Analysis of xx-top500-258-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6..8........2....3.......4....7..61..54............2......4.7.6....35...1........ initial

Autosolve

position: 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 5 => CTR => C1: 1,3
* DIS # C2: 8,9 => CTR => C2: 5,7
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* DIS # G3: 8,9 => CTR => G3: 1
* DIS # C2: 7,9 => CTR => C2: 5,8
* DIS # I3: 8 => CTR => I3: 7,9
* DIS # H5: 7,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* DIS # C2: 8,9 => CTR => C2: 5,7
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* PRF # C8: 8,9 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # I5: 8,9 => CTR => I5: 7
* DIS # G3: 8,9 => CTR => G3: 1
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* PRF # C8: 8,9 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # B8: 6,9 => CTR => B8: 2,7,8
* DIS # C8: 6,9 => CTR => C8: 2,7,8
* PRF # C9: 6,9 => SOL
* DIS # C9: 8 => CTR => C9: 6,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 8 => CTR => H8: 2,9
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # I5: 8,9 => CTR => I5: 7
* CNT  35 HDP CHAINS /  65 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 # C1: 5 => CTR => C1: 1,3
* DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7
* DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7
* PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL
* STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9
* CNT   4 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

6..8........2....3.......4....7..61..54............2......4.7.6....35...1........ initial
6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735. autosolve
613894572495271863827563149389752614254316987761489235532148796978635421146927358 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B1: 1,3
A3: 8,9
E1: 7,9
E2: 7,9
G1: 1,5
H1: 7,9
B4: 8,9
C4: 8,9
B6: 1,6
C6: 1,6
G5: 8,9
A8: 8,9
D8: 6,9
D9: 6,9
H7: 2,9
I9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,G3: 1.. / G1 = 1  =>  0 pairs (X) / G3 = 1  => 17 pairs (_)
B6,C6: 1.. / B6 = 1  =>  0 pairs (X) / C6 = 1  => 15 pairs (_)
B3,C3: 2.. / B3 = 2  => 17 pairs (_) / C3 = 2  => 17 pairs (_)
H7,H8: 2.. / H7 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
B1,C1: 3.. / B1 = 3  => 17 pairs (_) / C1 = 3  => 14 pairs (_)
B7,C7: 3.. / B7 = 3  => 14 pairs (_) / C7 = 3  => 17 pairs (_)
B1,B7: 3.. / B1 = 3  => 17 pairs (_) / B7 = 3  => 14 pairs (_)
C1,C7: 3.. / C1 = 3  => 14 pairs (_) / C7 = 3  => 17 pairs (_)
C1,C2: 5.. / C1 = 5  =>  0 pairs (X) / C2 = 5  => 17 pairs (_)
G1,G2: 5.. / G1 = 5  => 17 pairs (_) / G2 = 5  =>  0 pairs (X)
C1,G1: 5.. / C1 = 5  =>  0 pairs (X) / G1 = 5  => 17 pairs (_)
C2,G2: 5.. / C2 = 5  => 17 pairs (_) / G2 = 5  =>  0 pairs (X)
B6,C6: 6.. / B6 = 6  => 15 pairs (_) / C6 = 6  =>  0 pairs (X)
D8,D9: 6.. / D8 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
C9,D9: 6.. / C9 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
B6,B8: 6.. / B6 = 6  => 15 pairs (_) / B8 = 6  =>  0 pairs (X)
E1,E2: 7.. / E1 = 7  =>  0 pairs (X) / E2 = 7  => 20 pairs (_)
H1,I3: 7.. / H1 = 7  => 20 pairs (_) / I3 = 7  =>  0 pairs (X)
H5,I5: 7.. / H5 = 7  =>  0 pairs (X) / I5 = 7  => 20 pairs (_)
B8,C8: 7.. / B8 = 7  => 20 pairs (_) / C8 = 7  => 16 pairs (_)
E1,H1: 7.. / E1 = 7  =>  0 pairs (X) / H1 = 7  => 20 pairs (_)
H1,H5: 7.. / H1 = 7  => 20 pairs (_) / H5 = 7  =>  0 pairs (X)
I3,I5: 7.. / I3 = 7  =>  0 pairs (X) / I5 = 7  => 20 pairs (_)
B4,C4: 8.. / B4 = 8  => 19 pairs (_) / C4 = 8  =>  0 pairs (X)
H8,I9: 8.. / H8 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
C9,I9: 8.. / C9 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
A3,A8: 8.. / A3 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
H5,H8: 8.. / H5 = 8  =>  0 pairs (*) / H8 = 8  =>  0 pairs (X)
E1,E2: 9.. / E1 = 9  => 20 pairs (_) / E2 = 9  =>  0 pairs (X)
B4,C4: 9.. / B4 = 9  =>  0 pairs (X) / C4 = 9  => 19 pairs (_)
D8,D9: 9.. / D8 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
E1,H1: 9.. / E1 = 9  => 20 pairs (_) / H1 = 9  =>  0 pairs (X)
A3,A8: 9.. / A3 = 9  =>  0 pairs (X) / A8 = 9  =>  0 pairs (_)
* DURATION: 0:00:57.696674  START: 11:36:58.902007  END: 11:37:56.598681 2017-05-04
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B4,B6,C4,C6,D8,D9,E1,E2,G1,G5,H1,H7,I9)
* 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735.
