Analysis of xx-top95-052-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9 initial

Autosolve

position: .........9......84.623...51...6...453..41..96...9...7....1....74.57.2....3.8....9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 7,8 => CTR => A1: 1,5
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* DIS # A4: 7,8 => CTR => A4: 1,2
* DIS # G2: 3,6 => CTR => G2: 2,7
* DIS # H8: 3,6 => CTR => H8: 1
* DIS # I6: 8 => CTR => I6: 2,3
* DIS # A4: 7,8 => CTR => A4: 1,2
* DIS # C4: 7,8 => CTR => C4: 1,9
* DIS # F5: 7,8 => CTR => F5: 5
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* DIS # G6: 2,8 => CTR => G6: 1,3
* PRF # B5: 2,8 => SOL
* DIS # B5: 5,7 => CTR => B5: 2,8
* DIS # A9: 2 => CTR => A9: 1,7
* DIS # C1: 1,7 => CTR => C1: 3,4,8
* DIS # C2: 1,7 => CTR => C2: 3
* DIS # C4: 1,7 => CTR => C4: 8,9
* DIS # G8: 3,8 => CTR => G8: 6
* DIS # I6: 2 => CTR => I6: 3,8
* DIS # A9: 1,2 => CTR => A9: 7
* CNT  20 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 # A1: 7,8 => CTR => A1: 1,5
* DIS A1: 1,5 # C1: 7,8 => CTR => C1: 1,3,4
* DIS A1: 1,5 + C1: 1,3,4 # A4: 7,8 => CTR => A4: 1,2
* DIS A1: 1,5 + C1: 1,3,4 + A4: 1,2 # F2: 6,7 => CTR => F2: 1
* PRF A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 # G2: 6,7 => SOL
* STA A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 + G2: 6,7
* CNT   5 HDP CHAINS /  16 HYP OPENED

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

Details

Positions

.........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9 initial
.........9......84.623...51...6...453..41..96...9...7....1....74.57.2....3.8....9 autosolve
174589362953261784862347951219673845387415296546928173628194537495732618731856429 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
A3: 7,8
D1: 2,5
D2: 2,5
E2: 6,7
H1: 3,6
I1: 2,3
G3: 7,9
C5: 7,8
G5: 2,8
B8: 1,9
C9: 1,7
E8: 3,9
G7: 4,5
H7: 2,3
I8: 3,8
G9: 4,5
H9: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 1.. / F1 = 1  => 23 pairs (_) / F2 = 1  => 19 pairs (_)
G4,G6: 1.. / G4 = 1  =>  0 pairs (X) / G6 = 1  => 17 pairs (_)
H8,H9: 1.. / H8 = 1  => 15 pairs (_) / H9 = 1  =>  0 pairs (X)
B8,H8: 1.. / B8 = 1  =>  0 pairs (X) / H8 = 1  => 15 pairs (_)
D1,D2: 2.. / D1 = 2  =>  0 pairs (X) / D2 = 2  => 19 pairs (_)
E4,E6: 2.. / E4 = 2  => 21 pairs (_) / E6 = 2  => 19 pairs (_)
H7,H9: 2.. / H7 = 2  =>  0 pairs (X) / H9 = 2  => 15 pairs (_)
D2,G2: 2.. / D2 = 2  => 19 pairs (_) / G2 = 2  =>  0 pairs (X)
B5,G5: 2.. / B5 = 2  =>  0 pairs (X) / G5 = 2  => 23 pairs (_)
A9,H9: 2.. / A9 = 2  =>  0 pairs (X) / H9 = 2  => 15 pairs (_)
I1,I6: 2.. / I1 = 2  => 19 pairs (_) / I6 = 2  =>  0 pairs (X)
C1,C2: 3.. / C1 = 3  =>  0 pairs (X) / C2 = 3  => 17 pairs (_)
C2,G2: 3.. / C2 = 3  => 17 pairs (_) / G2 = 3  =>  0 pairs (X)
B1,C1: 4.. / B1 = 4  =>  0 pairs (X) / C1 = 4  => 17 pairs (_)
E3,F3: 4.. / E3 = 4  => 18 pairs (_) / F3 = 4  => 18 pairs (_)
B6,C6: 4.. / B6 = 4  => 17 pairs (_) / C6 = 4  =>  0 pairs (X)
G7,G9: 4.. / G7 = 4  => 17 pairs (_) / G9 = 4  => 17 pairs (_)
B1,B6: 4.. / B1 = 4  =>  0 pairs (X) / B6 = 4  => 17 pairs (_)
C1,C6: 4.. / C1 = 4  => 17 pairs (_) / C6 = 4  =>  0 pairs (X)
D1,D2: 5.. / D1 = 5  => 19 pairs (_) / D2 = 5  =>  0 pairs (X)
