Analysis of zz-sudoku-de-717677-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6...4.81..7.63.4.......1....85...6.22.......49.3...58....4.......7.58.4..19.2...8 initial

Autosolve

position: 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I1: 3,9 => CTR => I1: 5,7
* DIS # G3: 3,9 => CTR => G3: 2,7
* PRF # G3: 2,9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* DIS # F2: 5 => CTR => F2: 2,9
* PRF # H7: 2,9 => SOL
* DIS # H7: 3,7 => CTR => H7: 2,9
* DIS # I1: 5,9 => CTR => I1: 3,7
* DIS # F2: 5,9 => CTR => F2: 2
* PRF # F2: 2 => SOL
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* DIS # D5: 8,9 => CTR => D5: 3,5
* PRF # D5: 3,5 => SOL
* DIS # E3: 8,9 => CTR => E3: 7
* PRF # E3: 7 => SOL
* DIS # D3: 2,7 => CTR => D3: 8,9
* PRF # D3: 8,9 => SOL
* DIS # H5: 3,9 => CTR => H5: 7
* DIS # D4: 3,9 => CTR => D4: 1
* PRF # D4: 1 => SOL
* DIS # H7: 3,9 => CTR => H7: 2,7
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # F7: 3,7 => SOL
* DIS # F7: 9 => CTR => F7: 3,7
* DIS # G7: 1,9 => CTR => G7: 2,3,7
* PRF # G7: 2,3,7 => SOL
* PRF # G7: 3,7 => SOL
* DIS # H7: 3,7 => CTR => H7: 2,9
* PRF # H7: 2,9 => SOL
* DIS # I7: 3,7 => CTR => I7: 9
* PRF # I7: 9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* PRF # G3: 2,9 => SOL
* DIS # G5: 3,7 => CTR => G5: 9
* PRF # G5: 9 => SOL
* CNT  41 HDP CHAINS /  50 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 # I1: 3,9 => CTR => I1: 5,7
* PRF I1: 5,7 # H7: 2,9 => SOL
* STA I1: 5,7 + H7: 2,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