* PAIR B1: 1,3 BLK 1
C1: 1,3,5                                # reduction candidate for 1,3
C1: 5 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
C1: 1,3                                  # 17 pairs
* PAIR A3: 8,9 BLK 1
B2: 8,9,7                                # reduction candidate for 8,9
B2: 8,9                                  # 19 pairs
C2: 8,9,5,7                              # reduction candidate for 8,9
C2: 8,9 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
C2: 5,7                                  # 17 pairs
B3: 8,9,1,2,7                            # reduction candidate for 8,9
B3: 8,9 => CTR
* 6..8.4..24..2.1.63..25631473..752614254316.7.7..4892355..1487.6....35481148627359
B3: 1,2,7                                # 16 pairs
C3: 8,9,1,2,7                            # reduction candidate for 8,9
C3: 8,9 => CTR
* 6..8.4..24..2.1.63.2.5631473..752614254316.7.7..4892355..1487.6....35481148627359
C3: 1,2,7                                # 16 pairs
* PAIR A3: 8,9 ROW 3
G3: 8,9,1                                # reduction candidate for 8,9
G3: 8,9 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
G3: 1                                    # 17 pairs
I3: 8,9,7                                # reduction candidate for 8,9
I3: 8,9                                  # 20 pairs
* PAIR E2: 7,9 ROW 2
B2: 7,9,8                                # reduction candidate for 7,9
B2: 7,9                                  # 19 pairs
C2: 7,9,5,8                              # reduction candidate for 7,9
C2: 7,9 => CTR
* 6358.41.248.2.15639..5638473987526142543169787..4892355.31487.6....354.114..2735.
C2: 5,8                                  # 17 pairs
* PAIR G1: 1,5 ROW 1
C1: 1,5,3                                # reduction candidate for 1,5
C1: 1,5                                  # 17 pairs
C1: 3                                    # 14 pairs
* PAIR H1: 7,9 BLK 3
I3: 7,9,8                                # reduction candidate for 7,9
I3: 8 => CTR
* 6..8.4.724..271.63...563.483..7526142543168977..4892355..1487268...354.114..2735.
I3: 7,9                                  # 20 pairs
* PAIR H1: 7,9 COL H
H5: 7,9,8                                # reduction candidate for 7,9
H5: 7,9 => CTR
* 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....35481148627359
H5: 8 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR B4: 8,9 COL B
B2: 8,9,7                                # reduction candidate for 8,9
B2: 8,9                                  # 19 pairs
B3: 8,9,1,2,7                            # reduction candidate for 8,9
B3: 8,9 => CTR
* 6..8.4..24..2.1.63..25631473..752614254316.7.7..4892355..1487.6....35481148627359
B3: 1,2,7                                # 16 pairs
B8: 8,9,2,6,7                            # reduction candidate for 8,9
B8: 8,9 => CTR
* 6..894.724..271.63.725631493..752614254316987761489235523148796987635421146927358
B8: 2,6,7                                # 16 pairs
* PAIR C4: 8,9 COL C
C2: 8,9,5,7                              # reduction candidate for 8,9
C2: 8,9 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
C2: 5,7                                  # 17 pairs
C3: 8,9,1,2,7                            # reduction candidate for 8,9
C3: 8,9 => CTR
* 6..8.4..24..2.1.63.2.5631473..752614254316.7.7..4892355..1487.6....35481148627359
C3: 1,2,7                                # 16 pairs
C8: 8,9,2,6,7                            # reduction candidate for 8,9
C8: 8,9 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
C8: 2,6,7                                # 16 pairs
C9: 8,9,6                                # reduction candidate for 8,9
C9: 8,9 => CTR
* 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358
C9: 6 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR G5: 8,9 BLK 6
H5: 8,9,7                                # reduction candidate for 8,9
H5: 8,9                                  # 20 pairs
I5: 8,9,7                                # reduction candidate for 8,9
I5: 8,9 => CTR
* 6..8.4..24..2.1.63...563.473..752614254316.7.7..4892355..1487.6....35481148627359
I5: 7                                    # 20 pairs
* PAIR G5: 8,9 COL G
G2: 8,9,5                                # reduction candidate for 8,9
G2: 8,9                                  # 17 pairs
