Analysis of zz-www.sudokuoftheday.co.uk-20060824-absurd-base.sdk

Contents

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

level: medium

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

position: 7......5.....6...9......1.8.48.1..9..9..8...3.7.6.5.....9.2..4......1....3..4.861 initial

Autosolve

position: 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 1,4 => CTR => A2: 3,8
* DIS # C2: 1,4 => CTR => C2: 3,5
* DIS # D1: 1,4 => CTR => D1: 2,9
* DIS # D2: 5,7 => CTR => D2: 1,2,4
* DIS # A5: 2,5 => CTR => A5: 6
* DIS # C9: 2,5 => CTR => C9: 7
* DIS # A2: 1,3 => CTR => A2: 4,8
* PRF # A2: 4,8 => SOL
* DIS # C2: 1,3 => CTR => C2: 4,5
* DIS # D2: 2,7 => CTR => D2: 1,4,5
* DIS # G1: 2,4 => CTR => G1: 6
* PRF # G1: 6 => SOL
* PRF # G2: 2,4 => SOL
* DIS # G2: 3 => CTR => G2: 2,4
* PRF # I1: 2,4 => SOL
* DIS # I1: 6 => CTR => I1: 2,4
* DIS # B7: 1,8 => CTR => B7: 5
* PRF # B7: 5 => SOL
* PRF # A2: 1,8 => SOL
* PRF # A2: 4,8 => SOL
* DIS # A2: 1,3 => CTR => A2: 4,8
* DIS # C9: 2,5 => CTR => C9: 7
* DIS # A5: 2,5 => CTR => A5: 6
* DIS # D9: 9 => CTR => D9: 5,7
* DIS # C8: 5,7 => CTR => C8: 4,6
* DIS # D9: 7,9 => CTR => D9: 5
* DIS # G7: 5,7 => CTR => G7: 3
* PRF # G7: 3 => SOL
* DIS # I4: 5,7 => CTR => I4: 6
* PRF # I4: 6 => SOL
* PRF # H2: 2,3 => SOL
* CNT  31 HDP CHAINS /  53 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: 1,4 => CTR => A2: 3,8
* DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5
* DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9
* PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL
* STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