6...4.81..7.63.4.......1....85...6.22.......49.3...58....4.......7.58.4..19.2...8 initial
6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58 autosolve
632549817178632495594871263785194632261385974943267581856413729327958146419726358 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B1: 3,9
B3: 3,9
H2: 2,9
I2: 5,9
E4: 1,9
E5: 8,9
D6: 2,7
F6: 2,7
H4: 3,9
D8: 1,9
D9: 3,7
G8: 1,9
G9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,E4: 1.. / D4 = 1  =>  0 pairs (*) / E4 = 1  =>  0 pairs (X)
E7,D8: 1.. / E7 = 1  =>  0 pairs (*) / D8 = 1  =>  0 pairs (X)
G7,G8: 1.. / G7 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
E7,G7: 1.. / E7 = 1  =>  0 pairs (*) / G7 = 1  =>  0 pairs (X)
D8,G8: 1.. / D8 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
D4,D8: 1.. / D4 = 1  =>  0 pairs (*) / D8 = 1  =>  0 pairs (X)
E4,E7: 1.. / E4 = 1  =>  0 pairs (X) / E7 = 1  =>  0 pairs (_)
F2,D3: 2.. / F2 = 2  =>  0 pairs (*) / D3 = 2  =>  0 pairs (X)
H2,G3: 2.. / H2 = 2  =>  0 pairs (X) / G3 = 2  =>  0 pairs (_)
D6,F6: 2.. / D6 = 2  =>  0 pairs (*) / F6 = 2  =>  0 pairs (X)
G7,H7: 2.. / G7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
F2,H2: 2.. / F2 = 2  =>  0 pairs (*) / H2 = 2  =>  0 pairs (X)
D3,G3: 2.. / D3 = 2  =>  0 pairs (X) / G3 = 2  =>  0 pairs (_)
D3,D6: 2.. / D3 = 2  =>  0 pairs (X) / D6 = 2  =>  0 pairs (_)
F2,F6: 2.. / F2 = 2  =>  0 pairs (*) / F6 = 2  =>  0 pairs (X)
G3,G7: 2.. / G3 = 2  =>  0 pairs (*) / G7 = 2  =>  0 pairs (X)
H2,H7: 2.. / H2 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
B1,B3: 3.. / B1 = 3  => 13 pairs (_) / B3 = 3  =>  0 pairs (X)
F7,D9: 3.. / F7 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
B1,I1: 3.. / B1 = 3  => 13 pairs (_) / I1 = 3  =>  0 pairs (X)
D4,H4: 3.. / D4 = 3  =>  0 pairs (X) / H4 = 3  =>  0 pairs (_)
D9,G9: 3.. / D9 = 3  =>  0 pairs (X) / G9 = 3  =>  0 pairs (_)
F5,F7: 3.. / F5 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
I1,I2: 5.. / I1 = 5  =>  0 pairs (X) / I2 = 5  => 13 pairs (_)
D5,F5: 5.. / D5 = 5  =>  0 pairs (X) / F5 = 5  =>  0 pairs (_)
F2,I2: 5.. / F2 = 5  =>  0 pairs (X) / I2 = 5  => 13 pairs (_)
D1,D5: 5.. / D1 = 5  =>  0 pairs (*) / D5 = 5  =>  0 pairs (X)
D6,F6: 7.. / D6 = 7  =>  0 pairs (X) / F6 = 7  =>  0 pairs (_)
G5,H5: 7.. / G5 = 7  =>  0 pairs (X) / H5 = 7  => 14 pairs (_)
D9,G9: 7.. / D9 = 7  =>  0 pairs (*) / G9 = 7  =>  0 pairs (X)
E3,E7: 7.. / E3 = 7  =>  0 pairs (*) / E7 = 7  =>  0 pairs (X)
H5,H7: 7.. / H5 = 7  => 14 pairs (_) / H7 = 7  =>  0 pairs (X)
D3,E3: 8.. / D3 = 8  =>  0 pairs (*) / E3 = 8  =>  0 pairs (X)
D5,E5: 8.. / D5 = 8  =>  0 pairs (X) / E5 = 8  =>  0 pairs (_)
D3,D5: 8.. / D3 = 8  =>  0 pairs (*) / D5 = 8  =>  0 pairs (X)
E3,E5: 8.. / E3 = 8  =>  0 pairs (X) / E5 = 8  =>  0 pairs (_)
B1,B3: 9.. / B1 = 9  =>  0 pairs (X) / B3 = 9  => 13 pairs (_)
D8,G8: 9.. / D8 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
* DURATION: 0:01:02.031892  START: 08:12:49.573033  END: 08:13:51.604925 2017-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,D6,D8,D9,E4,E5,F6,G8,G9,H2,H4,I2)
* 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58
* PAIR B1: 3,9 ROW 1
I1: 3,9,5,7                              # reduction candidate for 3,9
I1: 3,9 => CTR
* 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758
I1: 5,7                                  # 15 pairs
* PAIR B3: 3,9 ROW 3
G3: 3,9,2,7                              # reduction candidate for 3,9
G3: 3,9 => CTR
* 6.2.4.81.17863.42.5.4281.67785..46.2261895..4943762581856473...327.58.46419.26.58
G3: 2,7                                  # 15 pairs
I3: 3,9,7                                # reduction candidate for 3,9
I3: 3,9                                  # 17 pairs
* PAIR H2: 2,9 BLK 3
