Analysis of zz-sudoku-de-677379-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8...6263...4...2...7..41.6..3.2..4.......9..8.6..1.94..8...3...2...9551...7... initial

Autosolve

position: ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F1: 5,9 => CTR => F1: 1,3
* PRF # G1: 5,9 => SOL
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D3: 5,9 => CTR => D3: 3,6
* PRF # F3: 5,9 => SOL
* DIS # C4: 1,7 => CTR => C4: 5,9
* PRF # G2: 7,8 => SOL
* DIS # G2: 5,9 => CTR => G2: 7,8
* DIS # H2: 7,8 => CTR => H2: 5
* PRF # H2: 5 => SOL
* DIS # I4: 4 => CTR => I4: 7,8
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D4: 1,7 => CTR => D4: 4,5,9
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D6: 5,9 => CTR => D6: 4,7
* PRF # D6: 4,7 => SOL
* DIS # D4: 1,5 => CTR => D4: 4,7,9
* DIS # F4: 1,5 => CTR => F4: 9
* PRF # F4: 9 => SOL
* PRF # D5: 1,5 => SOL
* PRF # C5: 7 => SOL
* PRF # E1: 1,5 => SOL
* DIS # E1: 9 => CTR => E1: 1,5
* DIS # H4: 8 => CTR => H4: 5,7
* PRF # D6: 5,7 => SOL
* DIS # G1: 5,7 => CTR => G1: 3,9
* DIS # G2: 5,7 => CTR => G2: 8,9
* DIS # I4: 4,7 => CTR => I4: 8
* PRF # D6: 4,7 => SOL
* DIS # D6: 5,9 => CTR => D6: 4,7
* PRF # F3: 5,9 => SOL
* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* CNT  33 HDP CHAINS /  56 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 # F1: 5,9 => CTR => F1: 1,3
* PRF F1: 1,3 # G1: 5,9 => SOL
* STA F1: 1,3 + G1: 5,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

