Analysis of zz-www.sudokuwiki.org-interesting-squeezed-naughts-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 9....165..5..6...7....9...2.....812...........137.....6...8....5...2..6..746....3 initial

Autosolve

position: 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 2,8 => CTR => B1: 4
* DIS # A2: 1,8 => CTR => A2: 3,4
* DIS # A3: 1,8 => CTR => A3: 3,4,7
* DIS # H2: 1,8 => CTR => H2: 3,4,9
* DIS # C4: 5 => CTR => C4: 6,7
* DIS # G2: 4,8 => CTR => G2: 3,9
* PRF # H2: 4,8 => SOL
* DIS # H3: 4,8 => CTR => H3: 1,3
* DIS # B1: 2 => CTR => B1: 4,8
* PRF # I5: 4,8 => SOL
* DIS # I6: 4,8 => CTR => I6: 5,6,9
* DIS # I8: 4,8 => CTR => I8: 1,9
* PRF # A3: 4,7 => SOL
* PRF # C4: 7 => SOL
* DIS # D5: 5,9 => CTR => D5: 1,2
* DIS # F5: 5,9 => CTR => F5: 2,6
* PRF # F6: 5,9 => SOL
* PRF # I4: 5,9 => SOL
* DIS # D7: 5,9 => CTR => D7: 1,4
* DIS # E5: 4,5 => CTR => E5: 1
* PRF # E5: 1 => SOL
* DIS # I6: 4,5 => CTR => I6: 6,8,9
* DIS # E5: 4 => CTR => E5: 1,5
* DIS # D7: 5,9 => CTR => D7: 1,4
* DIS # G9: 5,9 => CTR => G9: 2,8
* DIS # F5: 5,9 => CTR => F5: 2,6
* PRF # F6: 5,9 => SOL
* DIS # G9: 8,9 => CTR => G9: 2,5
* DIS # H2: 8,9 => CTR => H2: 1,3,4
* CNT  29 HDP CHAINS /  67 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 # B1: 2,8 => CTR => B1: 4
* DIS B1: 4 # A2: 1,8 => CTR => A2: 3
* DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7
* PRF B1: 4 + A2: 3 + A3: 7 => SOL
* STA B1: 4 + A2: 3 + A3: 7
* CNT   4 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

9....165..5..6...7....9...2.....812...........137.....6...8....5...2..6..746....3 initial
9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3 autosolve
942371658351862947786594312467938125895216734213745896629483571538127469174659283 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
C1: 2,8
C2: 1,8
C3: 6,7
D2: 2,8
F2: 2,4
D3: 5,8
F3: 4,5
I1: 4,8
A4: 4,7
C5: 5,6
D4: 5,9
E6: 4,5
G5: 3,7
H5: 3,7
B7: 2,3
B8: 3,8
F7: 3,7
F8: 3,7
E9: 1,5
F9: 5,9
H9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 1.. / H2 = 1  =>  0 pairs (X) / H3 = 1  => 21 pairs (_)
D5,E5: 1.. / D5 = 1  =>  0 pairs (X) / E5 = 1  =>  0 pairs (_)
I7,I8: 1.. / I7 = 1  => 24 pairs (_) / I8 = 1  => 23 pairs (_)
A3,H3: 1.. / A3 = 1  =>  0 pairs (X) / H3 = 1  => 21 pairs (_)
A9,E9: 1.. / A9 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
E5,E9: 1.. / E5 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
B1,C1: 2.. / B1 = 2  =>  0 pairs (X) / C1 = 2  => 22 pairs (_)
D2,F2: 2.. / D2 = 2  => 23 pairs (_) / F2 = 2  =>  0 pairs (*)
G7,G9: 2.. / G7 = 2  =>  0 pairs (X) / G9 = 2  => 22 pairs (_)
A6,F6: 2.. / A6 = 2  => 23 pairs (_) / F6 = 2  =>  0 pairs (X)
A9,G9: 2.. / A9 = 2  =>  0 pairs (X) / G9 = 2  => 22 pairs (_)
C1,C7: 2.. / C1 = 2  => 22 pairs (_) / C7 = 2  =>  0 pairs (X)
D2,D5: 2.. / D2 = 2  => 23 pairs (_) / D5 = 2  =>  0 pairs (*)
A2,A3: 3.. / A2 = 3  => 21 pairs (_) / A3 = 3  => 24 pairs (_)
G5,H5: 3.. / G5 = 3  => 24 pairs (_) / H5 = 3  => 17 pairs (_)
B7,B8: 3.. / B7 = 3  => 23 pairs (_) / B8 = 3  => 19 pairs (_)
F7,F8: 3.. / F7 = 3  => 19 pairs (_) / F8 = 3  => 23 pairs (_)
B7,F7: 3.. / B7 = 3  => 23 pairs (_) / F7 = 3  => 19 pairs (_)
B8,F8: 3.. / B8 = 3  => 19 pairs (_) / F8 = 3  => 23 pairs (_)
F2,F3: 4.. / F2 = 4  => 23 pairs (_) / F3 = 4  =>  0 pairs (*)
E5,E6: 4.. / E5 = 4  =>  0 pairs (X) / E6 = 4  => 26 pairs (_)
D7,D8: 4.. / D7 = 4  => 23 pairs (_) / D8 = 4  => 21 pairs (_)
