Analysis of zz-sudoku-de-680159-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 28...6..4.5.7...32....8....1......2...5.4.6...9......1....2....72...1.6.4..3...79 initial

Autosolve

position: 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F3: 3,9 => CTR => F3: 4,5
* DIS # D4: 6,8 => CTR => D4: 5,9
* DIS # F3: 3,5 => CTR => F3: 4,9
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* DIS # F3: 3,5 => CTR => F3: 4,9
* PRF # A6: 3,8 => SOL
* DIS # I5: 7 => CTR => I5: 3,8
* DIS # B4: 3,7 => CTR => B4: 4,6
* PRF # I5: 8 => SOL
* PRF # B3: 3,7 => SOL
* DIS # I4: 3,5 => CTR => I4: 7,8
* PRF # G6: 3,5 => SOL
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* DIS # F4: 3,5 => CTR => F4: 8,9
* PRF # G8: 4 => SOL
* DIS # B4: 3,6 => CTR => B4: 4,7
* DIS # I8: 3,8 => CTR => I8: 5
* DIS # C9: 1,6 => CTR => C9: 8
* PRF # C9: 8 => SOL
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* DIS # E4: 3 => CTR => E4: 5,6
* PRF # F4: 5,8 => SOL
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* DIS # I8: 3,8 => CTR => I8: 5
* DIS # I4: 3,8 => CTR => I4: 5,7
* CNT  29 HDP CHAINS /  55 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 # F3: 3,9 => CTR => F3: 4,5
* DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9
* PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL
* STA F3: 4,5 + D4: 5,9 + A6: 3,8
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