7......5.....6...9......1.8.48.1..9..9..8...3.7.6.5.....9.2..4......1....3..4.861 initial
7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861 autosolve
714938652825167439963452178548213796692784513371695284159826347486371925237549861 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
C1: 1,4
E3: 5,7
C5: 2,5
A6: 1,3
C6: 1,3
D4: 2,7
G6: 2,4
I6: 2,4
A7: 1,8
A8: 4,8
A9: 2,5
D7: 3,8
D8: 3,8
E8: 5,7
F9: 7,9
I7: 5,7
H8: 2,3
I8: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D2: 1.. / D1 = 1  =>  0 pairs (X) / D2 = 1  => 19 pairs (_)
A6,C6: 1.. / A6 = 1  =>  0 pairs (X) / C6 = 1  =>  0 pairs (_)
A7,B7: 1.. / A7 = 1  =>  0 pairs (*) / B7 = 1  =>  0 pairs (X)
G6,I6: 2.. / G6 = 2  => 19 pairs (_) / I6 = 2  =>  0 pairs (X)
A9,C9: 2.. / A9 = 2  => 21 pairs (_) / C9 = 2  =>  0 pairs (X)
H8,I8: 2.. / H8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
A4,D4: 2.. / A4 = 2  =>  0 pairs (X) / D4 = 2  => 21 pairs (_)
C5,C9: 2.. / C5 = 2  => 21 pairs (_) / C9 = 2  =>  0 pairs (X)
A6,C6: 3.. / A6 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
D7,D8: 3.. / D7 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
G7,H8: 3.. / G7 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
C3,H3: 3.. / C3 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
D7,G7: 3.. / D7 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
D8,H8: 3.. / D8 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
A2,A6: 3.. / A2 = 3  =>  0 pairs (X) / A6 = 3  =>  0 pairs (_)
G2,G7: 3.. / G2 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
D5,F5: 4.. / D5 = 4  => 19 pairs (_) / F5 = 4  => 22 pairs (_)
G6,I6: 4.. / G6 = 4  =>  0 pairs (X) / I6 = 4  => 19 pairs (_)
A8,C8: 4.. / A8 = 4  => 17 pairs (_) / C8 = 4  =>  0 pairs (X)
A2,A8: 4.. / A2 = 4  =>  0 pairs (X) / A8 = 4  => 17 pairs (_)
I1,I6: 4.. / I1 = 4  =>  0 pairs (X) / I6 = 4  => 19 pairs (_)
E8,D9: 5.. / E8 = 5  =>  0 pairs (X) / D9 = 5  => 19 pairs (_)
E3,E8: 5.. / E3 = 5  => 19 pairs (_) / E8 = 5  =>  0 pairs (X)
B3,C3: 6.. / B3 = 6  => 21 pairs (_) / C3 = 6  =>  0 pairs (X)
G1,I1: 6.. / G1 = 6  =>  0 pairs (*) / I1 = 6  =>  0 pairs (X)
A4,A5: 6.. / A4 = 6  =>  0 pairs (X) / A5 = 6  => 20 pairs (_)
B8,C8: 6.. / B8 = 6  =>  0 pairs (X) / C8 = 6  => 21 pairs (_)
A5,G5: 6.. / A5 = 6  => 20 pairs (_) / G5 = 6  =>  0 pairs (X)
B3,B8: 6.. / B3 = 6  => 21 pairs (_) / B8 = 6  =>  0 pairs (X)
C3,C8: 6.. / C3 = 6  =>  0 pairs (X) / C8 = 6  => 21 pairs (_)
I1,I4: 6.. / I1 = 6  =>  0 pairs (X) / I4 = 6  =>  0 pairs (_)
H2,H3: 7.. / H2 = 7  => 19 pairs (_) / H3 = 7  =>  0 pairs (*)
C8,C9: 7.. / C8 = 7  =>  0 pairs (X) / C9 = 7  => 19 pairs (_)
G7,I7: 7.. / G7 = 7  =>  0 pairs (X) / I7 = 7  => 19 pairs (_)
C8,E8: 7.. / C8 = 7  =>  0 pairs (X) / E8 = 7  => 19 pairs (_)
E3,E8: 7.. / E3 = 7  =>  0 pairs (X) / E8 = 7  => 19 pairs (_)
I4,I7: 7.. / I4 = 7  =>  0 pairs (X) / I7 = 7  => 19 pairs (_)
F1,F2: 8.. / F1 = 8  => 20 pairs (_) / F2 = 8  => 20 pairs (_)
D7,D8: 8.. / D7 = 8  =>  0 pairs (*) / D8 = 8  =>  0 pairs (X)
B1,F1: 8.. / B1 = 8  => 20 pairs (_) / F1 = 8  => 20 pairs (_)
D1,F1: 9.. / D1 = 9  => 19 pairs (_) / F1 = 9  =>  0 pairs (X)
D9,F9: 9.. / D9 = 9  =>  0 pairs (X) / F9 = 9  => 19 pairs (_)
D1,D9: 9.. / D1 = 9  => 19 pairs (_) / D9 = 9  =>  0 pairs (X)
F1,F9: 9.. / F1 = 9  =>  0 pairs (X) / F9 = 9  => 19 pairs (_)
* DURATION: 0:00:57.238499  START: 02:02:11.669360  END: 02:03:08.907859 2019-05-01
* CP COUNT: (44)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,A9,C1,C5,C6,D4,D7,D8,E3,E8,F9,G6,H8,I6,I7,I8)
* 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861
* PAIR C1: 1,4 BLK 1
A2: 1,4,3,8                              # reduction candidate for 1,4
A2: 1,4 => CTR
* 7.4.3..5.1...6.4.99.....1.8.48.13.9..9..8..13371695284819326.4.4..8.1932.3..4.861
A2: 3,8                                  # 18 pairs
C2: 1,4,3,5                              # reduction candidate for 1,4
C2: 1,4 => CTR
* 7...3..5.....6...99.....1.8.48.13.9..9..8..13173695.8.819326.4.4..8.1932.3..4.861
C2: 3,5                                  # 19 pairs
* PAIR C1: 1,4 ROW 1
D1: 1,4,2,9                              # reduction candidate for 1,4
