Analysis of zz-www.sudokuoftheday.co.uk-20060729-absurd-base.sdk

Contents

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

level: medium

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

position: ..2.....7......1.9...13..5.1.....79....74...88..2.95...2.8..9...6.9.1...58...4.6. initial

Autosolve

position: .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 4,6 => CTR => A2: 3
* DIS # D1: 4,6 => CTR => D1: 5
* PRF # C3: 4,7 => SOL
* DIS # C3: 8 => CTR => C3: 4,7
* DIS # D1: 4,6 => CTR => D1: 5
* DIS # A2: 4,6 => CTR => A2: 3
* DIS # F1: 5 => CTR => F1: 6,8
* DIS # E4: 5 => CTR => E4: 6,8
* DIS # G3: 4,6 => CTR => G3: 8
* PRF # G3: 8 => SOL
* DIS # I6: 3 => CTR => I6: 4,6
* DIS # C6: 3,7 => CTR => C6: 6
* PRF # C6: 6 => SOL
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F4: 5,6 => SOL
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # C4: 5,6 => CTR => C4: 3,4
* DIS # D1: 4 => CTR => D1: 5,6
* PRF # I6: 4 => SOL
* DIS # C5: 3,6 => CTR => C5: 5
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* DIS # H7: 3,4 => CTR => H7: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # A8: 3,4 => CTR => A8: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # C2: 3,4 => CTR => C2: 5,8
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* DIS # F1: 5,6 => CTR => F1: 8
* PRF # F1: 8 => SOL
* PRF # F4: 5,6 => SOL
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # H7: 3,4 => CTR => H7: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # A7: 7 => CTR => A7: 3,4
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* CNT  41 HDP CHAINS /  68 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 # A2: 4,6 => CTR => A2: 3
* PRF A2: 3 # C3: 4,7 => SOL
* STA A2: 3 + C3: 4,7
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..2.....7......1.9...13..5.1.....79....74...88..2.95...2.8..9...6.9.1...58...4.6. initial
.12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261 autosolve
612598347358467129947132856134685792295743618876219534421856973763921485589374261 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A1: 4,6
B3: 4,7
D2: 4,6
E2: 6,8
I3: 4,6
B6: 3,7
D4: 5,6
G5: 3,6
H6: 3,4
C8: 3,4
E7: 5,6
F7: 5,6
I7: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,H1: 3.. / G1 = 3  =>  0 pairs (*) / H1 = 3  =>  0 pairs (X)
F4,F5: 3.. / F4 = 3  =>  0 pairs (X) / F5 = 3  =>  0 pairs (_)
I6,I7: 3.. / I6 = 3  =>  0 pairs (X) / I7 = 3  => 16 pairs (_)
D1,D2: 4.. / D1 = 4  =>  0 pairs (X) / D2 = 4  => 15 pairs (_)
B4,C4: 4.. / B4 = 4  =>  0 pairs (X) / C4 = 4  => 23 pairs (_)
H6,I6: 4.. / H6 = 4  => 15 pairs (_) / I6 = 4  =>  0 pairs (*)
B2,C2: 5.. / B2 = 5  => 16 pairs (_) / C2 = 5  =>  0 pairs (X)
D1,F1: 5.. / D1 = 5  => 16 pairs (_) / F1 = 5  =>  0 pairs (X)
E7,F7: 5.. / E7 = 5  => 14 pairs (_) / F7 = 5  =>  0 pairs (X)
C5,F5: 5.. / C5 = 5  => 17 pairs (_) / F5 = 5  =>  0 pairs (X)
B2,B4: 5.. / B2 = 5  => 16 pairs (_) / B4 = 5  =>  0 pairs (X)
D1,D4: 5.. / D1 = 5  => 16 pairs (_) / D4 = 5  =>  0 pairs (X)
E4,E7: 5.. / E4 = 5  =>  0 pairs (X) / E7 = 5  => 14 pairs (_)
A1,A2: 6.. / A1 = 6  => 15 pairs (_) / A2 = 6  =>  0 pairs (X)
G3,I3: 6.. / G3 = 6  =>  0 pairs (X) / I3 = 6  =>  0 pairs (_)
G5,I6: 6.. / G5 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
E7,F7: 6.. / E7 = 6  =>  0 pairs (X) / F7 = 6  => 14 pairs (_)
C6,I6: 6.. / C6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
G3,G5: 6.. / G3 = 6  =>  0 pairs (X) / G5 = 6  =>  0 pairs (_)
I3,I6: 6.. / I3 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
B3,C3: 7.. / B3 = 7  =>  0 pairs (X) / C3 = 7  =>  0 pairs (_)
B6,C6: 7.. / B6 = 7  =>  0 pairs (*) / C6 = 7  =>  0 pairs (X)
A7,A8: 7.. / A7 = 7  =>  0 pairs (X) / A8 = 7  => 14 pairs (_)