28...6..4.5.7...32....8....1......2...5.4.6...9......1....2....72...1.6.4..3...79 initial
28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279 autosolve
287536914654719832931284756146958327375142698892673541569427183723891465418365279 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
A2: 6,9
C2: 4,6
A3: 3,9
D1: 5,9
E1: 3,5
F2: 4,9
G1: 7,9
H1: 1,5
G3: 7,9
H3: 1,5
A5: 3,8
B5: 3,7
G4: 3,5
H6: 4,8
B7: 3,6
C8: 3,8
B9: 1,6
D8: 4,8
E9: 5,6
F9: 5,8
H7: 4,8
I7: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 21 pairs (_) / H3 = 1  =>  0 pairs (X)
B9,C9: 1.. / B9 = 1  => 22 pairs (_) / C9 = 1  =>  0 pairs (X)
C1,H1: 1.. / C1 = 1  =>  0 pairs (X) / H1 = 1  => 21 pairs (_)
B3,B9: 1.. / B3 = 1  =>  0 pairs (X) / B9 = 1  => 22 pairs (_)
E1,F3: 3.. / E1 = 3  => 23 pairs (_) / F3 = 3  =>  0 pairs (X)
B7,C8: 3.. / B7 = 3  =>  0 pairs (X) / C8 = 3  =>  0 pairs (_)
C1,E1: 3.. / C1 = 3  =>  0 pairs (X) / E1 = 3  => 23 pairs (_)
B7,I7: 3.. / B7 = 3  =>  0 pairs (X) / I7 = 3  =>  0 pairs (_)
E1,E4: 3.. / E1 = 3  => 23 pairs (_) / E4 = 3  =>  0 pairs (X)
F2,F3: 4.. / F2 = 4  => 22 pairs (_) / F3 = 4  =>  0 pairs (*)
B4,C4: 4.. / B4 = 4  => 23 pairs (_) / C4 = 4  =>  0 pairs (X)
G6,H6: 4.. / G6 = 4  => 27 pairs (_) / H6 = 4  =>  0 pairs (*)
D7,D8: 4.. / D7 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
H7,G8: 4.. / H7 = 4  => 27 pairs (_) / G8 = 4  =>  0 pairs (*)
C2,F2: 4.. / C2 = 4  =>  0 pairs (*) / F2 = 4  =>  0 pairs (X)
D7,H7: 4.. / D7 = 4  =>  0 pairs (*) / H7 = 4  =>  0 pairs (X)
D8,G8: 4.. / D8 = 4  => 27 pairs (_) / G8 = 4  =>  0 pairs (*)
B3,B4: 4.. / B3 = 4  =>  0 pairs (X) / B4 = 4  => 23 pairs (_)
G6,G8: 4.. / G6 = 4  => 27 pairs (_) / G8 = 4  =>  0 pairs (*)
H6,H7: 4.. / H6 = 4  =>  0 pairs (*) / H7 = 4  =>  0 pairs (X)
H1,H3: 5.. / H1 = 5  =>  0 pairs (X) / H3 = 5  => 21 pairs (_)
E9,F9: 5.. / E9 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
G8,I8: 5.. / G8 = 5  =>  0 pairs (X) / I8 = 5  => 24 pairs (_)
F3,H3: 5.. / F3 = 5  =>  0 pairs (X) / H3 = 5  => 21 pairs (_)
I4,I8: 5.. / I4 = 5  =>  0 pairs (X) / I8 = 5  => 24 pairs (_)
A2,C2: 6.. / A2 = 6  =>  0 pairs (*) / C2 = 6  =>  0 pairs (X)
D7,E9: 6.. / D7 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
A6,D6: 6.. / A6 = 6  => 22 pairs (_) / D6 = 6  =>  0 pairs (*)
B7,D7: 6.. / B7 = 6  =>  0 pairs (*) / D7 = 6  =>  0 pairs (X)
A2,A6: 6.. / A2 = 6  =>  0 pairs (*) / A6 = 6  =>  0 pairs (X)
E4,E9: 6.. / E4 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
G1,G3: 7.. / G1 = 7  =>  0 pairs (X) / G3 = 7  => 19 pairs (_)
I4,I5: 7.. / I4 = 7  => 28 pairs (_) / I5 = 7  =>  0 pairs (X)
C1,G1: 7.. / C1 = 7  => 19 pairs (_) / G1 = 7  =>  0 pairs (X)
B5,I5: 7.. / B5 = 7  => 28 pairs (_) / I5 = 7  =>  0 pairs (X)
A5,A6: 8.. / A5 = 8  => 23 pairs (_) / A6 = 8  =>  0 pairs (*)
C8,C9: 8.. / C8 = 8  =>  0 pairs (X) / C9 = 8  =>  0 pairs (_)
A5,I5: 8.. / A5 = 8  => 23 pairs (_) / I5 = 8  =>  0 pairs (*)
C9,F9: 8.. / C9 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
H6,H7: 8.. / H6 = 8  => 27 pairs (_) / H7 = 8  =>  0 pairs (*)
A2,A3: 9.. / A2 = 9  => 22 pairs (_) / A3 = 9  =>  0 pairs (*)
G1,G3: 9.. / G1 = 9  => 19 pairs (_) / G3 = 9  =>  0 pairs (X)
D4,F4: 9.. / D4 = 9  => 19 pairs (_) / F4 = 9  =>  0 pairs (X)
D1,G1: 9.. / D1 = 9  =>  0 pairs (X) / G1 = 9  => 19 pairs (_)
A2,F2: 9.. / A2 = 9  => 22 pairs (_) / F2 = 9  =>  0 pairs (*)
D1,D4: 9.. / D1 = 9  =>  0 pairs (X) / D4 = 9  => 19 pairs (_)
* DURATION: 0:01:28.955567  START: 07:48:01.102611  END: 07:49:30.058178 2017-05-01
* CP COUNT: (46)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,B5,B7,B9,C2,C8,D1,D8,E1,E9,F2,F9,G1,G3,G4,H1,H3,H6,H7,I7)
* 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279
* PAIR C2: 4,6 COL C
C4: 4,6,3,7                              # reduction candidate for 4,6
C4: 4,6                                  # 24 pairs
C4: 3,7                                  # 24 pairs
* PAIR A3: 3,9 ROW 3
F3: 3,9,4,5                              # reduction candidate for 3,9
F3: 3,9 => CTR
* 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279
F3: 4,5                                  # 24 pairs
* PAIR D1: 5,9 BLK 2
F3: 5,9,3,4                              # reduction candidate for 5,9
F3: 5,9                                  # 22 pairs
F3: 3,4                                  # 22 pairs
* PAIR D1: 5,9 COL D
D4: 5,9,6,8                              # reduction candidate for 5,9
D4: 6,8 => CTR
* 28.9.67.49567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279
D4: 5,9                                  # 24 pairs
* PAIR E1: 3,5 BLK 2
F3: 3,5,4,9                              # reduction candidate for 3,5
F3: 3,5 => CTR
* 28.9.67.49567148323..2859161....9.2.8.514269.692.73..15.9.271..72..91.6.4183..279
F3: 4,9                                  # 19 pairs
* PAIR E1: 3,5 COL E
E4: 3,5,6                                # reduction candidate for 3,5
E4: 3,5 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
E4: 6 => CTR
* 287.3691495671483231428975614..6..2...514269.692.7...15.962714872.491.6.461358279
* PAIR F2: 4,9 BLK 2
F3: 4,9,3,5                              # reduction candidate for 4,9
F3: 3,5 => CTR
* 28.9.67.49567148323..2859161....9.2.8.514269.692.73..15.9.271..72..91.6.4183..279
F3: 4,9                                  # 19 pairs
* PAIR A5: 3,8 BLK 4
A6: 3,8,6                                # reduction candidate for 3,8
A6: 3,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
A6: 6                                    # 22 pairs
* PAIR A5: 3,8 ROW 5
I5: 3,8,7                                # reduction candidate for 3,8
I5: 7 => CTR
* 28..36..49567148323..28975617.....2.835142697692.7...1569.271.3723.91.6.418365279
I5: 3,8                                  # 28 pairs
* PAIR B5: 3,7 BLK 4
B4: 3,7,4,6                              # reduction candidate for 3,7
B4: 3,7 => CTR
* 28..36..495671483234.2897561.4....2.8.514269.692.7...1569.271.3723.91.6.418365279
B4: 4,6                                  # 23 pairs
C4: 3,7,4,6                              # reduction candidate for 3,7
C4: 3,7                                  # 24 pairs
* PAIR B5: 3,7 ROW 5
I5: 3,7,8                                # reduction candidate for 3,7
I5: 8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
I5: 3,7                                  # 23 pairs
* PAIR B5: 3,7 COL B
B3: 3,7,1,4                              # reduction candidate for 3,7
B3: 3,7 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
B3: 1,4                                  # 23 pairs
* PAIR G4: 3,5 BLK 6
I4: 3,5,7,8                              # reduction candidate for 3,5