B1,I1: 4.. / B1 = 4  => 24 pairs (_) / I1 = 4  =>  0 pairs (X)
D3,F3: 5.. / D3 = 5  =>  0 pairs (*) / F3 = 5  =>  0 pairs (X)
C4,C5: 5.. / C4 = 5  =>  0 pairs (X) / C5 = 5  => 22 pairs (_)
B3,C3: 6.. / B3 = 6  => 21 pairs (_) / C3 = 6  =>  0 pairs (*)
F5,F6: 6.. / F5 = 6  => 22 pairs (_) / F6 = 6  => 23 pairs (_)
F6,I6: 6.. / F6 = 6  => 23 pairs (_) / I6 = 6  => 22 pairs (_)
A3,C3: 7.. / A3 = 7  =>  0 pairs (*) / C3 = 7  =>  0 pairs (X)
A4,C4: 7.. / A4 = 7  => 21 pairs (_) / C4 = 7  =>  0 pairs (*)
G5,H5: 7.. / G5 = 7  => 17 pairs (_) / H5 = 7  => 24 pairs (_)
F7,F8: 7.. / F7 = 7  => 23 pairs (_) / F8 = 7  => 19 pairs (_)
F8,G8: 7.. / F8 = 7  => 19 pairs (_) / G8 = 7  => 23 pairs (_)
A3,A4: 7.. / A3 = 7  =>  0 pairs (*) / A4 = 7  =>  0 pairs (X)
C3,C4: 7.. / C3 = 7  => 21 pairs (_) / C4 = 7  =>  0 pairs (*)
H5,H7: 7.. / H5 = 7  => 24 pairs (_) / H7 = 7  => 17 pairs (_)
D2,D3: 8.. / D2 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
G2,H2: 9.. / G2 = 9  => 21 pairs (_) / H2 = 9  =>  0 pairs (X)
B4,B5: 9.. / B4 = 9  =>  0 pairs (X) / B5 = 9  =>  0 pairs (_)
C7,C8: 9.. / C7 = 9  => 23 pairs (_) / C8 = 9  => 25 pairs (_)
* DURATION: 0:00:53.295462  START: 23:25:57.258944  END: 23:26:50.554406 2019-04-28
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C1,C2,C3,C5,D2,D3,D4,E6,E9,F2,F3,F7,F8,F9,G5,H5,H9,I1)
* 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3
* PAIR C1: 2,8 BLK 1
B1: 2,8,4                                # reduction candidate for 2,8
B1: 2,8 => CTR
* 9..371654.51.6...7....9..12....3812.....4.....1375....6...8....5...2..6.1746....3
B1: 4                                    # 24 pairs
* PAIR C2: 1,8 BLK 1
A2: 1,8,3,4                              # reduction candidate for 1,8
A2: 1,8 => CTR
* 942371658.5.264..7367895412796538124485912.7621374689562.183.4.5..42..6..74659.83
A2: 3,4                                  # 22 pairs
A3: 1,8,3,4,7                            # reduction candidate for 1,8
A3: 1,8 => CTR
* 94237165835..6...7.67895..2796538124485912..621374689562..8357.538.27469174659.83
A3: 3,4,7                                # 21 pairs
* PAIR C2: 1,8 ROW 2
H2: 1,8,3,4,9                            # reduction candidate for 1,8
H2: 1,8 => CTR
* 9.2371658358264917167895..27...3812.82.1.6..94137..8..6...8....5...2..6.274619583
H2: 3,4,9                                # 21 pairs
* PAIR C2: 1,8 COL C
C8: 1,8,9                                # reduction candidate for 1,8
C8: 9                                    # 25 pairs
C8: 1,8                                  # 23 pairs
* PAIR C3: 6,7 COL C
C4: 6,7,5                                # reduction candidate for 6,7
C4: 5 => CTR
* 9..371654.51.6...7.67.9..12745938126896......2137.6...6...8....5...2..6.174659283
C4: 6,7                                  # 22 pairs
* PAIR I1: 4,8 BLK 3
G2: 4,8,3,9                              # reduction candidate for 4,8
G2: 4,8 => CTR
* 9..37165.351.6..97....9.312....3812.......73..137...4.6...83.7.538.27.6.17465..83
G2: 3,9                                  # 22 pairs
H2: 4,8,1,3,9                            # reduction candidate for 4,8
H2: 4,8 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
H2: 1,3,9                                # 21 pairs
G3: 4,8,3                                # reduction candidate for 4,8
G3: 4,8                                  # 25 pairs
H3: 4,8,1,3                              # reduction candidate for 4,8