H7,H8: 7.. / H7 = 7  => 14 pairs (_) / H8 = 7  =>  0 pairs (X)
A7,H7: 7.. / A7 = 7  =>  0 pairs (X) / H7 = 7  => 14 pairs (_)
A8,H8: 7.. / A8 = 7  => 14 pairs (_) / H8 = 7  =>  0 pairs (X)
B3,B6: 7.. / B3 = 7  =>  0 pairs (X) / B6 = 7  =>  0 pairs (_)
C3,C6: 7.. / C3 = 7  =>  0 pairs (*) / C6 = 7  =>  0 pairs (X)
C2,C3: 8.. / C2 = 8  =>  0 pairs (*) / C3 = 8  =>  0 pairs (X)
F1,E2: 8.. / F1 = 8  =>  0 pairs (*) / E2 = 8  =>  0 pairs (X)
E4,F4: 8.. / E4 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
G8,H8: 8.. / G8 = 8  =>  0 pairs (X) / H8 = 8  => 16 pairs (_)
C2,E2: 8.. / C2 = 8  =>  0 pairs (*) / E2 = 8  =>  0 pairs (X)
C3,G3: 8.. / C3 = 8  =>  0 pairs (X) / G3 = 8  =>  0 pairs (_)
E2,E4: 8.. / E2 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
F1,F4: 8.. / F1 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
H1,H8: 8.. / H1 = 8  =>  0 pairs (X) / H8 = 8  => 16 pairs (_)
* DURATION: 0:00:44.615226  START: 01:23:20.584294  END: 01:24:05.199520 2019-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C8,D2,D4,E2,E7,F7,G5,H6,I3,I7)
* .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261
* PAIR A1: 4,6 BLK 1
A2: 4,6,3                                # reduction candidate for 4,6
A2: 4,6 => CTR
* .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261
A2: 3                                    # 19 pairs
* PAIR A1: 4,6 ROW 1
D1: 4,6,5                                # reduction candidate for 4,6
D1: 4,6 => CTR
* .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261
D1: 5                                    # 16 pairs
* PAIR B3: 4,7 BLK 1
C3: 4,7,8                                # reduction candidate for 4,7
C3: 4,7 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
C3: 8 => CTR
* .12.9.837....871299781326541.....79229.74..18837219546.218..9.3.6.921485589374261
* PAIR D2: 4,6 BLK 2
D1: 4,6,5                                # reduction candidate for 4,6
D1: 4,6 => CTR
* .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261
D1: 5                                    # 16 pairs
* PAIR D2: 4,6 ROW 2
A2: 4,6,3                                # reduction candidate for 4,6
A2: 4,6 => CTR
* .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261
A2: 3                                    # 19 pairs
* PAIR E2: 6,8 BLK 2
F1: 6,8,5                                # reduction candidate for 6,8
F1: 5 => CTR
* .12.95..7....871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261
F1: 6,8                                  # 16 pairs
* PAIR E2: 6,8 COL E
E4: 6,8,5                                # reduction candidate for 6,8
E4: 5 => CTR
* .12.9...7....871299.8132.5.1...587922957436188..2195...218..9...6.921..5589374261
E4: 6,8                                  # 14 pairs
* PAIR I3: 4,6 BLK 3
G3: 4,6,8                                # reduction candidate for 4,6
G3: 4,6 => CTR
* .12.9...7....871299781326541....879229.743.188.72195.6.218..9.3.6.921..5589374261
G3: 8 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* PAIR I3: 4,6 COL I
I6: 4,6,3                                # reduction candidate for 4,6
I6: 3 => CTR
* .12.98437..84671299471328561.4...79229.74.618876219543.218..9.4.6.921385589374261
I6: 4,6                                  # 16 pairs
* PAIR B6: 3,7 BLK 4
C6: 3,7,6                                # reduction candidate for 3,7
C6: 3,7 => CTR
* 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261
C6: 6 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* PAIR D4: 5,6 BLK 5
E4: 5,6,8                                # reduction candidate for 5,6
E4: 5,6 => CTR
* .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
E4: 8 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