G3: 8,9,1                                # reduction candidate for 8,9
G3: 8,9 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
G3: 1                                    # 17 pairs
* PAIR A8: 8,9 BLK 7
B8: 8,9,2,6,7                            # reduction candidate for 8,9
B8: 8,9 => CTR
* 6..894.724..271.63.725631493..752614254316987761489235523148796987635421146927358
B8: 2,6,7                                # 16 pairs
C8: 8,9,2,6,7                            # reduction candidate for 8,9
C8: 8,9 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
C8: 2,6,7                                # 16 pairs
C9: 8,9,6                                # reduction candidate for 8,9
C9: 8,9 => CTR
* 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358
C9: 6 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR A8: 8,9 ROW 8
H8: 8,9,2                                # reduction candidate for 8,9
H8: 8,9 => CTR
* 6..8.4..24..2.1.639..563.4.3..752614254316...7..4892355..1487268...35491146927358
H8: 2 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR D8: 6,9 ROW 8
B8: 6,9,2,7,8                            # reduction candidate for 6,9
B8: 6,9 => CTR
* 6..8.4..24..2.1.63...563.4.3..752614254316.877..4892355..1487968.7.3542114..27358
B8: 2,7,8                                # 15 pairs
C8: 6,9,2,7,8                            # reduction candidate for 6,9
C8: 6,9 => CTR
* 6..8.4..24..2.1.63...563.4.3..752614254316.877614892355..14879687..3542114..27358
C8: 2,7,8                                # 16 pairs
* PAIR D9: 6,9 ROW 9
C9: 6,9,8                                # reduction candidate for 6,9
C9: 6,9 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
C9: 8 => CTR
* 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.1148627359
* PAIR H7: 2,9 BLK 9
H8: 2,9,8                                # reduction candidate for 2,9
H8: 2,9 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
H8: 8 => CTR
* 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..148726....35481148627359
* PAIR H7: 2,9 ROW 7
B7: 2,9,3                                # reduction candidate for 2,9
B7: 2,9                                  # 17 pairs
C7: 2,9,3                                # reduction candidate for 2,9
C7: 2,9                                  # 14 pairs
* PAIR I9: 8,9 BLK 9
H8: 8,9,2                                # reduction candidate for 8,9
H8: 8,9 => CTR
* 6..8.4..24..2.1.639..563.4.3..752614254316...7..4892355..1487268...35491146927358
H8: 2 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR I9: 8,9 ROW 9
C9: 8,9,6                                # reduction candidate for 8,9
C9: 8,9 => CTR
* 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358
C9: 6 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* PAIR I9: 8,9 COL I
I3: 8,9,7                                # reduction candidate for 8,9
I3: 8,9                                  # 20 pairs
I5: 8,9,7                                # reduction candidate for 8,9
I5: 8,9 => CTR
* 6..8.4..24..2.1.63...563.473..752614254316.7.7..4892355..1487.6....35481148627359
I5: 7                                    # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-258-base-pr-000.dot
* REASONING
* DIS # C1: 5 => CTR => C1: 1,3
* DIS # C2: 8,9 => CTR => C2: 5,7
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* DIS # G3: 8,9 => CTR => G3: 1
* DIS # C2: 7,9 => CTR => C2: 5,8
* DIS # I3: 8 => CTR => I3: 7,9
* DIS # H5: 7,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* DIS # C2: 8,9 => CTR => C2: 5,7
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* PRF # C8: 8,9 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # I5: 8,9 => CTR => I5: 7
* DIS # G3: 8,9 => CTR => G3: 1
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* PRF # C8: 8,9 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # B8: 6,9 => CTR => B8: 2,7,8
* DIS # C8: 6,9 => CTR => C8: 2,7,8
* PRF # C9: 6,9 => SOL
* DIS # C9: 8 => CTR => C9: 6,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 8 => CTR => H8: 2,9
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # I5: 8,9 => CTR => I5: 7
* CNT  35 HDP CHAINS /  65 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B4,B6,C4,C6,D8,D9,E1,E2,G1,G5,H1,H7,I9)
* 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735.