H3: 4,8 => CTR
* 9..37165.3582649171678953427...3812....1..73..137.....6..583.7.53.42786.874619..3
H3: 1,3                                  # 22 pairs
* PAIR I1: 4,8 ROW 1
B1: 4,8,2                                # reduction candidate for 4,8
B1: 2 => CTR
* 928371654.51.6...7....9..12....3812.....1.37..1374..9.6321874..589.23761174659283
B1: 4,8                                  # 22 pairs
* PAIR I1: 4,8 COL I
I5: 4,8,5,6,9                            # reduction candidate for 4,8
I5: 4,8 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
I5: 5,6,9                                # 22 pairs
I6: 4,8,5,6,9                            # reduction candidate for 4,8
I6: 4,8 => CTR
* 9..37165..51.6...7....9..12....3812.....1....2137465986...8...55...2..6.174659283
I6: 5,6,9                                # 21 pairs
I8: 4,8,1,9                              # reduction candidate for 4,8
I8: 4,8 => CTR
* 9..37165..5..6...7....9...2....3812.....4....21375....6...8...15...2..6..7461.2.3
I8: 1,9                                  # 22 pairs
* PAIR A4: 4,7 COL A
A3: 4,7,1,3,8                            # reduction candidate for 4,7
A3: 4,7 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
A3: 1,3,8                                # 21 pairs
* PAIR C5: 5,6 BLK 4
C4: 5,6,7                                # reduction candidate for 5,6
C4: 7 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
C4: 5,6                                  # 21 pairs
* PAIR C5: 5,6 ROW 5
F5: 5,6,2,9                              # reduction candidate for 5,6
F5: 5,6                                  # 23 pairs
I5: 5,6,4,8,9                            # reduction candidate for 5,6
I5: 5,6                                  # 26 pairs
* PAIR D4: 5,9 BLK 5
D5: 5,9,1,2                              # reduction candidate for 5,9
D5: 5,9 => CTR
* 94.37165..512649373.78954127...3812.4...1.37.2137468956..18.5495.942.761174659283
D5: 1,2                                  # 22 pairs
F5: 5,9,2,6                              # reduction candidate for 5,9
F5: 5,9 => CTR
* 94.37165..518629.7...594.12..593812.896215..4213746.9.6...8....5...2..6.174659283
F5: 2,6                                  # 22 pairs
F6: 5,9,2,6                              # reduction candidate for 5,9
F6: 5,9 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
F6: 2,6                                  # 22 pairs
* PAIR D4: 5,9 ROW 4
I4: 5,9,4,6                              # reduction candidate for 5,9
I4: 5,9 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
I4: 4,6                                  # 22 pairs
* PAIR D4: 5,9 COL D
D7: 5,9,1,4                              # reduction candidate for 5,9
D7: 5,9 => CTR
* 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583
D7: 1,4                                  # 22 pairs
* PAIR E6: 4,5 BLK 5
E5: 4,5,1                                # reduction candidate for 4,5
E5: 4,5 => CTR
* 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583
E5: 1 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
* PAIR E6: 4,5 ROW 6
G6: 4,5,8,9                              # reduction candidate for 4,5
G6: 4,5                                  # 25 pairs
I6: 4,5,6,8,9                            # reduction candidate for 4,5
I6: 4,5 => CTR
* 942371658351862947...594312..593812..96.1573.213746895629483571538127469174659283
I6: 6,8,9                                # 21 pairs
* PAIR E9: 1,5 BLK 8