F4: 5,6,3,8                              # reduction candidate for 5,6
F4: 5,6 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
F4: 3,8                                  # 14 pairs
F5: 5,6,3                                # reduction candidate for 5,6
F5: 5,6 => CTR
* 612598..7.584671299.713285614.68379229.7456188.62195...218569...6.921.85589374261
F5: 3 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* PAIR D4: 5,6 ROW 4
C4: 5,6,3,4                              # reduction candidate for 5,6
C4: 5,6 => CTR
* .12.98..7.58.6712997413285614.68379229.74561883.2195...218..9...6.921..5589374261
C4: 3,4                                  # 19 pairs
* PAIR D4: 5,6 COL D
D1: 5,6,4                                # reduction candidate for 5,6
D1: 4 => CTR
* .12495..7...6871299.8132.5.1..5687922957436188..2195...218..9...6.921..5589374261
D1: 5,6                                  # 15 pairs
* PAIR G5: 3,6 BLK 6
I6: 3,6,4                                # reduction candidate for 3,6
I6: 4 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
I6: 3,6                                  # 15 pairs
* PAIR G5: 3,6 ROW 5
C5: 3,6,5                                # reduction candidate for 3,6
C5: 3,6 => CTR
* 612598..73584671299..1328561.568379229.7456188.62195...218569...6.921.85589374261
C5: 5                                    # 17 pairs
F5: 3,6,5                                # reduction candidate for 3,6
F5: 3,6                                  # 17 pairs
* PAIR H6: 3,4 BLK 6
I6: 3,4,6                                # reduction candidate for 3,4
I6: 3,4 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
I6: 6 => CTR
* 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261
* PAIR H6: 3,4 COL H
H1: 3,4,8                                # reduction candidate for 3,4
H1: 3,4                                  # 16 pairs
H7: 3,4,7                                # reduction candidate for 3,4
H7: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261
H7: 7                                    # 14 pairs
H8: 3,4,7,8                              # reduction candidate for 3,4
H8: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
H8: 7,8                                  # 14 pairs
* PAIR C8: 3,4 BLK 7
A7: 3,4,7                                # reduction candidate for 3,4
A7: 3,4                                  # 14 pairs
A8: 3,4,7                                # reduction candidate for 3,4
A8: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261
A8: 7                                    # 14 pairs
* PAIR C8: 3,4 ROW 8
G8: 3,4,8                                # reduction candidate for 3,4
G8: 3,4                                  # 16 pairs
H8: 3,4,7,8                              # reduction candidate for 3,4
H8: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
H8: 7,8                                  # 14 pairs
* PAIR C8: 3,4 COL C
C2: 3,4,5,8                              # reduction candidate for 3,4
C2: 3,4 => CTR
* .12.9...7.5..871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
C2: 5,8                                  # 14 pairs
C4: 3,4,5,6                              # reduction candidate for 3,4
C4: 3,4                                  # 19 pairs
* PAIR E7: 5,6 COL E
E4: 5,6,8                                # reduction candidate for 5,6
E4: 5,6 => CTR
* .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
E4: 8 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* PAIR F7: 5,6 COL F
F1: 5,6,8                                # reduction candidate for 5,6
F1: 5,6 => CTR
* .12.9...7....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