D1: 1,4 => CTR
* 78..39256....684.99...7.1.8.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3.947861
D1: 2,9                                  # 20 pairs
* PAIR E3: 5,7 BLK 2
D2: 5,7,1,2,4                            # reduction candidate for 5,7
D2: 5,7 => CTR
* 784139.5.....684.99...7.1.8.48.13.9..9..8..13.7.695284..9.263474.7..19...3.947861
D2: 1,2,4                                # 19 pairs
D3: 5,7,2,4                              # reduction candidate for 5,7
D3: 5,7                                  # 22 pairs
* PAIR C5: 2,5 BLK 4
A4: 2,5,6                                # reduction candidate for 2,5
A4: 2,5                                  # 20 pairs
A5: 2,5,6                                # reduction candidate for 2,5
A5: 2,5 => CTR
* 7...3.456....6.3.99.3...1.8648213.9..9..8.613371695284..9.26.4......1932.3..4.861
A5: 6                                    # 20 pairs
* PAIR C5: 2,5 COL C
C9: 2,5,7                                # reduction candidate for 2,5
C9: 2,5 => CTR
* 7...3..5.....6...99.6.7.138.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3..4.861
C9: 7                                    # 19 pairs
* PAIR A6: 1,3 COL A
A2: 1,3,4,8                              # reduction candidate for 1,3
A2: 1,3 => CTR
* 7...3..5.....6.3.99.3...1.8.48.13.9..9..8..13371695284819326.4.4.6871932.37549861
A2: 4,8 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
* PAIR C6: 1,3 COL C
C2: 1,3,4,5                              # reduction candidate for 1,3
C2: 1,3 => CTR
* 7.493.652.5.162479926.5.138.48.13.96695284713.71695284..9.263474..3.1925.3.549861
C2: 4,5                                  # 19 pairs
* PAIR D4: 2,7 BLK 5
D5: 2,7,4                                # reduction candidate for 2,7
D5: 2,7                                  # 22 pairs
F5: 2,7,4                                # reduction candidate for 2,7
F5: 2,7                                  # 19 pairs
* PAIR D4: 2,7 COL D
D2: 2,7,1,4,5                            # reduction candidate for 2,7
D2: 2,7 => CTR
* 784139.5.....684.99..5741.8.48.13.9..9.482713.7.695284..9.263474.7..19...3.947861
D2: 1,4,5                                # 18 pairs
D3: 2,7,4,5                              # reduction candidate for 2,7
D3: 2,7                                  # 23 pairs
* PAIR G6: 2,4 COL G
G1: 2,4,6                                # reduction candidate for 2,4
G1: 2,4 => CTR
* 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861
G1: 6 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
G2: 2,4,3                                # reduction candidate for 2,4
G2: 2,4 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
G2: 3 => CTR
* 7.493..56..5164379963.5.128.48.13.9..9..8..13371695.8...9326.4...6871932.37549861
* PAIR I6: 2,4 COL I
I1: 2,4,6                                # reduction candidate for 2,4
I1: 2,4 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
I1: 6 => CTR
* 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861
* PAIR A7: 1,8 BLK 7
B7: 1,8,5                                # reduction candidate for 1,8
B7: 1,8 => CTR
* 7...3..56....6.3.99.3...1.8.48.13.9..9..8..13371695284..9326.4...6871932.37549861
B7: 5 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
* PAIR A7: 1,8 COL A
A2: 1,8,3,4                              # reduction candidate for 1,8
A2: 1,8 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
A2: 3,4                                  # 21 pairs
* PAIR A8: 4,8 COL A
A2: 4,8,1,3                              # reduction candidate for 4,8
A2: 4,8 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
A2: 1,3 => CTR
* 7...3..5.....6.3.99.3...1.8.48.13.9..9..8..13371695284819326.4.4.6871932.37549861
* PAIR A9: 2,5 BLK 7
C9: 2,5,7                                # reduction candidate for 2,5
C9: 2,5 => CTR
* 7...3..5.....6...99.6.7.138.48.13.9..9..8..13.7.695.8...9.26.4...7.519.2.3..4.861
C9: 7                                    # 19 pairs
* PAIR A9: 2,5 COL A
A4: 2,5,6                                # reduction candidate for 2,5
A4: 2,5                                  # 20 pairs
A5: 2,5,6                                # reduction candidate for 2,5
