Analysis of xx-top500-294-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...3.41..8..5...6.9.........3.2..4......8..2..1.......6...9.....7....3........... initial

Autosolve

position: ...3.41..8.3519.6.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........ autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 2,4 => CTR => B3: 6
* DIS # I2: 2,4 => CTR => I2: 7
* DIS # B1: 2,6 => CTR => B1: 5
* DIS # C1: 2,6 => CTR => C1: 5,7
* DIS # E8: 2,6 => CTR => E8: 4,5
* PRF # E9: 2,6 => SOL
* DIS # H4: 8,9 => CTR => H4: 1
* PRF # H6: 8,9 => SOL
* DIS # H6: 5,7 => CTR => H6: 8,9
* DIS # H8: 8,9 => CTR => H8: 4,5
* DIS # H9: 8,9 => CTR => H9: 1,4,5,7
* DIS # I6: 8,9 => CTR => I6: 5,6,7
* DIS # I8: 8,9 => CTR => I8: 2,5,6
* DIS # I9: 8,9 => CTR => I9: 1,2,5,6,7
* DIS # I2: 4 => CTR => I2: 2,7
* DIS # G7: 2,7 => CTR => G7: 5,8
* DIS # G9: 2,7 => CTR => G9: 5,6,8,9
* DIS # I3: 2,5 => CTR => I3: 4
* DIS # G7: 2,5 => CTR => G7: 7,8
* DIS # G9: 2,5 => CTR => G9: 6,7,8,9
* DIS # C5: 5,7 => CTR => C5: 6,9
* DIS # A6: 5,7 => CTR => A6: 2,4
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* DIS # F4: 5,7 => CTR => F4: 6
* DIS # A1: 5,7 => CTR => A1: 2
* DIS # C6: 8,9 => CTR => C6: 2,5,6,7
* DIS # H4: 8,9 => CTR => H4: 1
* DIS # F4: 5,7 => CTR => F4: 6
* DIS # A6: 5,7 => CTR => A6: 2,4
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* DIS # G6: 5,7 => CTR => G6: 6,8,9
* DIS # H6: 5,7 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* PRF # I6: 5,7 => SOL
* CNT  34 HDP CHAINS /  80 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 # B3: 2,4 => CTR => B3: 6
* PRF B3: 6 # E9: 2,7 => SOL
* STA B3: 6 + E9: 2,7
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

...3.41..8..5...6.9.........3.2..4......8..2..1.......6...9.....7....3........... initial
...3.41..8.3519.6.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........ autosolve
257364198843519267961872534738256419596481723412937685625793841179648352384125976 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
B2: 2,4
E1: 2,6
H1: 8,9
I1: 8,9
G2: 2,7
G3: 2,5
A4: 5,7
C4: 8,9
D5: 4,9
D6: 4,9
F6: 5,7
D8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H4,I4: 1.. / H4 = 1  => 13 pairs (_) / I4 = 1  =>  0 pairs (X)
D7,D9: 1.. / D7 = 1  => 12 pairs (_) / D9 = 1  => 13 pairs (_)
A6,C6: 2.. / A6 = 2  =>  0 pairs (X) / C6 = 2  => 19 pairs (_)
A1,A6: 2.. / A1 = 2  => 19 pairs (_) / A6 = 2  =>  0 pairs (X)
B2,B3: 4.. / B2 = 4  => 19 pairs (_) / B3 = 4  =>  0 pairs (X)
I2,I3: 4.. / I2 = 4  =>  0 pairs (X) / I3 = 4  => 19 pairs (_)
A5,A6: 4.. / A5 = 4  =>  0 pairs (X) / A6 = 4  => 19 pairs (_)
D5,D6: 4.. / D5 = 4  => 19 pairs (_) / D6 = 4  =>  0 pairs (X)
E8,E9: 4.. / E8 = 4  => 12 pairs (_) / E9 = 4  => 12 pairs (_)
B2,I2: 4.. / B2 = 4  => 19 pairs (_) / I2 = 4  =>  0 pairs (X)
B3,I3: 4.. / B3 = 4  =>  0 pairs (X) / I3 = 4  => 19 pairs (_)
A5,D5: 4.. / A5 = 4  =>  0 pairs (X) / D5 = 4  => 19 pairs (_)