D7: 1,5,4,9                              # reduction candidate for 1,5
D7: 1,5                                  # 25 pairs
D7: 4,9                                  # 22 pairs
* PAIR E9: 1,5 COL E
E5: 1,5,4                                # reduction candidate for 1,5
E5: 4 => CTR
* 9..37165..5.264..7...895..2...93812..9.14.....1375....6..58.2..5..42..6.274619583
E5: 1,5                                  # 26 pairs
* PAIR F9: 5,9 BLK 8
D7: 5,9,1,4                              # reduction candidate for 5,9
D7: 5,9 => CTR
* 9..37165..5.264..7...895..2...93812..9.1......137.....6..58.2..5..42..6.274619583
D7: 1,4                                  # 22 pairs
* PAIR F9: 5,9 ROW 9
G9: 5,9,2,8                              # reduction candidate for 5,9
G9: 5,9 => CTR
* 942371658.58264..7.67895..279653812..2.1......137.2..663..872..58..2376.27461..83
G9: 2,8                                  # 22 pairs
* PAIR F9: 5,9 COL F
F5: 5,9,2,6                              # reduction candidate for 5,9
F5: 5,9 => CTR
* 94.37165..518629.7...594.12..593812.896215..4213746.9.6...8....5...2..6.174659283
F5: 2,6                                  # 22 pairs
F6: 5,9,2,6                              # reduction candidate for 5,9
F6: 5,9 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
F6: 2,6                                  # 22 pairs
* PAIR H9: 8,9 BLK 9
G8: 8,9,4,7                              # reduction candidate for 8,9
G8: 8,9                                  # 27 pairs
I8: 8,9,1,4                              # reduction candidate for 8,9
I8: 8,9                                  # 27 pairs
G9: 8,9,2,5                              # reduction candidate for 8,9
G9: 8,9 => CTR
* 9.237165..5..6...7...594..2..593812...........137.....6...8.2.55...2..61274615..3
G9: 2,5                                  # 22 pairs
* PAIR H9: 8,9 COL H
H2: 8,9,1,3,4                            # reduction candidate for 8,9
H2: 8,9 => CTR
* 9.237165.1582643973.7895.12....3812.....4.73..1375..4.62..83.7.53..27.6..7461.2.3
H2: 1,3,4                                # 21 pairs
H6: 8,9,4                                # reduction candidate for 8,9
H6: 8,9                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-squeezed-naughts-base-pr-000.dot
* REASONING
* DIS # B1: 2,8 => CTR => B1: 4
* DIS # A2: 1,8 => CTR => A2: 3,4
* DIS # A3: 1,8 => CTR => A3: 3,4,7
* DIS # H2: 1,8 => CTR => H2: 3,4,9
* DIS # C4: 5 => CTR => C4: 6,7
* DIS # G2: 4,8 => CTR => G2: 3,9
* PRF # H2: 4,8 => SOL
* DIS # H3: 4,8 => CTR => H3: 1,3
* DIS # B1: 2 => CTR => B1: 4,8
* PRF # I5: 4,8 => SOL
* DIS # I6: 4,8 => CTR => I6: 5,6,9
* DIS # I8: 4,8 => CTR => I8: 1,9
* PRF # A3: 4,7 => SOL
* PRF # C4: 7 => SOL
* DIS # D5: 5,9 => CTR => D5: 1,2
* DIS # F5: 5,9 => CTR => F5: 2,6
* PRF # F6: 5,9 => SOL
* PRF # I4: 5,9 => SOL
* DIS # D7: 5,9 => CTR => D7: 1,4
* DIS # E5: 4,5 => CTR => E5: 1
* PRF # E5: 1 => SOL
* DIS # I6: 4,5 => CTR => I6: 6,8,9
* DIS # E5: 4 => CTR => E5: 1,5
* DIS # D7: 5,9 => CTR => D7: 1,4
* DIS # G9: 5,9 => CTR => G9: 2,8
* DIS # F5: 5,9 => CTR => F5: 2,6
* PRF # F6: 5,9 => SOL
* DIS # G9: 8,9 => CTR => G9: 2,5
* DIS # H2: 8,9 => CTR => H2: 1,3,4
* CNT  29 HDP CHAINS /  67 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,B8,C1,C2,C3,C5,D2,D3,D4,E6,E9,F2,F3,F7,F8,F9,G5,H5,H9,I1)
* 9..37165..5..6...7....9...2....3812...........137.....6...8....5...2..6..746....3
* PAIR C1: 2,8 BLK 1