G7,G9: 5.. / G7 = 5  => 17 pairs (_) / G9 = 5  => 17 pairs (_)
B2,D2: 5.. / B2 = 5  => 19 pairs (_) / D2 = 5  =>  0 pairs (X)
B5,F5: 5.. / B5 = 5  =>  0 pairs (X) / F5 = 5  => 22 pairs (_)
A1,A6: 5.. / A1 = 5  =>  0 pairs (X) / A6 = 5  => 20 pairs (_)
A6,C6: 6.. / A6 = 6  =>  0 pairs (X) / C6 = 6  => 18 pairs (_)
A7,C7: 6.. / A7 = 6  => 18 pairs (_) / C7 = 6  =>  0 pairs (X)
E9,F9: 6.. / E9 = 6  => 23 pairs (_) / F9 = 6  => 19 pairs (_)
G8,H8: 6.. / G8 = 6  => 17 pairs (_) / H8 = 6  =>  0 pairs (X)
A6,A7: 6.. / A6 = 6  =>  0 pairs (X) / A7 = 6  => 18 pairs (_)
C6,C7: 6.. / C6 = 6  => 18 pairs (_) / C7 = 6  =>  0 pairs (X)
H1,H8: 6.. / H1 = 6  => 17 pairs (_) / H8 = 6  =>  0 pairs (X)
A9,C9: 7.. / A9 = 7  => 16 pairs (_) / C9 = 7  =>  0 pairs (X)
G8,I8: 8.. / G8 = 8  =>  0 pairs (X) / I8 = 8  => 18 pairs (_)
I6,I8: 8.. / I6 = 8  =>  0 pairs (X) / I8 = 8  => 18 pairs (_)
G1,G3: 9.. / G1 = 9  => 18 pairs (_) / G3 = 9  => 16 pairs (_)
B4,C4: 9.. / B4 = 9  =>  0 pairs (X) / C4 = 9  => 18 pairs (_)
B8,E8: 9.. / B8 = 9  => 15 pairs (_) / E8 = 9  =>  0 pairs (X)
C4,C7: 9.. / C4 = 9  => 18 pairs (_) / C7 = 9  =>  0 pairs (X)
* DURATION: 0:01:07.727997  START: 23:54:58.350021  END: 23:56:06.078018 2017-05-03
* CP COUNT: (38)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B8,C5,C9,D1,D2,E2,E8,G3,G5,G7,G9,H1,H7,H9,I1,I8)
* .........9......84.623...51...6...453..41..96...9...7....1....74.57.2....3.8....9
* PAIR A3: 7,8 BLK 1
A1: 7,8,1,5                              # reduction candidate for 7,8
A1: 7,8 => CTR
* ..4....6.9.3....84.623...5128.6...453..415.965469..17.6..1....7495732.18.3.8...29
A1: 1,5                                  # 18 pairs
B1: 7,8,1,4,5                            # reduction candidate for 7,8
B1: 7,8                                  # 20 pairs
C1: 7,8,1,3,4                            # reduction candidate for 7,8
C1: 7,8 => CTR
* 54.2.1..39135..284.623...511.96...4532.4158966549..1722861....74.57.2....318...29
C1: 1,3,4                                # 17 pairs
* PAIR A3: 7,8 ROW 3
E3: 7,8,4,9                              # reduction candidate for 7,8
E3: 7,8                                  # 18 pairs
F3: 7,8,4,9                              # reduction candidate for 7,8
F3: 7,8                                  # 22 pairs
* PAIR A3: 7,8 COL A
A4: 7,8,1,2                              # reduction candidate for 7,8
A4: 7,8 => CTR
* ........29..2...848623...517..6...45358417296...9...7..8.1....74.57.2....378....9
A4: 1,2                                  # 18 pairs
* PAIR E2: 6,7 BLK 2
E1: 6,7,8,9                              # reduction candidate for 6,7
E1: 6,7                                  # 22 pairs
F1: 6,7,1,8,9                            # reduction candidate for 6,7
F1: 6,7                                  # 21 pairs
F2: 6,7,1                                # reduction candidate for 6,7
F2: 6,7                                  # 23 pairs
* PAIR E2: 6,7 ROW 2
G2: 6,7,2,3                              # reduction candidate for 6,7
G2: 6,7                                  # 19 pairs
G2: 2,3                                  # 19 pairs
* PAIR H1: 3,6 BLK 3
G1: 3,6,2,7,9                            # reduction candidate for 3,6
G1: 3,6                                  # 17 pairs