F1: 8 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
F4: 5,6,3,8                              # reduction candidate for 5,6
F4: 5,6 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
F4: 3,8                                  # 14 pairs
F5: 5,6,3                                # reduction candidate for 5,6
F5: 5,6 => CTR
* 612598..7.584671299.713285614.68379229.7456188.62195...218569...6.921.85589374261
F5: 3 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* PAIR I7: 3,4 BLK 9
H7: 3,4,7                                # reduction candidate for 3,4
H7: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261
H7: 7                                    # 14 pairs
G8: 3,4,8                                # reduction candidate for 3,4
G8: 3,4                                  # 16 pairs
H8: 3,4,7,8                              # reduction candidate for 3,4
H8: 3,4 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195...218..9...6.921..5589374261
H8: 7,8                                  # 14 pairs
* PAIR I7: 3,4 ROW 7
A7: 3,4,7                                # reduction candidate for 3,4
A7: 7 => CTR
* .12.9..87....871299.8132.5.1....879229.7436188..2195..7218..9...6.921.75589374261
A7: 3,4                                  # 14 pairs
* PAIR I7: 3,4 COL I
I6: 3,4,6                                # reduction candidate for 3,4
I6: 3,4 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
I6: 6 => CTR
* 6124958373..6871299781326541..5..79229.74.3188..2195464218..973763921485589374261
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060729-absurd-base-pr-000.dot
* REASONING
* DIS # A2: 4,6 => CTR => A2: 3
* DIS # D1: 4,6 => CTR => D1: 5
* PRF # C3: 4,7 => SOL
* DIS # C3: 8 => CTR => C3: 4,7
* DIS # D1: 4,6 => CTR => D1: 5
* DIS # A2: 4,6 => CTR => A2: 3
* DIS # F1: 5 => CTR => F1: 6,8
* DIS # E4: 5 => CTR => E4: 6,8
* DIS # G3: 4,6 => CTR => G3: 8
* PRF # G3: 8 => SOL
* DIS # I6: 3 => CTR => I6: 4,6
* DIS # C6: 3,7 => CTR => C6: 6
* PRF # C6: 6 => SOL
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F4: 5,6 => SOL
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # C4: 5,6 => CTR => C4: 3,4
* DIS # D1: 4 => CTR => D1: 5,6
* PRF # I6: 4 => SOL
* DIS # C5: 3,6 => CTR => C5: 5
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* DIS # H7: 3,4 => CTR => H7: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # A8: 3,4 => CTR => A8: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # C2: 3,4 => CTR => C2: 5,8
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* DIS # F1: 5,6 => CTR => F1: 8
* PRF # F1: 8 => SOL
* PRF # F4: 5,6 => SOL
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # H7: 3,4 => CTR => H7: 7
* DIS # H8: 3,4 => CTR => H8: 7,8
* DIS # A7: 7 => CTR => A7: 3,4
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* CNT  41 HDP CHAINS /  68 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C8,D2,D4,E2,E7,F7,G5,H6,I3,I7)
* .12.9...7.....71299..132.5.1.....79229.74..188..2195...218..9...6.921..5589374261
* PAIR A1: 4,6 BLK 1
A2: 4,6,3                                # reduction candidate for 4,6
A2: 4,6 => CTR
* .12.9...7.53.87129978132.5.14....79229.74..188..2195...218..9...64921..5589374261
* PAIR B3: 4,7 BLK 1
C3: 4,7,8                                # reduction candidate for 4,7
C3: 4,7 => SOLVED
* 612598347358467129947132856134685792295743618876219534421856973763921485589374261
* DURATION: 0:00:02.987188  START: 01:24:53.314719  END: 01:24:56.301907 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060729-absurd-base-pr-001.dot
* REASONING
* DIS # A2: 4,6 => CTR => A2: 3
* PRF A2: 3 # C3: 4,7 => SOL
* STA A2: 3 + C3: 4,7
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060729, absurd