...8...6263...4...2...7..41.6..3.2..4.......9..8.6..1.94..8...3...2...9551...7... initial
..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6 autosolve
754813962631924857289675341165439278427158639398762514946581723873246195512397486 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
A1: 1,7
B1: 5,9
C2: 1,7
C3: 5,9
I2: 7,8
A4: 1,7
B6: 5,9
E5: 1,5
G6: 5,7
I6: 4,7
C7: 2,6
C8: 3,6
C9: 2,3
E8: 1,4
F8: 3,6
D9: 3,9
E9: 4,9
G7: 1,7
H7: 2,7
G8: 1,4
G9: 4,8
H9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C2: 1.. / A1 = 1  =>  0 pairs (X) / C2 = 1  => 22 pairs (_)
G7,G8: 1.. / G7 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
C2,D2: 1.. / C2 = 1  => 22 pairs (_) / D2 = 1  =>  0 pairs (X)
E8,G8: 1.. / E8 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
A1,A4: 1.. / A1 = 1  =>  0 pairs (X) / A4 = 1  => 22 pairs (_)
C7,C9: 2.. / C7 = 2  =>  0 pairs (X) / C9 = 2  =>  0 pairs (_)
H7,H9: 2.. / H7 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
C7,H7: 2.. / C7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
C9,H9: 2.. / C9 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
G1,G3: 3.. / G1 = 3  => 26 pairs (_) / G3 = 3  =>  0 pairs (*)
C8,C9: 3.. / C8 = 3  =>  0 pairs (*) / C9 = 3  =>  0 pairs (X)
F8,D9: 3.. / F8 = 3  =>  0 pairs (X) / D9 = 3  =>  0 pairs (_)
F1,G1: 3.. / F1 = 3  =>  0 pairs (*) / G1 = 3  =>  0 pairs (X)
C8,F8: 3.. / C8 = 3  =>  0 pairs (*) / F8 = 3  =>  0 pairs (X)
C9,D9: 3.. / C9 = 3  =>  0 pairs (X) / D9 = 3  =>  0 pairs (_)
D3,D9: 3.. / D3 = 3  =>  0 pairs (X) / D9 = 3  =>  0 pairs (_)
D4,D6: 4.. / D4 = 4  => 22 pairs (_) / D6 = 4  =>  0 pairs (X)
I4,I6: 4.. / I4 = 4  =>  0 pairs (X) / I6 = 4  => 22 pairs (_)
E8,E9: 4.. / E8 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
G8,G9: 4.. / G8 = 4  =>  0 pairs (X) / G9 = 4  =>  0 pairs (_)
D4,I4: 4.. / D4 = 4  => 22 pairs (_) / I4 = 4  =>  0 pairs (X)
D6,I6: 4.. / D6 = 4  =>  0 pairs (X) / I6 = 4  => 22 pairs (_)
E8,G8: 4.. / E8 = 4  =>  0 pairs (*) / G8 = 4  =>  0 pairs (X)
E9,G9: 4.. / E9 = 4  =>  0 pairs (X) / G9 = 4  =>  0 pairs (_)
B1,C3: 5.. / B1 = 5  =>  0 pairs (*) / C3 = 5  =>  0 pairs (X)
H4,G6: 5.. / H4 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
D7,F7: 5.. / D7 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (*) / B6 = 5  =>  0 pairs (X)
E1,E5: 5.. / E1 = 5  =>  0 pairs (X) / E5 = 5  => 26 pairs (_)
H2,H4: 5.. / H2 = 5  =>  0 pairs (*) / H4 = 5  =>  0 pairs (X)
D3,F3: 6.. / D3 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
C7,C8: 6.. / C7 = 6  =>  0 pairs (*) / C8 = 6  =>  0 pairs (X)
C8,F8: 6.. / C8 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
D3,D7: 6.. / D3 = 6  =>  0 pairs (*) / D7 = 6  =>  0 pairs (X)
A1,C2: 7.. / A1 = 7  => 22 pairs (_) / C2 = 7  =>  0 pairs (X)
G7,H7: 7.. / G7 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
A1,G1: 7.. / A1 = 7  => 22 pairs (_) / G1 = 7  =>  0 pairs (X)
C5,D5: 7.. / C5 = 7  =>  0 pairs (*) / D5 = 7  =>  0 pairs (X)
A1,A4: 7.. / A1 = 7  => 22 pairs (_) / A4 = 7  =>  0 pairs (X)
H4,I4: 8.. / H4 = 8  =>  0 pairs (X) / I4 = 8  => 22 pairs (_)
G9,H9: 8.. / G9 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
G2,G9: 8.. / G2 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
I2,I4: 8.. / I2 = 8  =>  0 pairs (X) / I4 = 8  => 22 pairs (_)
B1,C3: 9.. / B1 = 9  =>  0 pairs (X) / C3 = 9  =>  0 pairs (_)
C4,B6: 9.. / C4 = 9  =>  0 pairs (X) / B6 = 9  =>  0 pairs (_)
D9,E9: 9.. / D9 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
D2,G2: 9.. / D2 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
B6,D6: 9.. / B6 = 9  =>  0 pairs (*) / D6 = 9  =>  0 pairs (X)
B1,B6: 9.. / B1 = 9  =>  0 pairs (X) / B6 = 9  =>  0 pairs (_)
C3,C4: 9.. / C3 = 9  =>  0 pairs (*) / C4 = 9  =>  0 pairs (X)
E1,E9: 9.. / E1 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
* DURATION: 0:01:23.487693  START: 07:43:39.069848  END: 07:45:02.557541 2017-05-01
* CP COUNT: (51)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B6,C2,C3,C7,C8,C9,D9,E5,E8,E9,F8,G6,G7,G8,G9,H7,H9,I2,I6)
* ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6
* PAIR B1: 5,9 ROW 1
E1: 5,9,1                                # reduction candidate for 5,9
E1: 5,9                                  # 25 pairs
F1: 5,9,1,3                              # reduction candidate for 5,9
