,7 => SOL
* STA B2: 1,5 + E2: 4,7
* CNT   3 HDP CHAINS /   3 HYP OPENED