G2: 3,6,2,7                              # reduction candidate for 3,6
G2: 3,6 => CTR
* ..45...32953271684.623...51..16.7.453..415.9654692.17.6.91...27415792.6.2378...19
G2: 2,7                                  # 18 pairs
* PAIR H1: 3,6 COL H
H8: 3,6,1                                # reduction candidate for 3,6
H8: 3,6 => CTR
* ...5....295.2...84.623...51...6...453784152965.69..17.6891...27415792...2378...19
H8: 1                                    # 15 pairs
* PAIR I1: 2,3 BLK 3
G1: 2,3,6,7,9                            # reduction candidate for 2,3
G1: 2,3                                  # 18 pairs
G2: 2,3,6,7                              # reduction candidate for 2,3
G2: 2,3                                  # 19 pairs
* PAIR I1: 2,3 COL I
I6: 2,3,8                                # reduction candidate for 2,3
I6: 8 => CTR
* ..45...329532.1.84.6234..51..16..3453784152965.69.31786..13.527415792863237856419
I6: 2,3                                  # 18 pairs
* PAIR G3: 7,9 BLK 3
G1: 7,9,2,3,6                            # reduction candidate for 7,9
G1: 7,9                                  # 18 pairs
G1: 2,3,6                                # 16 pairs
* PAIR G3: 7,9 ROW 3
E3: 7,9,4,8                              # reduction candidate for 7,9
E3: 7,9                                  # 19 pairs
F3: 7,9,4,8                              # reduction candidate for 7,9
F3: 7,9                                  # 19 pairs
* PAIR C5: 7,8 BLK 4
A4: 7,8,1,2                              # reduction candidate for 7,8
A4: 7,8 => CTR
* ........29..2...848623...517..6...45358417296...9...7..8.1....74.57.2....378....9
A4: 1,2                                  # 18 pairs
B4: 7,8,1,2,9                            # reduction candidate for 7,8
B4: 7,8                                  # 21 pairs
C4: 7,8,1,9                              # reduction candidate for 7,8
C4: 7,8 => CTR
* .........9......84.623...51.9.6...453..41..96...9...7...91....7415792....378...19
C4: 1,9                                  # 18 pairs
B5: 7,8,2,5                              # reduction candidate for 7,8
B5: 7,8                                  # 23 pairs
* PAIR C5: 7,8 ROW 5
F5: 7,8,5                                # reduction candidate for 7,8
F5: 7,8 => CTR
* .........9......84.623...51...6...4535.41.296...9...7....1....74.57.2....3.8....9
F5: 5                                    # 22 pairs
* PAIR C5: 7,8 COL C
C1: 7,8,1,3,4                            # reduction candidate for 7,8
C1: 7,8 => CTR
* 54.2.1..39135..284.623...511.96...4532.4158966549..1722861....74.57.2....318...29
C1: 1,3,4                                # 17 pairs
* PAIR G5: 2,8 BLK 6
G4: 2,8,1,3                              # reduction candidate for 2,8
G4: 2,8                                  # 20 pairs
G6: 2,8,1,3                              # reduction candidate for 2,8
G6: 2,8 => CTR
* ...5....295.2...84.623...51...6..1453..415.965.69.8.73...1....74.57.2..8.3.8....9
G6: 1,3                                  # 18 pairs
I6: 2,8,3                                # reduction candidate for 2,8
I6: 2,8                                  # 21 pairs
* PAIR G5: 2,8 ROW 5
B5: 2,8,5,7                              # reduction candidate for 2,8