F1: 5,9 => CTR
* 7.481.362631.248.728..73941169.3.2..42.1586393.8.62.1.94..8172387.24.195512397486
F1: 1,3                                  # 23 pairs
G1: 5,9,3,7                              # reduction candidate for 5,9
G1: 5,9 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
G1: 3,7                                  # 23 pairs
* PAIR C2: 1,7 COL C
C4: 1,7,5,9                              # reduction candidate for 1,7
C4: 1,7 => CTR
* ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486
C4: 5,9                                  # 25 pairs
C5: 1,7,5                                # reduction candidate for 1,7
C5: 1,7                                  # 25 pairs
* PAIR C3: 5,9 ROW 3
D3: 5,9,3,6                              # reduction candidate for 5,9
D3: 5,9 => CTR
* ..48...6263..24...28..76341.6..3.2..42...86393.8.62.1.94.685173876213495513947826
D3: 3,6                                  # 23 pairs
F3: 5,9,3,6                              # reduction candidate for 5,9
F3: 5,9 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
F3: 3,6                                  # 26 pairs
G3: 5,9,3                                # reduction candidate for 5,9
G3: 5,9                                  # 26 pairs
* PAIR C3: 5,9 COL C
C4: 5,9,1,7                              # reduction candidate for 5,9
C4: 1,7 => CTR
* ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486
C4: 5,9                                  # 25 pairs
* PAIR I2: 7,8 BLK 3
G2: 7,8,5,9                              # reduction candidate for 7,8
G2: 7,8 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
G2: 5,9 => CTR
* ..489.36263..249.7289376541.6..392584257186393.8.62.1.942.8..738762.3495513947826
H2: 7,8,5                                # reduction candidate for 7,8
H2: 7,8 => CTR
* 7.4891362631524987289.7.54116..3.25842...86393.8.6271494..8.17387.21.49551..47826
H2: 5 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
* PAIR I2: 7,8 COL I
I4: 7,8,4                                # reduction candidate for 7,8
I4: 4 => CTR
* .548...6263..24.58289.7.341.6..3.28442..58639398462517942.8..738762.3495513947826
I4: 7,8                                  # 22 pairs
* PAIR A4: 1,7 BLK 4
C4: 1,7,5,9                              # reduction candidate for 1,7
C4: 1,7 => CTR
* ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486
C4: 5,9                                  # 25 pairs
C5: 1,7,5                                # reduction candidate for 1,7
C5: 1,7                                  # 25 pairs
* PAIR A4: 1,7 ROW 4
D4: 1,7,4,5,9                            # reduction candidate for 1,7
D4: 1,7 => CTR
* .548...6263..24.58289.7.341.65.3928442..58639398462517942.8..738762.3495513947826
D4: 4,5,9                                # 22 pairs
* PAIR B6: 5,9 BLK 4
C4: 5,9,1,7                              # reduction candidate for 5,9
C4: 1,7 => CTR
* ..48...6263..24...289.7..41.6..3.2..425718639398.62.1.94..8...387.24.19551..97486
C4: 5,9                                  # 25 pairs
* PAIR B6: 5,9 ROW 6
D6: 5,9,4,7                              # reduction candidate for 5,9
D6: 5,9 => CTR
* 7.4891.6263..24...28..7..41.6.43.2..42.7.86393.8.6271494..8.17387.21.49551..47826
D6: 4,7 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
* PAIR E5: 1,5 BLK 5
D4: 1,5,4,7,9                            # reduction candidate for 1,5
D4: 1,5 => CTR
* .548...6263..24.58289.7.341.6..3928442.758639398462517942.8..738762.3495513947826
D4: 4,7,9                                # 22 pairs
F4: 1,5,9                                # reduction candidate for 1,5
F4: 1,5 => CTR
* ..48...6263..249..28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551.397..6
F4: 9 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
D5: 1,5,7                                # reduction candidate for 1,5
D5: 1,5 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
D5: 7                                    # 25 pairs
* PAIR E5: 1,5 ROW 5
C5: 1,5,7                                # reduction candidate for 1,5
C5: 7 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
C5: 1,5                                  # 25 pairs
* PAIR E5: 1,5 COL E
E1: 1,5,9                                # reduction candidate for 1,5
E1: 1,5 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
E1: 9 => CTR