G3: 2,9,3,7                              # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
G3: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
* PAIR H2: 2,9 ROW 2
F2: 2,9,5                                # reduction candidate for 2,9
F2: 5 => CTR
* 6.2.4.81.1786354295.4281.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58
F2: 2,9                                  # 13 pairs
* PAIR H2: 2,9 COL H
H7: 2,9,3,7                              # reduction candidate for 2,9
H7: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
H7: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
* PAIR I2: 5,9 BLK 3
I1: 5,9,3,7                              # reduction candidate for 5,9
I1: 5,9 => CTR
* 632.4.81.17863.4..594.81.6.785..46.2261895..4943.6.581856473...327.58.46419.26.58
I1: 3,7                                  # 14 pairs
* PAIR I2: 5,9 ROW 2
F2: 5,9,2                                # reduction candidate for 5,9
F2: 5,9 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
F2: 2 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR E4: 1,9 BLK 5
D4: 1,9,3                                # reduction candidate for 1,9
D4: 1,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
D4: 3 => CTR
* 6.2.4.81.17863.4..5.4..1.6.785314692261.....4943.6.5818564.312.327.58.46419.26.58
* PAIR E4: 1,9 COL E
E7: 1,9,7                                # reduction candidate for 1,9
E7: 1,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
E7: 7 => CTR
* 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758
* PAIR E5: 8,9 BLK 5
D5: 8,9,3,5                              # reduction candidate for 8,9
D5: 8,9 => CTR
* 6.254.81.17863.4.55.4.71.6.785314692261.857349432675818564.3...327.58.46419726358
D5: 3,5 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR E5: 8,9 COL E
E3: 8,9,7                                # reduction candidate for 8,9
E3: 8,9 => CTR
* 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758
E3: 7 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR D6: 2,7 COL D
D3: 2,7,8,9                              # reduction candidate for 2,7
D3: 2,7 => CTR
* 6.2.4.81.17863.4..5.4.81.6.785..46.2261895..4943.6.581856473...327.58.46419.26.58
D3: 8,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR H4: 3,9 BLK 6
G5: 3,9,7                                # reduction candidate for 3,9
G5: 3,9                                  # 14 pairs
H5: 3,9,7                                # reduction candidate for 3,9
H5: 3,9 => CTR
* 6.2.4.81.17863.42.5.42.1.6.785..46.2261...7.4943.6.5818564...7.327.58.46419726358
H5: 7                                    # 14 pairs
* PAIR H4: 3,9 ROW 4
D4: 3,9,1                                # reduction candidate for 3,9
D4: 3,9 => CTR
* 6.2.4.81.1786324955.4..126.785914632261.8.7.4943.6.5818564..12.327158946419.26.58
D4: 1 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR H4: 3,9 COL H
H7: 3,9,2,7                              # reduction candidate for 3,9
H7: 3,9 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895.74943762581856473...327.58.46419.26.58
H7: 2,7                                  # 15 pairs
* PAIR D8: 1,9 BLK 8
E7: 1,9,7                                # reduction candidate for 1,9
E7: 1,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
E7: 7 => CTR
* 6.2.4.81.1786324955.4..126.785914632261.....4943.6.58185647.12.327158946419326758
* PAIR D8: 1,9 COL D
D4: 1,9,3                                # reduction candidate for 1,9
D4: 1,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
D4: 3 => CTR
* 6.2.4.81.17863.4..5.4..1.6.785314692261.....4943.6.5818564.312.327.58.46419.26.58
* PAIR D9: 3,7 BLK 8
F7: 3,7,9                                # reduction candidate for 3,7
F7: 3,7 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
F7: 9 => CTR
* 6.2.4.81.17863.4..5.4..1.6.785..46.2261..3..4943.6.5818564.9...327158946419326758