B5: 2,8 => SOLVED
* 174589362953261784862347951219673845387415296546928173628194537495732618731856429
B5: 5,7 => CTR
* ...5....295.2...84.623...51...6...453784152965.69...7.6891...27415792...2378...19
* PAIR B8: 1,9 COL B
B4: 1,9,2,7,8                            # reduction candidate for 1,9
B4: 1,9                                  # 20 pairs
B4: 2,7,8                                # 18 pairs
* PAIR C9: 1,7 BLK 7
A9: 1,7,2                                # reduction candidate for 1,7
A9: 2 => CTR
* ...5....295.2...84.623...51...6...453784152965.69..17.6891...27415792...2378...19
A9: 1,7                                  # 15 pairs
* PAIR C9: 1,7 COL C
C1: 1,7,3,4,8                            # reduction candidate for 1,7
C1: 1,7 => CTR
* 54.2.....9.3....84.623...51..96...453.841.2966.49...7..861....7495732.18.3.8...29
C1: 3,4,8                                # 17 pairs
C2: 1,7,3                                # reduction candidate for 1,7
C2: 1,7 => CTR
* .435...6295.2..384.623...51..96...453..41..96..49...73..61....74.57.26.8.3.8....9
C2: 3                                    # 17 pairs
C4: 1,7,8,9                              # reduction candidate for 1,7
C4: 1,7 => CTR
* .........9......84.623...51.916...453.841.296..69..17.6891...27415792...2378...19
C4: 8,9                                  # 18 pairs
* PAIR E8: 3,9 BLK 8
E7: 3,9,4,5                              # reduction candidate for 3,9
E7: 3,9                                  # 19 pairs
F7: 3,9,4,5                              # reduction candidate for 3,9
F7: 3,9                                  # 19 pairs
* PAIR G7: 4,5 ROW 7
E7: 4,5,3,9                              # reduction candidate for 4,5
E7: 4,5                                  # 19 pairs
F7: 4,5,3,9                              # reduction candidate for 4,5
F7: 4,5                                  # 19 pairs
* PAIR I8: 3,8 BLK 9
G8: 3,8,6                                # reduction candidate for 3,8
G8: 3,8 => CTR
* ..45...329532.1.84.623...51.916...453.84152965.69..17.6891...27415792.6.2378...19
G8: 6                                    # 17 pairs
* PAIR I8: 3,8 COL I
I6: 3,8,2                                # reduction candidate for 3,8
I6: 2 => CTR
* .......639.3....848623...511..627345327415896...9..1722.61...374957326187318...29
I6: 3,8                                  # 19 pairs
* PAIR G9: 4,5 ROW 9
E9: 4,5,6                                # reduction candidate for 4,5
E9: 4,5                                  # 19 pairs
F9: 4,5,6                                # reduction candidate for 4,5
F9: 4,5                                  # 23 pairs
* PAIR H9: 1,2 ROW 9
A9: 1,2,7                                # reduction candidate for 1,2
A9: 1,2 => CTR
* ...5....295.2...84.623...51...6...453784152965.69...7.6891...27415792...2378...19
A9: 7                                    # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-052-base-pr-000.dot
* REASONING
* DIS # A1: 7,8 => CTR => A1: 1,5
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* DIS # A4: 7,8 => CTR => A4: 1,2
* DIS # G2: 3,6 => CTR => G2: 2,7
* DIS # H8: 3,6 => CTR => H8: 1
* DIS # I6: 8 => CTR => I6: 2,3
* DIS # A4: 7,8 => CTR => A4: 1,2