* .5489136263..249..289.7..41.6..392..42..58639398.6251.94..8...387.21.49551.947826
* PAIR G6: 5,7 BLK 6
H4: 5,7,8                                # reduction candidate for 5,7
H4: 8 => CTR
* .548...6263..24.58289.7.341.6..3.28.42..58639398.6251.942.8.173876213495513947826
H4: 5,7                                  # 22 pairs
* PAIR G6: 5,7 ROW 6
D6: 5,7,4,9                              # reduction candidate for 5,7
D6: 5,7 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
D6: 4,9                                  # 25 pairs
* PAIR G6: 5,7 COL G
G1: 5,7,3,9                              # reduction candidate for 5,7
G1: 5,7 => CTR
* ..48.3.6263..24...28..7.341.6..3.2..42...86393.8.62.1.94..8...38732.6.95512397486
G1: 3,9                                  # 23 pairs
G2: 5,7,8,9                              # reduction candidate for 5,7
G2: 5,7 => CTR
* ..48...6263.924...28..7..41.6..392..42...8639398.62.1.94..8...387.2...9551.397..6
G2: 8,9                                  # 23 pairs
* PAIR I6: 4,7 BLK 6
I4: 4,7,8                                # reduction candidate for 4,7
I4: 4,7 => CTR
* .548...6263..24.58289.7.341.6..3.28.42..58639398.6251.942.8..738762.3495513947826
I4: 8                                    # 22 pairs
* PAIR I6: 4,7 ROW 6
D6: 4,7,5,9                              # reduction candidate for 4,7
D6: 4,7 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
D6: 5,9 => CTR
* 7.4891.6263..24...28..7..41.6.43.2..42.7.86393.8.6271494..8.17387.21.49551..47826
* PAIR F8: 3,6 COL F
F3: 3,6,5,9                              # reduction candidate for 3,6
F3: 5,9 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
F3: 3,6                                  # 26 pairs
* PAIR D9: 3,9 COL D
D3: 3,9,5,6                              # reduction candidate for 3,9
D3: 3,9 => CTR
* ..489136263152498728937654116..3.2..42...86393.8.62.1.94.685173876213495513947826
D3: 5,6 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-677379-base-pr-000.dot
* REASONING
* DIS # F1: 5,9 => CTR => F1: 1,3
* PRF # G1: 5,9 => SOL
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D3: 5,9 => CTR => D3: 3,6
* PRF # F3: 5,9 => SOL
* DIS # C4: 1,7 => CTR => C4: 5,9
* PRF # G2: 7,8 => SOL
* DIS # G2: 5,9 => CTR => G2: 7,8
* DIS # H2: 7,8 => CTR => H2: 5
* PRF # H2: 5 => SOL
* DIS # I4: 4 => CTR => I4: 7,8
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D4: 1,7 => CTR => D4: 4,5,9
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D6: 5,9 => CTR => D6: 4,7
* PRF # D6: 4,7 => SOL
* DIS # D4: 1,5 => CTR => D4: 4,7,9
* DIS # F4: 1,5 => CTR => F4: 9
* PRF # F4: 9 => SOL
* PRF # D5: 1,5 => SOL
* PRF # C5: 7 => SOL
* PRF # E1: 1,5 => SOL
* DIS # E1: 9 => CTR => E1: 1,5
* DIS # H4: 8 => CTR => H4: 5,7
* PRF # D6: 5,7 => SOL
* DIS # G1: 5,7 => CTR => G1: 3,9
* DIS # G2: 5,7 => CTR => G2: 8,9
* DIS # I4: 4,7 => CTR => I4: 8
* PRF # D6: 4,7 => SOL
* DIS # D6: 5,9 => CTR => D6: 4,7
* PRF # F3: 5,9 => SOL
* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* CNT  33 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B1,B6,C2,C3,C7,C8,C9,D9,E5,E8,E9,F8,G6,G7,G8,G9,H7,H9,I2,I6)
* ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6
* PAIR B1: 5,9 ROW 1
E1: 5,9,1                                # reduction candidate for 5,9
E1: 5,9                                  # 25 pairs
F1: 5,9,1,3                              # reduction candidate for 5,9
F1: 5,9 => CTR
* 7.481.362631.248.728..73941169.3.2..42.1586393.8.62.1.94..8172387.24.195512397486
G1: 5,9,3,7                              # reduction candidate for 5,9
G1: 5,9 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
* DURATION: 0:00:04.270236  START: 07:45:59.104841  END: 07:46:03.375077 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-677379-base-pr-001.dot
* REASONING
* DIS # F1: 5,9 => CTR => F1: 1,3
* PRF F1: 1,3 # G1: 5,9 => SOL
* STA F1: 1,3 + G1: 5,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokus.de/677379.html
sehr schwierig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: ..48...6263..24...28..7..41.6..3.2..42...86393.8.62.1.94..8...387.2...9551...7..6
A1: 1,7
B1: 5,9
E1: 1,5,9                                # reduction candidate for 5,9
E1: 1 => SOLVED
* 754813962631924857289675341165439278427158639398762514946581723873246195512397486
* SOLVED!