I4: 3,5 => CTR
* 28...6..4.5.71.832...28...61......2.83514269769257348156982714372349156841836.279
I4: 7,8                                  # 25 pairs
G6: 3,5,4                                # reduction candidate for 3,5
G6: 3,5 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
G6: 4                                    # 27 pairs
* PAIR G4: 3,5 ROW 4
E4: 3,5,6                                # reduction candidate for 3,5
E4: 3,5 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
E4: 6 => CTR
* 287.3691495671483231428975614..6..2...514269.692.7...15.962714872.491.6.461358279
F4: 3,5,8,9                              # reduction candidate for 3,5
F4: 3,5 => CTR
* 28.536914.5.71.832..128.75617.9...288.5142697.92.7..415.94271837238914654.8365279
F4: 8,9                                  # 23 pairs
* PAIR G4: 3,5 COL G
G8: 3,5,4                                # reduction candidate for 3,5
G8: 4 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
G8: 3,5                                  # 27 pairs
* PAIR B7: 3,6 COL B
B4: 3,6,4,7                              # reduction candidate for 3,6
B4: 3,6 => CTR
* 28...6..4.56714832.4.28...61.4....27.7514269.692.7...1569.271.3723891465418365279
B4: 4,7                                  # 24 pairs
* PAIR C8: 3,8 ROW 8
I8: 3,8,5                                # reduction candidate for 3,8
I8: 3,8 => CTR
* 28...6..4.5.71.832...28...61.....32583514269769257348156982714372349156841836.279
I8: 5                                    # 24 pairs
* PAIR B9: 1,6 BLK 7
C9: 1,6,8                                # reduction candidate for 1,6
C9: 1,6 => CTR
* 28..36..4.5.71.832...28...61..869.2.875142693692573481539627148728491365461358279
C9: 8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
* PAIR D8: 4,8 BLK 8
D7: 4,8,6                                # reduction candidate for 4,8
D7: 4,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
D7: 6 => CTR
* 28..36..4.5.71.832...28...61..869.2.8.514269.692573481539627148728491.6.461358279
* PAIR E9: 5,6 COL E
E4: 5,6,3                                # reduction candidate for 5,6
E4: 3 => CTR
* 283.56714.5.71.8329..28...61...3.52...514269..92.7...15.9.271..72..91.654..365279
E4: 5,6                                  # 23 pairs
* PAIR F9: 5,8 COL F
F4: 5,8,3,9                              # reduction candidate for 5,8
F4: 5,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
F4: 3,9                                  # 23 pairs
F6: 5,8,3                                # reduction candidate for 5,8
F6: 5,8                                  # 27 pairs
* PAIR H7: 4,8 ROW 7
D7: 4,8,6                                # reduction candidate for 4,8
D7: 4,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
D7: 6 => CTR
* 28..36..4.5.71.832...28...61..869.2.8.514269.692573481539627148728491.6.461358279
* PAIR I7: 3,8 BLK 9
I8: 3,8,5                                # reduction candidate for 3,8
I8: 3,8 => CTR
* 28...6..4.5.71.832...28...61.....32583514269769257348156982714372349156841836.279
I8: 5                                    # 24 pairs
* PAIR I7: 3,8 COL I
I4: 3,8,5,7                              # reduction candidate for 3,8
I4: 3,8 => CTR
* 28..36..49567148323..28975617.....2.835142697692.7...1569.271.3723891465418365279
I4: 5,7                                  # 27 pairs
I5: 3,8,7                                # reduction candidate for 3,8
I5: 3,8                                  # 28 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-680159-base-pr-000.dot
* REASONING
* DIS # F3: 3,9 => CTR => F3: 4,5
* DIS # D4: 6,8 => CTR => D4: 5,9
* DIS # F3: 3,5 => CTR => F3: 4,9
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* DIS # F3: 3,5 => CTR => F3: 4,9
* PRF # A6: 3,8 => SOL
* DIS # I5: 7 => CTR => I5: 3,8
* DIS # B4: 3,7 => CTR => B4: 4,6
* PRF # I5: 8 => SOL
* PRF # B3: 3,7 => SOL
* DIS # I4: 3,5 => CTR => I4: 7,8
* PRF # G6: 3,5 => SOL
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* DIS # F4: 3,5 => CTR => F4: 8,9
* PRF # G8: 4 => SOL
* DIS # B4: 3,6 => CTR => B4: 4,7
* DIS # I8: 3,8 => CTR => I8: 5
* DIS # C9: 1,6 => CTR => C9: 8
* PRF # C9: 8 => SOL
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* DIS # E4: 3 => CTR => E4: 5,6
* PRF # F4: 5,8 => SOL
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* DIS # I8: 3,8 => CTR => I8: 5
* DIS # I4: 3,8 => CTR => I4: 5,7
* CNT  29 HDP CHAINS /  55 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,B5,B7,B9,C2,C8,D1,D8,E1,E9,F2,F9,G1,G3,G4,H1,H3,H6,H7,I7)
* 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279
* PAIR C2: 4,6 COL C
C4: 4,6,3,7                              # reduction candidate for 4,6
C4: 4,6                                  # 24 pairs
C4: 3,7                                  # 24 pairs
* PAIR A3: 3,9 ROW 3
F3: 3,9,4,5                              # reduction candidate for 3,9
F3: 3,9 => CTR
* 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279
* PAIR RESTART
* PAIR D1: 5,9 COL D
D4: 5,9,6,8                              # reduction candidate for 5,9
D4: 6,8 => CTR
* 28.9367549567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279
* PAIR RESTART
* PAIR A5: 3,8 BLK 4
A6: 3,8,6                                # reduction candidate for 3,8
A6: 3,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
* DURATION: 0:00:08.643104  START: 07:50:35.596725  END: 07:50:44.239829 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-680159-base-pr-001.dot
* REASONING
* DIS # F3: 3,9 => CTR => F3: 4,5
* DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9
* PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL
* STA F3: 4,5 + D4: 5,9 + A6: 3,8
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokus.de/680159.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 28...6..4.5.71.832...28...61......2...514269..92.7...15.9.271..72..91.6.4..3..279
A2: 6,9
C2: 4,6
C4: 3,4,6,7                              # reduction candidate for 4,6
A3: 3,9
F3: 3,4,5,9                              # reduction candidate for 3,9
F3: 3,9 => CTR
* 28...6.149567148323..2897561..9...2.8.514269.692.7...15.962714872.491.6.461358279
D1: 5,9
D4: 5,6,8,9                              # reduction candidate for 5,9
D4: 6,8 => CTR
* 28.9367549567148323..2859161....9.2.8.514269.6925734815.9.2714.72.491.6.4183..279
F2: 4,9
G1: 7,9
H1: 1,5
G3: 7,9
H3: 1,5
A5: 3,8
A6: 3,6,8                                # reduction candidate for 3,8
A6: 3,8 => SOLVED
* 287536914654719832931284756146958327375142698892673541569427183723891465418365279
* SOLVED!
--------------------------------------------------