* PAIR G8: 1,9 BLK 9
G7: 1,9,2,3,7                            # reduction candidate for 1,9
G7: 1,9 => CTR
* 6.2.4.81.1786324955.4..126.785..4632261...9749432675818564..12.327.58.46419.26.58
G7: 2,3,7 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR G9: 3,7 BLK 9
G7: 3,7,1,2,9                            # reduction candidate for 3,7
G7: 3,7 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
G7: 1,2,9                                # 13 pairs
H7: 3,7,2,9                              # reduction candidate for 3,7
H7: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
H7: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
I7: 3,7,9                                # reduction candidate for 3,7
I7: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
I7: 9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* PAIR G9: 3,7 COL G
G3: 3,7,2,9                              # reduction candidate for 3,7
G3: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
G3: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
G5: 3,7,9                                # reduction candidate for 3,7
G5: 3,7 => CTR
* 6.2.4.81.17863.42.5.4281.6.785..46.2261895..4943762581856473...327.58.46419.26.58
G5: 9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-717677-base-pr-000.dot
* REASONING
* DIS # I1: 3,9 => CTR => I1: 5,7
* DIS # G3: 3,9 => CTR => G3: 2,7
* PRF # G3: 2,9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* DIS # F2: 5 => CTR => F2: 2,9
* PRF # H7: 2,9 => SOL
* DIS # H7: 3,7 => CTR => H7: 2,9
* DIS # I1: 5,9 => CTR => I1: 3,7
* DIS # F2: 5,9 => CTR => F2: 2
* PRF # F2: 2 => SOL
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* DIS # D5: 8,9 => CTR => D5: 3,5
* PRF # D5: 3,5 => SOL
* DIS # E3: 8,9 => CTR => E3: 7
* PRF # E3: 7 => SOL
* DIS # D3: 2,7 => CTR => D3: 8,9
* PRF # D3: 8,9 => SOL
* DIS # H5: 3,9 => CTR => H5: 7
* DIS # D4: 3,9 => CTR => D4: 1
* PRF # D4: 1 => SOL
* DIS # H7: 3,9 => CTR => H7: 2,7
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # F7: 3,7 => SOL
* DIS # F7: 9 => CTR => F7: 3,7
* DIS # G7: 1,9 => CTR => G7: 2,3,7
* PRF # G7: 2,3,7 => SOL
* PRF # G7: 3,7 => SOL
* DIS # H7: 3,7 => CTR => H7: 2,9
* PRF # H7: 2,9 => SOL
* DIS # I7: 3,7 => CTR => I7: 9
* PRF # I7: 9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* PRF # G3: 2,9 => SOL
* DIS # G5: 3,7 => CTR => G5: 9
* PRF # G5: 9 => SOL
* CNT  41 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,D6,D8,D9,E4,E5,F6,G8,G9,H2,H4,I2)
* 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58
* PAIR B1: 3,9 ROW 1
I1: 3,9,5,7                              # reduction candidate for 3,9
I1: 3,9 => CTR
* 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758
* PAIR RESTART
* PAIR H2: 2,9 COL H
H7: 2,9,3,7                              # reduction candidate for 2,9
H7: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* DURATION: 0:00:04.300861  START: 08:14:44.050270  END: 08:14:48.351131 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-717677-base-pr-001.dot
* REASONING
* DIS # I1: 3,9 => CTR => I1: 5,7
* PRF I1: 5,7 # H7: 2,9 => SOL
* STA I1: 5,7 + H7: 2,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokus.de/717677.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 6.2.4.81.17863.4..5.4..1.6.785..46.2261.....4943.6.5818564.....327.58.46419.26.58
B1: 3,9
I1: 3,5,7,9                              # reduction candidate for 3,9
I1: 3,9 => CTR
* 6.2.4.81.1786324955.4..1267785914632261.....4943.6.58185647.12.327158946419326758
H2: 2,9
H7: 2,3,7,9                              # reduction candidate for 2,9
H7: 2,9 => SOLVED
* 632549817178632495594871263785194632261385974943267581856413729327958146419726358
* SOLVED!
--------------------------------------------------