A6,D6: 4.. / A6 = 4  => 19 pairs (_) / D6 = 4  =>  0 pairs (X)
C7,H7: 4.. / C7 = 4  => 12 pairs (_) / H7 = 4  => 13 pairs (_)
G3,I3: 5.. / G3 = 5  => 19 pairs (_) / I3 = 5  =>  0 pairs (X)
E4,F4: 6.. / E4 = 6  =>  0 pairs (X) / F4 = 6  => 13 pairs (_)
A1,C1: 7.. / A1 = 7  =>  0 pairs (X) / C1 = 7  => 14 pairs (_)
G2,I2: 7.. / G2 = 7  =>  0 pairs (X) / I2 = 7  => 19 pairs (_)
D3,F3: 8.. / D3 = 8  => 13 pairs (_) / F3 = 8  => 13 pairs (_)
H1,I1: 8.. / H1 = 8  => 12 pairs (_) / I1 = 8  => 12 pairs (_)
C4,C6: 8.. / C4 = 8  => 19 pairs (_) / C6 = 8  =>  0 pairs (X)
B7,B9: 8.. / B7 = 8  =>  0 pairs (X) / B9 = 8  => 19 pairs (_)
H1,I1: 9.. / H1 = 9  => 12 pairs (_) / I1 = 9  => 12 pairs (_)
D5,D6: 9.. / D5 = 9  =>  0 pairs (X) / D6 = 9  => 19 pairs (_)
B5,B9: 9.. / B5 = 9  => 19 pairs (_) / B9 = 9  =>  0 pairs (X)
* DURATION: 0:00:50.469907  START: 13:00:35.154262  END: 13:01:25.624169 2017-05-04
* CP COUNT: (25)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,C4,D5,D6,D8,E1,F6,G2,G3,H1,I1)
* ...3.41..8.3519.6.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........
* PAIR B2: 2,4 BLK 1
B3: 2,4,6                                # reduction candidate for 2,4
B3: 2,4 => CTR
* ...3241..8.3519.6.9.1....3..392..4..4..98162321.43.9..68..93...17....3..39....8..
B3: 6                                    # 19 pairs
* PAIR B2: 2,4 ROW 2
I2: 2,4,7                                # reduction candidate for 2,4
I2: 2,4 => CTR
* ...3241..823519764941...23553.2..4...96481523.1..35...6...938..17....3..38.......
I2: 7                                    # 19 pairs
* PAIR E1: 2,6 BLK 2
E3: 2,6,7                                # reduction candidate for 2,6
E3: 2,6                                  # 17 pairs
F3: 2,6,7,8                              # reduction candidate for 2,6
F3: 2,6                                  # 15 pairs
* PAIR E1: 2,6 ROW 1
B1: 2,6,5                                # reduction candidate for 2,6
B1: 2,6 => CTR
* 5.73.41..8.3519.6.9.1....3.7392..4..456981.2321.43.9..68..93...17....3..39....8..
B1: 5                                    # 15 pairs
C1: 2,6,5,7                              # reduction candidate for 2,6
C1: 2,6 => CTR
* 75.3.41..8.3519.6.9.1...23553.2..4..46798152321.4359.668..937..17....3..39.......
C1: 5,7                                  # 14 pairs
* PAIR E1: 2,6 COL E
E8: 2,6,4,5                              # reduction candidate for 2,6
E8: 2,6 => CTR
* 2573641..8435192679618725347382564..5964817234129376..62..938..17962834.38..4.9..
E8: 4,5                                  # 13 pairs
E9: 2,6,4,5,7                            # reduction candidate for 2,6
E9: 2,6 => SOLVED
* 257364198843519267961872534738256419596481723412937685625793841179648352384125976
E9: 4,5,7                                # 12 pairs
* PAIR H1: 8,9 COL H
H4: 8,9,1                                # reduction candidate for 8,9
H4: 8,9 => CTR
* 257364189843519267961.72534738256491596481723412937658624.938.5179.2.34.38..4.9..