B1: 2,8,4                                # reduction candidate for 2,8
B1: 2,8 => CTR
* 9..371654.51.6...7....9..12....3812.....4.....1375....6...8....5...2..6.1746....3
* PAIR C2: 1,8 BLK 1
A2: 1,8,3                                # reduction candidate for 1,8
A2: 1,8 => CTR
* 942371658.5.264.3736789541279653812448591237621374689562.183.4.5..42..6..74659.83
A3: 1,8,7                                # reduction candidate for 1,8
A3: 1,8 => CTR
* 94237165835..6...7.67895..2796538124..5.......1374....6...8....5...2..6..74659.83
A3: 7 => SOLVED
* 942371658351862947786594312467938125895216734213745896629483571538127469174659283
* DURATION: 0:00:03.765794  START: 23:27:38.908198  END: 23:27:42.673992 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-squeezed-naughts-base-pr-001.dot
* REASONING
* DIS # B1: 2,8 => CTR => B1: 4
* DIS B1: 4 # A2: 1,8 => CTR => A2: 3
* DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7
* PRF B1: 4 + A2: 3 + A3: 7 => SOL
* STA B1: 4 + A2: 3 + A3: 7
* CNT   4 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuwiki.org/Interesting_Sudokus

24 Clues, minimal "2 squeezed naughts mirrored by diagonal"

Discovered by Klaus Brenner

Solution

position: 942371658351862947786594312467938125895216734213745896629483571538127469174659283 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:

* DIS # B1: 2,8 => CTR => B1: 4
* INC # B1: 4 => UNS
* DIS # A2: 1,8 => CTR => A2: 3,4
* INC # A2: 3,4 => UNS
* DIS # A3: 1,8 => CTR => A3: 3,4,7
* INC # A3: 3,4,7 => UNS
* DIS # H2: 1,8 => CTR => H2: 3,4,9
* INC # H2: 3,4,9 => UNS
* INC # C8: 1,8 => UNS
* INC # C8: 9 => UNS
* INC # C4: 6,7 => UNS
* DIS # C4: 5 => CTR => C4: 6,7
* DIS # G2: 4,8 => CTR => G2: 3,9
* INC # G2: 3,9 => UNS
* PRF # H2: 4,8 => SOL
* INC # H2: 1,3,9 => UNS
* INC # G3: 4,8 => UNS
* DIS # H3: 4,8 => CTR => H3: 1,3
* INC # H3: 1,3 => UNS
* INC # B1: 4,8 => UNS
* DIS # B1: 2 => CTR => B1: 4,8
* PRF # I5: 4,8 => SOL
* INC # I5: 5,6,9 => UNS
* DIS # I6: 4,8 => CTR => I6: 5,6,9
* INC # I6: 5,6,9 => UNS
* DIS # I8: 4,8 => CTR => I8: 1,9
* INC # I8: 1,9 => UNS
* PRF # A3: 4,7 => SOL
* INC # A3: 1,3,8 => UNS
* INC # C4: 5,6 => UNS
* PRF # C4: 7 => SOL
* INC # F5: 5,6 => UNS
* INC # I5: 5,6 => UNS
* DIS # D5: 5,9 => CTR => D5: 1,2
* INC # D5: 1,2 => UNS
* DIS # F5: 5,9 => CTR => F5: 2,6
* INC # F5: 2,6 => UNS
* PRF # F6: 5,9 => SOL
* INC # F6: 2,6 => UNS
* PRF # I4: 5,9 => SOL
* INC # I4: 4,6 => UNS
* DIS # D7: 5,9 => CTR => D7: 1,4
* INC # D7: 1,4 => UNS
* DIS # E5: 4,5 => CTR => E5: 1
* PRF # E5: 1 => SOL
* INC # G6: 4,5 => UNS
* DIS # I6: 4,5 => CTR => I6: 6,8,9
* INC # I6: 6,8,9 => UNS
* INC # D7: 1,5 => UNS
* INC # D7: 4,9 => UNS
* INC # E5: 1,5 => UNS
* DIS # E5: 4 => CTR => E5: 1,5
* DIS # D7: 5,9 => CTR => D7: 1,4
* INC # D7: 1,4 => UNS
* DIS # G9: 5,9 => CTR => G9: 2,8
* INC # G9: 2,8 => UNS
* DIS # F5: 5,9 => CTR => F5: 2,6
* INC # F5: 2,6 => UNS
* PRF # F6: 5,9 => SOL
* INC # F6: 2,6 => UNS
* INC # G8: 8,9 => UNS
* INC # I8: 8,9 => UNS
* DIS # G9: 8,9 => CTR => G9: 2,5
* INC # G9: 2,5 => UNS
* DIS # H2: 8,9 => CTR => H2: 1,3,4
* INC # H2: 1,3,4 => UNS
* INC # H6: 8,9 => UNS
* CNT  67 HDP CHAINS /  67 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 2,8 => CTR => B1: 4
* DIS B1: 4 # A2: 1,8 => CTR => A2: 3
* DIS B1: 4 + A2: 3 # A3: 1,8 => CTR => A3: 7
* PRF B1: 4 + A2: 3 + A3: 7 => SOL
* STA B1: 4 + A2: 3 + A3: 7
* CNT   4 HDP CHAINS /   3 HYP OPENED