--------------------------------------------------
* AUTO ..
G2 = 8                # set value
I3 = 6                # set value
D5 = 1                # set value
C6 = 2                # set value
A7 = 5                # set value
F7 = 7                # set value
G9 = 2                # set value
F5: 2..               # hidden single
D3: 2..               # hidden single
D3 = 2                # set value
F5 = 2                # set value
H5: 9..               # hidden single
H5 = 9                # set value
Q4: 4.. = B4,C4: 4.. => G4 != 4
Q9: 1.. = G7,H7: 1.. => B7,C7 != 1
E8: 9                 # naked single
Q9: 5.. = G8,I8: 5.. => D8,E8 != 5
Q7: 8.. = C7,C8,C9: 8.. => C4 != 8
Q7: 9.. = C7,C8: 9.. => C1,C2,C3 != 9
Q3: 7.. = G1,G3: 7.. => G4,G6 != 7
E6: 7..               # hidden single
E6 = 7                # set value
E8 = 9                # set value
E2: 1                 # naked single
C7: 9..               # hidden single
E2 = 1                # set value
C7 = 9                # set value
G1,G3: 7,9.. => G1,G3 != 1,5 # hidden pair
H6,H7: 4,8.. => H6,H7 != 1,5 # hidden pair
G7: 1..               # hidden single
G7 = 1                # set value
* UNSOLVED!