H4: 1                                    # 13 pairs
H6: 8,9,5,7                              # reduction candidate for 8,9
H6: 8,9 => SOLVED
* 257364198843519267961872534738256419596481723412937685625793841179648352384125976
H6: 5,7 => CTR
* 257364189843519267961.72534738256491596481723412937658624.938.5179.2.34.38..4.9..
H8: 8,9,4,5                              # reduction candidate for 8,9
H8: 8,9 => CTR
* ...3.41898.3519.6.9.1....3..392..418....81.23.18.3.9.66...938..17....39.3.....6..
H8: 4,5                                  # 13 pairs
H9: 8,9,1,4,5,7                          # reduction candidate for 8,9
H9: 8,9 => CTR
* ...3.41898.3519.6.9.1....3..3.2..41.....81.23.1..3...66...93...179...3..3.....69.
H9: 1,4,5,7                              # 12 pairs
* PAIR I1: 8,9 COL I
I4: 8,9,1                                # reduction candidate for 8,9
I4: 8,9                                  # 13 pairs
I6: 8,9,5,6,7                            # reduction candidate for 8,9
I6: 8,9 => CTR
* 257364189843519267961.72534738256491596481723412937658624.938.5179.2.34.38..4.9..
I6: 5,6,7                                # 12 pairs
I8: 8,9,2,5,6                            # reduction candidate for 8,9
I8: 8,9 => CTR
* ...3.41988.3519.6.9.1....3..392..481....81.23.18.3.9.66...938..17....3.93.....6..
I8: 2,5,6                                # 12 pairs
I9: 8,9,1,2,5,6,7                        # reduction candidate for 8,9
I9: 8,9 => CTR
* ...3.41..8.3519.6.9.1....3..382..491.9.481.2341293.8.66...93...179...3..3........
I9: 1,2,5,6,7                            # 12 pairs
* PAIR G2: 2,7 BLK 3
I2: 2,7,4                                # reduction candidate for 2,7
I2: 4 => CTR
* 7..3241..823519764941....3.53.2..4..46798152321.4359.668..932..17....3..39.......
I2: 2,7                                  # 19 pairs
* PAIR G2: 2,7 COL G
G7: 2,7,5,8                              # reduction candidate for 2,7
G7: 2,7 => CTR
* ...3.41..8.3519.6.9.1...53..3.2..4......81.23.1..3....6...93...17....3..3........
G7: 5,8                                  # 13 pairs
G9: 2,7,5,6,8,9                          # reduction candidate for 2,7
G9: 2,7 => CTR
* ...3.41..8.3519.6.9.1....3..392..4......81.23.18.3.6..6...938..17....3..3........
G9: 5,6,8,9                              # 12 pairs
* PAIR G3: 2,5 BLK 3
I3: 2,5,4                                # reduction candidate for 2,5
I3: 2,5 => CTR
* 7..3241..823519764941....3.53.2..4..46798152321.4359.668..932..17....3..39.......
I3: 4                                    # 19 pairs
* PAIR G3: 2,5 COL G
G7: 2,5,7,8                              # reduction candidate for 2,5
G7: 2,5 => CTR
* ...3.41..8.351976.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........
G7: 7,8                                  # 13 pairs
G9: 2,5,6,7,8,9                          # reduction candidate for 2,5
G9: 2,5 => CTR
* ...3.41..8.3519.6.9.1....3..392..4......81.23.18.3.6..6...938..17....3..3........
G9: 6,7,8,9                              # 12 pairs
* PAIR A4: 5,7 BLK 4
A5: 5,7,4                                # reduction candidate for 5,7
A5: 5,7                                  # 19 pairs
C5: 5,7,6,9                              # reduction candidate for 5,7
C5: 5,7 => CTR
* ...3.41..8.3519.6.9.1....3..3.2..4..46.981.2321.43....6...938..17....3..3........
C5: 6,9                                  # 13 pairs
A6: 5,7,2,4                              # reduction candidate for 5,7
A6: 5,7 => CTR
* 2.73641..843519.6.961....34.3.2.64..4..981723.1243....6...93...17....3..39.......