A5: 2,5 => CTR
* 7...3.456....6.3.99.3...1.8648213.9..9..8.613371695284..9.26.4......1932.3..4.861
A5: 6                                    # 20 pairs
* PAIR E8: 5,7 BLK 8
D9: 5,7,9                                # reduction candidate for 5,7
D9: 9 => CTR
* 7...39.5.....68..99...7.1.8.48.13.9..9..8..13.7.695284..9.26.4...7.51932.3.947861
D9: 5,7                                  # 19 pairs
* PAIR E8: 5,7 ROW 8
C8: 5,7,4,6                              # reduction candidate for 5,7
C8: 5,7 => CTR
* 7...3..5.....6...99.6...138.48.13.9..9..8..13.7.695.8...9.2634746...19...3..4.861
C8: 4,6                                  # 21 pairs
* PAIR F9: 7,9 BLK 8
D9: 7,9,5                                # reduction candidate for 7,9
D9: 7,9 => CTR
* 7...3..5.....6...99...7.1.8.48.13.9..9..8..13.7.695284..9.26.4...7.51932.3..4.861
D9: 5                                    # 19 pairs
* PAIR I7: 5,7 BLK 9
G7: 5,7,3                                # reduction candidate for 5,7
G7: 5,7 => CTR
* 7.493..56..5164379963.5.128.48.13.9..9..8..13371695.8...9326.4...6871932.37549861
G7: 3 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
* PAIR I7: 5,7 COL I
I4: 5,7,6                                # reduction candidate for 5,7
I4: 5,7 => CTR
* 7...3.456....6.3.99.3...1.8.48.13.9..9..8..13371695284..9.26.4......1932.3..4.861
I4: 6 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
* PAIR H8: 2,3 COL H
H2: 2,3,7                                # reduction candidate for 2,3
H2: 2,3 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
H2: 7                                    # 19 pairs
H3: 2,3,7                                # reduction candidate for 2,3
H3: 2,3                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060824-absurd-base-pr-000.dot
* REASONING
* DIS # A2: 1,4 => CTR => A2: 3,8
* DIS # C2: 1,4 => CTR => C2: 3,5
* DIS # D1: 1,4 => CTR => D1: 2,9
* DIS # D2: 5,7 => CTR => D2: 1,2,4
* DIS # A5: 2,5 => CTR => A5: 6
* DIS # C9: 2,5 => CTR => C9: 7
* DIS # A2: 1,3 => CTR => A2: 4,8
* PRF # A2: 4,8 => SOL
* DIS # C2: 1,3 => CTR => C2: 4,5
* DIS # D2: 2,7 => CTR => D2: 1,4,5
* DIS # G1: 2,4 => CTR => G1: 6
* PRF # G1: 6 => SOL
* PRF # G2: 2,4 => SOL
* DIS # G2: 3 => CTR => G2: 2,4
* PRF # I1: 2,4 => SOL
* DIS # I1: 6 => CTR => I1: 2,4
* DIS # B7: 1,8 => CTR => B7: 5
* PRF # B7: 5 => SOL
* PRF # A2: 1,8 => SOL
* PRF # A2: 4,8 => SOL
* DIS # A2: 1,3 => CTR => A2: 4,8
* DIS # C9: 2,5 => CTR => C9: 7
* DIS # A5: 2,5 => CTR => A5: 6
* DIS # D9: 9 => CTR => D9: 5,7
* DIS # C8: 5,7 => CTR => C8: 4,6
* DIS # D9: 7,9 => CTR => D9: 5
* DIS # G7: 5,7 => CTR => G7: 3
* PRF # G7: 3 => SOL
* DIS # I4: 5,7 => CTR => I4: 6
* PRF # I4: 6 => SOL
* PRF # H2: 2,3 => SOL
* CNT  31 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A8,A9,C1,C5,C6,D4,D7,D8,E3,E8,F9,G6,H8,I6,I7,I8)
* 7...3..5.....6...99.....1.8.48.13.9..9..8..13.7.695.8...9.26.4......19...3..4.861
* PAIR C1: 1,4 BLK 1
A2: 1,4,3,8                              # reduction candidate for 1,4
A2: 1,4 => CTR
* 7.4.3..5.1...6.4.99.....1.8.48.13.9..9..8..13371695284819326.4.4..8.1932.3..4.861
C2: 1,4,3,5                              # reduction candidate for 1,4
C2: 1,4 => CTR
* 7...3..5.....6...99.....1.8.48.13.9..9..8..13173695.8.819326.4.4..8.1932.3..4.861
* RESTART
* PAIR C1: 1,4 ROW 1
D1: 1,4,2,9                              # reduction candidate for 1,4
D1: 1,4 => CTR
* 78143925.....68..99.....1.8.48.13.9..9..8..13.7.695.8.819326.4.4..8.1932.3.947861
* PAIR RESTART
* PAIR E3: 5,7 BLK 2
D3: 5,7,2,4                              # reduction candidate for 5,7
D3: 2,4 => SOLVED
* 714938652825167439963452178548213796692784513371695284159826347486371925237549861
* DURATION: 0:00:05.521228  START: 02:03:49.382831  END: 02:03:54.904059 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060824-absurd-base-pr-001.dot
* REASONING
* DIS # A2: 1,4 => CTR => A2: 3,8
* DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5
* DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9
* PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL
* STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060824, absurd