* PAIR B1: 1,3 BLK 1
C1: 1,3,5                                # reduction candidate for 1,3
C1: 5 => CTR
* 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735.
* PAIR A3: 8,9 BLK 1
B2: 8,9,7                                # reduction candidate for 8,9
B2: 8,9                                  # 20 pairs
B3: 8,9,2,7                              # reduction candidate for 8,9
B3: 8,9 => CTR
* 6..8.45.24.52.1.63..25631473..752614254316.7.7..4892355..1487.6..7.35481148627359
C3: 8,9,2,7                              # reduction candidate for 8,9
C3: 8,9 => CTR
* 6..8.45.24.52.1.63.2.5631473..752614254316.7.7..4892355..1487.6..7.354.114..2735.
* RESTART
* PAIR C4: 8,9 COL C
C8: 8,9,2,6,7                            # reduction candidate for 8,9
C8: 8,9 => SOLVED
* 613894572495271863827563149389752614254316987761489235532148796978635421146927358
* DURATION: 0:00:07.638494  START: 11:39:01.362695  END: 11:39:09.001189 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-258-base-pr-001.dot
* REASONING
* DIS # C1: 5 => CTR => C1: 1,3
* DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7
* DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7
* PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL
* STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

Top 500 Minimum 17 258

solution: 613894572495271863827563149389752614254316987761489235532148796978635421146927358
info: 2080     FNBTWXY  S8.f     35253

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 613894572495271863827563149389752614254316987761489235532148796978635421146927358 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 # C1: 1,3 => UNS
* DIS # C1: 5 => CTR => C1: 1,3
* INC # B2: 8,9 => UNS
* DIS # C2: 8,9 => CTR => C2: 5,7
* INC # C2: 5,7 => UNS
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* INC # B3: 1,2,7 => UNS
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* INC # C3: 1,2,7 => UNS
* DIS # G3: 8,9 => CTR => G3: 1
* INC # G3: 1 => UNS
* INC # I3: 8,9 => UNS
* INC # B2: 7,9 => UNS
* DIS # C2: 7,9 => CTR => C2: 5,8
* INC # C2: 5,8 => UNS
* INC # C1: 1,5 => UNS
* INC # C1: 3 => UNS
* INC # I3: 7,9 => UNS
* DIS # I3: 8 => CTR => I3: 7,9
* DIS # H5: 7,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* INC # B2: 8,9 => UNS
* DIS # B3: 8,9 => CTR => B3: 1,2,7
* INC # B3: 1,2,7 => UNS
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* INC # B8: 2,6,7 => UNS
* DIS # C2: 8,9 => CTR => C2: 5,7
* INC # C2: 5,7 => UNS
* DIS # C3: 8,9 => CTR => C3: 1,2,7
* INC # C3: 1,2,7 => UNS
* PRF # C8: 8,9 => SOL
* INC # C8: 2,6,7 => UNS
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* INC # H5: 8,9 => UNS
* DIS # I5: 8,9 => CTR => I5: 7
* INC # I5: 7 => UNS
* INC # G2: 8,9 => UNS
* DIS # G3: 8,9 => CTR => G3: 1
* INC # G3: 1 => UNS
* DIS # B8: 8,9 => CTR => B8: 2,6,7
* INC # B8: 2,6,7 => UNS
* PRF # C8: 8,9 => SOL
* INC # C8: 2,6,7 => UNS
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # B8: 6,9 => CTR => B8: 2,7,8
* INC # B8: 2,7,8 => UNS
* DIS # C8: 6,9 => CTR => C8: 2,7,8
* INC # C8: 2,7,8 => UNS
* PRF # C9: 6,9 => SOL
* DIS # C9: 8 => CTR => C9: 6,9
* PRF # H8: 2,9 => SOL
* DIS # H8: 8 => CTR => H8: 2,9
* INC # B7: 2,9 => UNS
* INC # C7: 2,9 => UNS
* DIS # H8: 8,9 => CTR => H8: 2
* PRF # H8: 2 => SOL
* DIS # C9: 8,9 => CTR => C9: 6
* PRF # C9: 6 => SOL
* INC # I3: 8,9 => UNS
* DIS # I5: 8,9 => CTR => I5: 7
* INC # I5: 7 => UNS
* CNT  65 HDP CHAINS /  65 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,3 => UNS
* DIS # C1: 5 => CTR => C1: 1,3
* INC C1: 1,3 # B2: 8,9 => UNS
* DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7
* DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7
* PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL
* STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9
* CNT   6 HDP CHAINS /   6 HYP OPENED