A6: 2,4                                  # 13 pairs
C6: 5,7,2,6,8,9                          # reduction candidate for 5,7
C6: 5,7 => CTR
* ...3.41..8.3519.6.9.1....3..382..4..4..981.2321.43....6...93...17....3..39.......
C6: 2,6,8,9                              # 12 pairs
* PAIR A4: 5,7 ROW 4
E4: 5,7,6                                # reduction candidate for 5,7
E4: 5,7                                  # 13 pairs
F4: 5,7,6                                # reduction candidate for 5,7
F4: 5,7 => CTR
* ...3241..8.3519.6.9.1.7..3..3926.4..4..98162321.43.9..68..93...17....3..39....8..
F4: 6                                    # 13 pairs
* PAIR A4: 5,7 COL A
A1: 5,7,2                                # reduction candidate for 5,7
A1: 5,7 => CTR
* ...3.41..8.3519.6.9.1....3..392..4..4..98162321.43.9..68..93...17....3..39....8..
A1: 2                                    # 19 pairs
* PAIR C4: 8,9 BLK 4
C6: 8,9,2,5,6,7                          # reduction candidate for 8,9
C6: 8,9 => CTR
* ...3.41..8.3519.6.9.1....3..3.2..4..4..981.2321.43.9.668..93...17....3..39.......
C6: 2,5,6,7                              # 19 pairs
* PAIR C4: 8,9 ROW 4
H4: 8,9,1                                # reduction candidate for 8,9
H4: 8,9 => CTR
* 257364189843519267961.72534738256491596481723412937658624.938.5179.2.34.38..4.9..
H4: 1                                    # 13 pairs
I4: 8,9,1                                # reduction candidate for 8,9
I4: 8,9                                  # 13 pairs
* PAIR F6: 5,7 BLK 5
E4: 5,7,6                                # reduction candidate for 5,7
E4: 5,7                                  # 13 pairs
F4: 5,7,6                                # reduction candidate for 5,7
F4: 5,7 => CTR
* ...3241..8.3519.6.9.1.7..3..3926.4..4..98162321.43.9..68..93...17....3..39....8..
F4: 6                                    # 13 pairs
* PAIR F6: 5,7 ROW 6
A6: 5,7,2,4                              # reduction candidate for 5,7
A6: 5,7 => CTR
* 2.73641..843519.6.961....34.3.2.64..4..981723.1243....6...93...17....3..39.......
A6: 2,4                                  # 13 pairs
C6: 5,7,2,6,8,9                          # reduction candidate for 5,7
C6: 5,7 => CTR
* ...3.41..8.3519.6.9.1....3..382..4..4..981.2321.43....6...93...17....3..39.......
C6: 2,6,8,9                              # 12 pairs
G6: 5,7,6,8,9                            # reduction candidate for 5,7
G6: 5,7 => CTR
* ...3.41..8.3519.6.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........
G6: 6,8,9                                # 12 pairs
H6: 5,7,8,9                              # reduction candidate for 5,7
H6: 5,7 => CTR
* 257364189843519267961.72534738256491596481723412937658624.938.5179.2.34.38..4.9..