Solution

position: 714938652825167439963452178548213796692784513371695284159826347486371925237549861 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: 1,4 => CTR => A2: 3,8
* INC # A2: 3,8 => UNS
* DIS # C2: 1,4 => CTR => C2: 3,5
* INC # C2: 3,5 => UNS
* DIS # D1: 1,4 => CTR => D1: 2,9
* INC # D1: 2,9 => UNS
* DIS # D2: 5,7 => CTR => D2: 1,2,4
* INC # D2: 1,2,4 => UNS
* INC # D3: 5,7 => UNS
* INC # A4: 2,5 => UNS
* DIS # A5: 2,5 => CTR => A5: 6
* INC # A5: 6 => UNS
* DIS # C9: 2,5 => CTR => C9: 7
* INC # C9: 7 => UNS
* DIS # A2: 1,3 => CTR => A2: 4,8
* PRF # A2: 4,8 => SOL
* DIS # C2: 1,3 => CTR => C2: 4,5
* INC # C2: 4,5 => UNS
* INC # D5: 2,7 => UNS
* INC # F5: 2,7 => UNS
* DIS # D2: 2,7 => CTR => D2: 1,4,5
* INC # D2: 1,4,5 => UNS
* INC # D3: 2,7 => UNS
* DIS # G1: 2,4 => CTR => G1: 6
* PRF # G1: 6 => SOL
* PRF # G2: 2,4 => SOL
* DIS # G2: 3 => CTR => G2: 2,4
* PRF # I1: 2,4 => SOL
* DIS # I1: 6 => CTR => I1: 2,4
* DIS # B7: 1,8 => CTR => B7: 5
* PRF # B7: 5 => SOL
* PRF # A2: 1,8 => SOL
* INC # A2: 3,4 => UNS
* PRF # A2: 4,8 => SOL
* DIS # A2: 1,3 => CTR => A2: 4,8
* DIS # C9: 2,5 => CTR => C9: 7
* INC # C9: 7 => UNS
* INC # A4: 2,5 => UNS
* DIS # A5: 2,5 => CTR => A5: 6
* INC # A5: 6 => UNS
* INC # D9: 5,7 => UNS
* DIS # D9: 9 => CTR => D9: 5,7
* DIS # C8: 5,7 => CTR => C8: 4,6
* INC # C8: 4,6 => UNS
* DIS # D9: 7,9 => CTR => D9: 5
* INC # D9: 5 => UNS
* DIS # G7: 5,7 => CTR => G7: 3
* PRF # G7: 3 => SOL
* DIS # I4: 5,7 => CTR => I4: 6
* PRF # I4: 6 => SOL
* PRF # H2: 2,3 => SOL
* INC # H2: 7 => UNS
* INC # H3: 2,3 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 1,4 => CTR => A2: 3,8
* DIS A2: 3,8 # C2: 1,4 => CTR => C2: 3,5
* DIS A2: 3,8 + C2: 3,5 # D1: 1,4 => CTR => D1: 2,9
* INC A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 5,7 => UNS
* PRF A2: 3,8 + C2: 3,5 + D1: 2,9 # D3: 2,4 => SOL
* STA A2: 3,8 + C2: 3,5 + D1: 2,9 + D3: 2,4
* CNT   5 HDP CHAINS /   5 HYP OPENED