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

* DISABLE VALUE:: D7 != 6
E9: 6..               # hidden single
B7: 6..               # hidden single

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

Solution

position: 287536914654719832931284756146958327375142698892673541569427183723891465418365279 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 # C4: 4,6 => UNS
* INC # C4: 3,7 => UNS
* DIS # F3: 3,9 => CTR => F3: 4,5
* INC # F3: 4,5 => UNS
* INC # F3: 5,9 => UNS
* INC # F3: 3,4 => UNS
* INC # D4: 5,9 => UNS
* DIS # D4: 6,8 => CTR => D4: 5,9
* DIS # F3: 3,5 => CTR => F3: 4,9
* INC # F3: 4,9 => UNS
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* INC # F3: 4,9 => UNS
* DIS # F3: 3,5 => CTR => F3: 4,9
* PRF # A6: 3,8 => SOL
* INC # A6: 6 => UNS
* INC # I5: 3,8 => UNS
* DIS # I5: 7 => CTR => I5: 3,8
* DIS # B4: 3,7 => CTR => B4: 4,6
* INC # B4: 4,6 => UNS
* INC # C4: 3,7 => UNS
* INC # I5: 3,7 => UNS
* PRF # I5: 8 => SOL
* PRF # B3: 3,7 => SOL
* INC # B3: 1,4 => UNS
* DIS # I4: 3,5 => CTR => I4: 7,8
* INC # I4: 7,8 => UNS
* PRF # G6: 3,5 => SOL
* INC # G6: 4 => UNS
* PRF # E4: 3,5 => SOL
* DIS # E4: 6 => CTR => E4: 3,5
* DIS # F4: 3,5 => CTR => F4: 8,9
* INC # F4: 8,9 => UNS
* INC # G8: 3,5 => UNS
* PRF # G8: 4 => SOL
* DIS # B4: 3,6 => CTR => B4: 4,7
* INC # B4: 4,7 => UNS
* DIS # I8: 3,8 => CTR => I8: 5
* INC # I8: 5 => UNS
* DIS # C9: 1,6 => CTR => C9: 8
* PRF # C9: 8 => SOL
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* INC # E4: 5,6 => UNS
* DIS # E4: 3 => CTR => E4: 5,6
* PRF # F4: 5,8 => SOL
* INC # F4: 3,9 => UNS
* INC # F6: 5,8 => UNS
* PRF # D7: 4,8 => SOL
* DIS # D7: 6 => CTR => D7: 4,8
* DIS # I8: 3,8 => CTR => I8: 5
* INC # I8: 5 => UNS
* DIS # I4: 3,8 => CTR => I4: 5,7
* INC # I4: 5,7 => UNS
* INC # I5: 3,8 => UNS
* CNT  55 HDP CHAINS /  55 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 4,6 => UNS
* INC # C4: 3,7 => UNS
* DIS # F3: 3,9 => CTR => F3: 4,5
* INC F3: 4,5 # D4: 5,9 => UNS
* DIS F3: 4,5 # D4: 6,8 => CTR => D4: 5,9
* PRF F3: 4,5 + D4: 5,9 # A6: 3,8 => SOL
* STA F3: 4,5 + D4: 5,9 + A6: 3,8
* CNT   6 HDP CHAINS /   6 HYP OPENED