* DIS # C4: 7,8 => CTR => C4: 1,9
* DIS # F5: 7,8 => CTR => F5: 5
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* DIS # G6: 2,8 => CTR => G6: 1,3
* PRF # B5: 2,8 => SOL
* DIS # B5: 5,7 => CTR => B5: 2,8
* DIS # A9: 2 => CTR => A9: 1,7
* DIS # C1: 1,7 => CTR => C1: 3,4,8
* DIS # C2: 1,7 => CTR => C2: 3
* DIS # C4: 1,7 => CTR => C4: 8,9
* DIS # G8: 3,8 => CTR => G8: 6
* DIS # I6: 2 => CTR => I6: 3,8
* DIS # A9: 1,2 => CTR => A9: 7
* CNT  20 HDP CHAINS /  65 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B8,C5,C9,D1,D2,E2,E8,G3,G5,G7,G9,H1,H7,H9,I1,I8)
* .........9......84.623...51...6...453..41..96...9...7....1....74.57.2....3.8....9
* PAIR A3: 7,8 BLK 1
A1: 7,8,1,5                              # reduction candidate for 7,8
A1: 7,8 => CTR
* ..4....6.9.3....84.623...5128.6...453..415.965469..17.6..1....7495732.18.3.8...29
B1: 7,8,1,4,5                            # reduction candidate for 7,8
B1: 7,8                                  # 20 pairs
C1: 7,8,1,3,4                            # reduction candidate for 7,8
C1: 7,8 => CTR
* 54.2.1..39135..284.623...511.96...4532.4158966549..1722861....74.57.2....318...29
* RESTART
* PAIR A3: 7,8 BLK 1
B1: 7,8,1,4,5                            # reduction candidate for 7,8
B1: 1,4,5                                # 22 pairs
B1: 7,8                                  # 20 pairs
* PAIR A3: 7,8 ROW 3
E3: 7,8,4,9                              # reduction candidate for 7,8
E3: 7,8                                  # 19 pairs
F3: 7,8,4,9                              # reduction candidate for 7,8
F3: 7,8                                  # 23 pairs
* PAIR A3: 7,8 COL A
A4: 7,8,1,2                              # reduction candidate for 7,8
A4: 7,8 => CTR
* ........29..2...848623...517..6...45358417296...9...7..8.1....74.57.2....378....9
* PAIR RESTART
* PAIR A3: 7,8 BLK 1
B1: 7,8,1,4,5                            # reduction candidate for 7,8
B1: 7,8                                  # 21 pairs
B1: 1,4,5                                # 20 pairs
* PAIR A3: 7,8 ROW 3
E3: 7,8,4,9                              # reduction candidate for 7,8
E3: 7,8                                  # 20 pairs
F3: 7,8,4,9                              # reduction candidate for 7,8
F3: 7,8                                  # 24 pairs
* PAIR E2: 6,7 BLK 2
E1: 6,7,8,9                              # reduction candidate for 6,7
E1: 6,7                                  # 24 pairs
F1: 6,7,1,8,9                            # reduction candidate for 6,7
F1: 6,7                                  # 23 pairs
F2: 6,7,1                                # reduction candidate for 6,7
F2: 6,7 => CTR
* 5..2.1..39.35..284.623...51...6...4532.415896.549...7....1....74.57.2....3.8....9
* PAIR E2: 6,7 ROW 2
G2: 6,7,2,3                              # reduction candidate for 6,7
G2: 6,7 => SOLVED
* 174589362953261784862347951219673845387415296546928173628194537495732618731856429
* DURATION: 0:00:17.992957  START: 23:57:06.756575  END: 23:57:24.749532 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-052-base-pr-001.dot
* REASONING
* DIS # A1: 7,8 => CTR => A1: 1,5
* DIS A1: 1,5 # C1: 7,8 => CTR => C1: 1,3,4
* DIS A1: 1,5 + C1: 1,3,4 # A4: 7,8 => CTR => A4: 1,2