Solution

position: 612598347358467129947132856134685792295743618876219534421856973763921485589374261 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 # A2: 4,6 => CTR => A2: 3
* INC # A2: 3 => UNS
* DIS # D1: 4,6 => CTR => D1: 5
* INC # D1: 5 => UNS
* PRF # C3: 4,7 => SOL
* DIS # C3: 8 => CTR => C3: 4,7
* DIS # D1: 4,6 => CTR => D1: 5
* INC # D1: 5 => UNS
* DIS # A2: 4,6 => CTR => A2: 3
* INC # A2: 3 => UNS
* INC # F1: 6,8 => UNS
* DIS # F1: 5 => CTR => F1: 6,8
* INC # E4: 6,8 => UNS
* DIS # E4: 5 => CTR => E4: 6,8
* DIS # G3: 4,6 => CTR => G3: 8
* PRF # G3: 8 => SOL
* INC # I6: 4,6 => UNS
* DIS # I6: 3 => CTR => I6: 4,6
* DIS # C6: 3,7 => CTR => C6: 6
* PRF # C6: 6 => SOL
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # F4: 5,6 => SOL
* INC # F4: 3,8 => UNS
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # C4: 5,6 => CTR => C4: 3,4
* INC # C4: 3,4 => UNS
* INC # D1: 5,6 => UNS
* DIS # D1: 4 => CTR => D1: 5,6
* INC # I6: 3,6 => UNS
* PRF # I6: 4 => SOL
* DIS # C5: 3,6 => CTR => C5: 5
* INC # C5: 5 => UNS
* INC # F5: 3,6 => UNS
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* INC # H1: 3,4 => UNS
* DIS # H7: 3,4 => CTR => H7: 7
* INC # H7: 7 => UNS
* DIS # H8: 3,4 => CTR => H8: 7,8
* INC # H8: 7,8 => UNS
* INC # A7: 3,4 => UNS
* DIS # A8: 3,4 => CTR => A8: 7
* INC # A8: 7 => UNS
* INC # G8: 3,4 => UNS
* DIS # H8: 3,4 => CTR => H8: 7,8
* INC # H8: 7,8 => UNS
* DIS # C2: 3,4 => CTR => C2: 5,8
* INC # C2: 5,8 => UNS
* INC # C4: 3,4 => UNS
* DIS # E4: 5,6 => CTR => E4: 8
* PRF # E4: 8 => SOL
* DIS # F1: 5,6 => CTR => F1: 8
* PRF # F1: 8 => SOL
* PRF # F4: 5,6 => SOL
* INC # F4: 3,8 => UNS
* DIS # F5: 5,6 => CTR => F5: 3
* PRF # F5: 3 => SOL
* DIS # H7: 3,4 => CTR => H7: 7
* INC # H7: 7 => UNS
* INC # G8: 3,4 => UNS
* DIS # H8: 3,4 => CTR => H8: 7,8
* INC # H8: 7,8 => UNS
* INC # A7: 3,4 => UNS
* DIS # A7: 7 => CTR => A7: 3,4
* PRF # I6: 3,4 => SOL
* DIS # I6: 6 => CTR => I6: 3,4
* CNT  68 HDP CHAINS /  68 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 4,6 => CTR => A2: 3
* PRF A2: 3 # C3: 4,7 => SOL
* STA A2: 3 + C3: 4,7
* CNT   2 HDP CHAINS /   2 HYP OPENED