H6: 8,9 => SOLVED
* 257364198843519267961872534738256419596481723412937685625793841179648352384125976
I6: 5,7,6,8,9                            # reduction candidate for 5,7
I6: 5,7 => SOLVED
* 257364198843519267961872534738256419596481723412937685625793841179648352384125976
I6: 6,8,9                                # 12 pairs
* PAIR F6: 5,7 COL F
F9: 5,7,2,6,8                            # reduction candidate for 5,7
F9: 5,7                                  # 16 pairs
F9: 2,6,8                                # 12 pairs
* PAIR D8: 6,8 BLK 8
F8: 6,8,2,5                              # reduction candidate for 6,8
F8: 6,8                                  # 17 pairs
D9: 6,8,1,7                              # reduction candidate for 6,8
D9: 6,8                                  # 17 pairs
F9: 6,8,2,5,7                            # reduction candidate for 6,8
F9: 6,8                                  # 17 pairs
* PAIR D8: 6,8 ROW 8
I8: 6,8,2,5,9                            # reduction candidate for 6,8
I8: 6,8                                  # 14 pairs
I8: 2,5,9                                # 12 pairs
* PAIR D8: 6,8 COL D
D3: 6,8,7                                # reduction candidate for 6,8
D3: 7                                    # 17 pairs
D3: 6,8                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-294-base-pr-000.dot
* REASONING
* DIS # B3: 2,4 => CTR => B3: 6
* DIS # I2: 2,4 => CTR => I2: 7
* DIS # B1: 2,6 => CTR => B1: 5
* DIS # C1: 2,6 => CTR => C1: 5,7
* DIS # E8: 2,6 => CTR => E8: 4,5
* PRF # E9: 2,6 => SOL
* DIS # H4: 8,9 => CTR => H4: 1
* PRF # H6: 8,9 => SOL
* DIS # H6: 5,7 => CTR => H6: 8,9
* DIS # H8: 8,9 => CTR => H8: 4,5
* DIS # H9: 8,9 => CTR => H9: 1,4,5,7
* DIS # I6: 8,9 => CTR => I6: 5,6,7
* DIS # I8: 8,9 => CTR => I8: 2,5,6
* DIS # I9: 8,9 => CTR => I9: 1,2,5,6,7
* DIS # I2: 4 => CTR => I2: 2,7
* DIS # G7: 2,7 => CTR => G7: 5,8
* DIS # G9: 2,7 => CTR => G9: 5,6,8,9
* DIS # I3: 2,5 => CTR => I3: 4
* DIS # G7: 2,5 => CTR => G7: 7,8
* DIS # G9: 2,5 => CTR => G9: 6,7,8,9
* DIS # C5: 5,7 => CTR => C5: 6,9
* DIS # A6: 5,7 => CTR => A6: 2,4
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* DIS # F4: 5,7 => CTR => F4: 6
* DIS # A1: 5,7 => CTR => A1: 2
* DIS # C6: 8,9 => CTR => C6: 2,5,6,7
* DIS # H4: 8,9 => CTR => H4: 1
* DIS # F4: 5,7 => CTR => F4: 6
* DIS # A6: 5,7 => CTR => A6: 2,4
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* DIS # G6: 5,7 => CTR => G6: 6,8,9
* DIS # H6: 5,7 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* PRF # I6: 5,7 => SOL
* CNT  34 HDP CHAINS /  80 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,C4,D5,D6,D8,E1,F6,G2,G3,H1,I1)
* ...3.41..8.3519.6.9.1....3..3.2..4......81.23.1..3....6...93...17....3..3........
* PAIR B2: 2,4 BLK 1
B3: 2,4,6                                # reduction candidate for 2,4
B3: 2,4 => CTR
* ...3241..8.3519.6.9.1....3..392..4..4..98162321.43.9..68..93...17....3..39....8..

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (C7,C9,D3,D7,D8,E3,E8,F3,F9,H1,H4,H6,H8,I1,I4,I6,I7,I8,I9)
* 2573641..843519267961...5347382564..5964817234129376..62..938..179...3..38....9..