* DIS A1: 1,5 + C1: 1,3,4 + A4: 1,2 # F2: 6,7 => CTR => F2: 1
* PRF A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 # G2: 6,7 => SOL
* STA A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 + G2: 6,7
* CNT   5 HDP CHAINS /  16 HYP OPENED

Header Info

Top 95 Sudokus 052
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 174589362953261784862347951219673845387415296546928173628194537495732618731856429 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 # A1: 7,8 => CTR => A1: 1,5
* INC # A1: 1,5 => UNS
* INC # B1: 7,8 => UNS
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* INC # C1: 1,3,4 => UNS
* INC # E3: 7,8 => UNS
* INC # F3: 7,8 => UNS
* DIS # A4: 7,8 => CTR => A4: 1,2
* INC # A4: 1,2 => UNS
* INC # E1: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # F2: 6,7 => UNS
* INC # G2: 6,7 => UNS
* INC # G2: 2,3 => UNS
* INC # G1: 3,6 => UNS
* DIS # G2: 3,6 => CTR => G2: 2,7
* INC # G2: 2,7 => UNS
* DIS # H8: 3,6 => CTR => H8: 1
* INC # H8: 1 => UNS
* INC # G1: 2,3 => UNS
* INC # G2: 2,3 => UNS
* INC # I6: 2,3 => UNS
* DIS # I6: 8 => CTR => I6: 2,3
* INC # G1: 7,9 => UNS
* INC # G1: 2,3,6 => UNS
* INC # E3: 7,9 => UNS
* INC # F3: 7,9 => UNS
* DIS # A4: 7,8 => CTR => A4: 1,2
* INC # A4: 1,2 => UNS
* INC # B4: 7,8 => UNS
* DIS # C4: 7,8 => CTR => C4: 1,9
* INC # C4: 1,9 => UNS
* INC # B5: 7,8 => UNS
* DIS # F5: 7,8 => CTR => F5: 5
* INC # F5: 5 => UNS
* DIS # C1: 7,8 => CTR => C1: 1,3,4
* INC # C1: 1,3,4 => UNS
* INC # G4: 2,8 => UNS
* DIS # G6: 2,8 => CTR => G6: 1,3
* INC # G6: 1,3 => UNS
* INC # I6: 2,8 => UNS
* PRF # B5: 2,8 => SOL
* DIS # B5: 5,7 => CTR => B5: 2,8
* INC # B4: 1,9 => UNS
* INC # B4: 2,7,8 => UNS
* INC # A9: 1,7 => UNS
* DIS # A9: 2 => CTR => A9: 1,7
* DIS # C1: 1,7 => CTR => C1: 3,4,8
* INC # C1: 3,4,8 => UNS
* DIS # C2: 1,7 => CTR => C2: 3
* INC # C2: 3 => UNS
* DIS # C4: 1,7 => CTR => C4: 8,9
* INC # C4: 8,9 => UNS
* INC # E7: 3,9 => UNS
* INC # F7: 3,9 => UNS
* INC # E7: 4,5 => UNS
* INC # F7: 4,5 => UNS
* DIS # G8: 3,8 => CTR => G8: 6
* INC # G8: 6 => UNS
* INC # I6: 3,8 => UNS
* DIS # I6: 2 => CTR => I6: 3,8
* INC # E9: 4,5 => UNS
* INC # F9: 4,5 => UNS
* DIS # A9: 1,2 => CTR => A9: 7
* INC # A9: 7 => UNS
* CNT  65 HDP CHAINS /  65 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 7,8 => CTR => A1: 1,5
* INC A1: 1,5 # B1: 7,8 => UNS
* DIS A1: 1,5 # C1: 7,8 => CTR => C1: 1,3,4
* INC A1: 1,5 + C1: 1,3,4 # B1: 7,8 => UNS
* INC A1: 1,5 + C1: 1,3,4 # B1: 1,4,5 => UNS
* INC A1: 1,5 + C1: 1,3,4 # E3: 7,8 => UNS
* INC A1: 1,5 + C1: 1,3,4 # F3: 7,8 => UNS
* DIS A1: 1,5 + C1: 1,3,4 # A4: 7,8 => CTR => A4: 1,2
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # B1: 7,8 => UNS
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # B1: 1,4,5 => UNS
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # E3: 7,8 => UNS
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # F3: 7,8 => UNS
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # E1: 6,7 => UNS
* INC A1: 1,5 + C1: 1,3,4 + A4: 1,2 # F1: 6,7 => UNS
* DIS A1: 1,5 + C1: 1,3,4 + A4: 1,2 # F2: 6,7 => CTR => F2: 1
* PRF A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 # G2: 6,7 => SOL
* STA A1: 1,5 + C1: 1,3,4 + A4: 1,2 + F2: 1 + G2: 6,7
* CNT  16 HDP CHAINS /  16 HYP OPENED