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

highlight 1

* FORCE VALUE:: F7 = 9
F7 = 9                # set value
D8: 1                 # naked single
D9: 3..               # hidden single
G8: 9..               # hidden single
F5: 3..               # hidden single
* FORCE VALUE:: D9 = 3
D9 = 3                # set value
G9: 7                 # naked single
E7: 7..               # hidden single
H4: 3..               # hidden single
* FORCE VALUE:: G7 = 1
G7 = 1                # set value
G8: 9                 # naked single
E7: 7                 # naked single
H7: 2..               # hidden single
E4: 1..               # hidden single
G3: 2..               # hidden single
* FORCE VALUE:: G3 = 2
G3 = 2                # set value
H2: 9                 # naked single
F2: 2..               # hidden single
D6: 2..               # hidden single
G5: 3..               # hidden single
* ANALYZE ..
F2: 2                 # naked single
E4: 1                 # naked single
H4: 3                 # naked single
F5: 3                 # naked single
G5: 3                 # naked single
D6: 2                 # naked single
H7: 2                 # naked single
D5: 5..               # hidden single
F6: 7..               # hidden single
H5: 7..               # hidden single
H5 = 7,9 => CTR
I7: 3..               # hidden single
I2: 5..               # hidden single
D4: 9..               # hidden single
F1: 5..               # hidden single
* CTR!

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

Solution

position: 632549817178632495594871263785194632261385974943267581856413729327958146419726358 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 # I1: 3,9 => CTR => I1: 5,7
* INC # I1: 5,7 => UNS
* DIS # G3: 3,9 => CTR => G3: 2,7
* INC # G3: 2,7 => UNS
* INC # I3: 3,9 => UNS
* PRF # G3: 2,9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* INC # F2: 2,9 => UNS
* DIS # F2: 5 => CTR => F2: 2,9
* PRF # H7: 2,9 => SOL
* DIS # H7: 3,7 => CTR => H7: 2,9
* DIS # I1: 5,9 => CTR => I1: 3,7
* INC # I1: 3,7 => UNS
* DIS # F2: 5,9 => CTR => F2: 2
* PRF # F2: 2 => SOL
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* DIS # D5: 8,9 => CTR => D5: 3,5
* PRF # D5: 3,5 => SOL
* DIS # E3: 8,9 => CTR => E3: 7
* PRF # E3: 7 => SOL
* DIS # D3: 2,7 => CTR => D3: 8,9
* PRF # D3: 8,9 => SOL
* INC # G5: 3,9 => UNS
* DIS # H5: 3,9 => CTR => H5: 7
* INC # H5: 7 => UNS
* DIS # D4: 3,9 => CTR => D4: 1
* PRF # D4: 1 => SOL
* DIS # H7: 3,9 => CTR => H7: 2,7
* INC # H7: 2,7 => UNS
* PRF # E7: 1,9 => SOL
* DIS # E7: 7 => CTR => E7: 1,9
* PRF # D4: 1,9 => SOL
* DIS # D4: 3 => CTR => D4: 1,9
* PRF # F7: 3,7 => SOL
* DIS # F7: 9 => CTR => F7: 3,7
* DIS # G7: 1,9 => CTR => G7: 2,3,7
* PRF # G7: 2,3,7 => SOL
* PRF # G7: 3,7 => SOL
* INC # G7: 1,2,9 => UNS
* DIS # H7: 3,7 => CTR => H7: 2,9
* PRF # H7: 2,9 => SOL
* DIS # I7: 3,7 => CTR => I7: 9
* PRF # I7: 9 => SOL
* DIS # G3: 3,7 => CTR => G3: 2,9
* PRF # G3: 2,9 => SOL
* DIS # G5: 3,7 => CTR => G5: 9
* PRF # G5: 9 => SOL
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # I1: 3,9 => CTR => I1: 5,7
* PRF I1: 5,7 # H7: 2,9 => SOL
* STA I1: 5,7 + H7: 2,9
* CNT   2 HDP CHAINS /   2 HYP OPENED