* PAIR E3: 2,7 COL E
E9: 2,7,4                                # reduction candidate for 2,7
E9: 2,7 => SOLVED
* 257364198843519267961872534738256419596481723412937685625793841179648352384125976
* DURATION: 0:00:05.951086  START: 13:02:47.903360  END: 13:02:53.854446 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-294-base-pr-001.dot
* REASONING
* DIS # B3: 2,4 => CTR => B3: 6
* PRF B3: 6 # E9: 2,7 => SOL
* STA B3: 6 + E9: 2,7
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 294

solution: 257364198843519267961872534738256419596481723412937685625793841179648352384125976
info: 2413     FNBTHWY  S8.f     8587

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

Solution

position: 257364198843519267961872534738256419596481723412937685625793841179648352384125976 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 # B3: 2,4 => CTR => B3: 6
* INC # B3: 6 => UNS
* DIS # I2: 2,4 => CTR => I2: 7
* INC # I2: 7 => UNS
* INC # E3: 2,6 => UNS
* INC # F3: 2,6 => UNS
* DIS # B1: 2,6 => CTR => B1: 5
* INC # B1: 5 => UNS
* DIS # C1: 2,6 => CTR => C1: 5,7
* INC # C1: 5,7 => UNS
* DIS # E8: 2,6 => CTR => E8: 4,5
* INC # E8: 4,5 => UNS
* PRF # E9: 2,6 => SOL
* INC # E9: 4,5,7 => UNS
* DIS # H4: 8,9 => CTR => H4: 1
* INC # H4: 1 => UNS
* PRF # H6: 8,9 => SOL
* DIS # H6: 5,7 => CTR => H6: 8,9
* DIS # H8: 8,9 => CTR => H8: 4,5
* INC # H8: 4,5 => UNS
* DIS # H9: 8,9 => CTR => H9: 1,4,5,7
* INC # H9: 1,4,5,7 => UNS
* INC # I4: 8,9 => UNS
* DIS # I6: 8,9 => CTR => I6: 5,6,7
* INC # I6: 5,6,7 => UNS
* DIS # I8: 8,9 => CTR => I8: 2,5,6
* INC # I8: 2,5,6 => UNS
* DIS # I9: 8,9 => CTR => I9: 1,2,5,6,7
* INC # I9: 1,2,5,6,7 => UNS
* INC # I2: 2,7 => UNS
* DIS # I2: 4 => CTR => I2: 2,7
* DIS # G7: 2,7 => CTR => G7: 5,8
* INC # G7: 5,8 => UNS
* DIS # G9: 2,7 => CTR => G9: 5,6,8,9
* INC # G9: 5,6,8,9 => UNS
* DIS # I3: 2,5 => CTR => I3: 4
* INC # I3: 4 => UNS
* DIS # G7: 2,5 => CTR => G7: 7,8
* INC # G7: 7,8 => UNS
* DIS # G9: 2,5 => CTR => G9: 6,7,8,9
* INC # G9: 6,7,8,9 => UNS
* INC # A5: 5,7 => UNS
* DIS # C5: 5,7 => CTR => C5: 6,9
* INC # C5: 6,9 => UNS
* DIS # A6: 5,7 => CTR => A6: 2,4
* INC # A6: 2,4 => UNS
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* INC # C6: 2,6,8,9 => UNS
* INC # E4: 5,7 => UNS
* DIS # F4: 5,7 => CTR => F4: 6
* INC # F4: 6 => UNS
* DIS # A1: 5,7 => CTR => A1: 2
* INC # A1: 2 => UNS
* DIS # C6: 8,9 => CTR => C6: 2,5,6,7
* INC # C6: 2,5,6,7 => UNS
* DIS # H4: 8,9 => CTR => H4: 1
* INC # H4: 1 => UNS
* INC # I4: 8,9 => UNS
* INC # E4: 5,7 => UNS
* DIS # F4: 5,7 => CTR => F4: 6
* INC # F4: 6 => UNS
* DIS # A6: 5,7 => CTR => A6: 2,4
* INC # A6: 2,4 => UNS
* DIS # C6: 5,7 => CTR => C6: 2,6,8,9
* INC # C6: 2,6,8,9 => UNS
* DIS # G6: 5,7 => CTR => G6: 6,8,9
* INC # G6: 6,8,9 => UNS
* DIS # H6: 5,7 => CTR => H6: 8,9
* PRF # H6: 8,9 => SOL
* PRF # I6: 5,7 => SOL
* INC # I6: 6,8,9 => UNS
* INC # F9: 5,7 => UNS
* INC # F9: 2,6,8 => UNS
* INC # F8: 6,8 => UNS
* INC # D9: 6,8 => UNS
* INC # F9: 6,8 => UNS
* INC # I8: 6,8 => UNS
* INC # I8: 2,5,9 => UNS
* INC # D3: 6,8 => UNS
* INC # D3: 7 => UNS
* CNT  80 HDP CHAINS /  80 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 2,4 => CTR => B3: 6
* PRF B3: 6 # E9: 2,7 => SOL
* STA B3: 6 + E9: 2,7
* CNT   2 HDP CHAINS /   2 HYP OPENED