--------------------------------------------------
* AUTO ..
C1 = 4                # set value
E2 = 2                # set value
B3 = 8                # set value
B8: 7                 # naked single
G5 = 6                # set value
H5 = 3                # set value
A8 = 8                # set value
B8 = 7                # set value
I9 = 6                # set value
A6: 3..               # hidden single
F5: 8..               # hidden single
F5 = 8                # set value
A6 = 3                # set value
F6: 2..               # hidden single
F6 = 2                # set value
B5: 2..               # hidden single
B5 = 2                # set value
Q5: 4.. = D4,D6: 4.. => D9 != 4
Q9: 4.. = G8,G9: 4.. => G6 != 4
A1,C2: 1,7.. => C2 != 5,9 # hidden pair
C8,F8: 3,6.. => F8 != 1 # hidden pair
* UNSOLVED!

|:step:| 00
--------------------------------------------------

* DISABLE VALUE:: H2 != 5
* FORCE VALUE:: H2 = 5

|:step:| 01
--------------------------------------------------

Solution

position: 754813962631924857289675341165439278427158639398762514946581723873246195512397486 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 # E1: 5,9 => UNS
* DIS # F1: 5,9 => CTR => F1: 1,3
* INC # F1: 1,3 => UNS
* PRF # G1: 5,9 => SOL
* INC # G1: 3,7 => UNS
* DIS # C4: 1,7 => CTR => C4: 5,9
* INC # C4: 5,9 => UNS
* INC # C5: 1,7 => UNS
* DIS # D3: 5,9 => CTR => D3: 3,6
* INC # D3: 3,6 => UNS
* PRF # F3: 5,9 => SOL
* INC # F3: 3,6 => UNS
* INC # G3: 5,9 => UNS
* INC # C4: 5,9 => UNS
* DIS # C4: 1,7 => CTR => C4: 5,9
* PRF # G2: 7,8 => SOL
* DIS # G2: 5,9 => CTR => G2: 7,8
* DIS # H2: 7,8 => CTR => H2: 5
* PRF # H2: 5 => SOL
* INC # I4: 7,8 => UNS
* DIS # I4: 4 => CTR => I4: 7,8
* DIS # C4: 1,7 => CTR => C4: 5,9
* INC # C4: 5,9 => UNS
* INC # C5: 1,7 => UNS
* DIS # D4: 1,7 => CTR => D4: 4,5,9
* INC # D4: 4,5,9 => UNS
* INC # C4: 5,9 => UNS
* DIS # C4: 1,7 => CTR => C4: 5,9
* DIS # D6: 5,9 => CTR => D6: 4,7
* PRF # D6: 4,7 => SOL
* DIS # D4: 1,5 => CTR => D4: 4,7,9
* INC # D4: 4,7,9 => UNS
* DIS # F4: 1,5 => CTR => F4: 9
* PRF # F4: 9 => SOL
* PRF # D5: 1,5 => SOL
* INC # D5: 7 => UNS
* INC # C5: 1,5 => UNS
* PRF # C5: 7 => SOL
* PRF # E1: 1,5 => SOL
* DIS # E1: 9 => CTR => E1: 1,5
* INC # H4: 5,7 => UNS
* DIS # H4: 8 => CTR => H4: 5,7
* PRF # D6: 5,7 => SOL
* INC # D6: 4,9 => UNS
* DIS # G1: 5,7 => CTR => G1: 3,9
* INC # G1: 3,9 => UNS
* DIS # G2: 5,7 => CTR => G2: 8,9
* INC # G2: 8,9 => UNS
* DIS # I4: 4,7 => CTR => I4: 8
* INC # I4: 8 => UNS
* PRF # D6: 4,7 => SOL
* DIS # D6: 5,9 => CTR => D6: 4,7
* INC # F3: 3,6 => UNS
* PRF # F3: 5,9 => SOL
* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 5,9 => UNS
* DIS # F1: 5,9 => CTR => F1: 1,3
* PRF F1: 1,3 # G1: 5,9 => SOL
* STA F1: 1,3 + G1: 5,9
* CNT   3 HDP CHAINS /   3 HYP OPENED