Analysis of zz-www.sudokuwiki.org-0016-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=16

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=16

position: ......9.......3.8127..1..3.....41.7.41..7..62.9.68.....3..6..1556.1.......4...... initial

Autosolve

position: 3.1...9.......3.8127..1..3.....41.7941..7..6279.68.1...3..6..1556.1.....1.4...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4,5 => CTR => B1: 8
* DIS # D2: 4,5 => CTR => D2: 2,7,9
* PRF # G2: 4,5 => SOL
* DIS # D1: 2,5 => CTR => D1: 4,7,8
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* DIS # D2: 2,5 => CTR => D2: 4,7,9
* DIS # H1: 4 => CTR => H1: 2,5
* DIS # E9: 2,5 => CTR => E9: 3,9
* DIS # I1: 4,6 => CTR => I1: 7
* DIS # G2: 4,6 => CTR => G2: 2,5,7
* DIS # F3: 4,6 => CTR => F3: 5,8,9
* DIS # C6: 2,5 => CTR => C6: 3
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* PRF # H1: 2 => SOL
* DIS # B4: 2,8 => CTR => B4: 5
* PRF # H8: 4 => SOL
* DIS # D9: 2,9 => CTR => D9: 5,7,8
* DIS # E9: 2,9 => CTR => E9: 3,5
* DIS # F9: 2,9 => CTR => F9: 5,7,8
* CNT  19 HDP CHAINS /  61 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 # B1: 4,5 => CTR => B1: 8
* DIS B1: 8 # D1: 2,5 => CTR => D1: 4,7
* DIS B1: 8 + D1: 4,7 # F1: 2,5 => CTR => F1: 4,6,7
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 # D2: 2,5 => CTR => D2: 7,9
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 # E2: 9 => CTR => E2: 2,5
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 # I1: 4,6 => CTR => I1: 7
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 # G3: 5 => CTR => G3: 4,6
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 # C4: 6,8 => CTR => C4: 2,3
* PRF B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3 => SOL
* STA B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3
* CNT   9 HDP CHAINS /  14 HYP OPENED

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

Details

Positions

......9.......3.8127..1..3.....41.7.41..7..62.9.68.....3..6..1556.1.......4...... initial
3.1...9.......3.8127..1..3.....41.7941..7..6279.68.1...3..6..1556.1.....1.4...... autosolve
381456927946723581275819436652341879418975362793682154839264715567198243124537698 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A2: 6,9
B2: 4,5
E1: 2,5
I3: 4,6
A4: 6,8
F5: 5,9
F6: 2,5
H6: 4,5
I6: 3,4
A7: 8,9
B9: 2,8
H9: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,G2: 2.. / H1 = 2  =>  0 pairs (*) / G2 = 2  =>  0 pairs (X)
D4,F6: 2.. / D4 = 2  =>  0 pairs (X) / F6 = 2  => 13 pairs (_)
C6,F6: 2.. / C6 = 2  =>  0 pairs (X) / F6 = 2  => 13 pairs (_)
B4,B9: 2.. / B4 = 2  =>  0 pairs (X) / B9 = 2  => 13 pairs (_)
D4,D5: 3.. / D4 = 3  => 16 pairs (_) / D5 = 3  => 14 pairs (_)
E8,E9: 3.. / E8 = 3  => 14 pairs (_) / E9 = 3  => 13 pairs (_)
C6,I6: 3.. / C6 = 3  => 16 pairs (_) / I6 = 3  =>  0 pairs (X)
B1,B2: 4.. / B1 = 4  =>  0 pairs (X) / B2 = 4  => 12 pairs (_)
H6,I6: 4.. / H6 = 4  =>  0 pairs (X) / I6 = 4  => 16 pairs (_)
H1,H6: 5.. / H1 = 5  =>  0 pairs (X) / H6 = 5  => 16 pairs (_)
F1,F3: 6.. / F1 = 6  => 13 pairs (_) / F3 = 6  =>  0 pairs (X)
A4,C4: 6.. / A4 = 6  => 13 pairs (_) / C4 = 6  => 13 pairs (_)
G9,I9: 6.. / G9 = 6  => 13 pairs (_) / I9 = 6  =>  0 pairs (X)
F1,I1: 6.. / F1 = 6  => 13 pairs (_) / I1 = 6  =>  0 pairs (X)
A2,A4: 6.. / A2 = 6  => 13 pairs (_) / A4 = 6  => 13 pairs (_)
I1,G2: 7.. / I1 = 7  => 12 pairs (_) / G2 = 7  =>  0 pairs (X)
C7,C8: 7.. / C7 = 7  => 14 pairs (_) / C8 = 7  => 12 pairs (_)
D2,G2: 7.. / D2 = 7  => 12 pairs (_) / G2 = 7  =>  0 pairs (X)
B1,C3: 8.. / B1 = 8  => 15 pairs (_) / C3 = 8  =>  0 pairs (X)
G4,G5: 8.. / G4 = 8  =>  0 pairs (*) / G5 = 8  =>  0 pairs (X)
I8,I9: 8.. / I8 = 8  => 12 pairs (_) / I9 = 8  => 16 pairs (_)
C5,G5: 8.. / C5 = 8  =>  0 pairs (*) / G5 = 8  =>  0 pairs (X)
A4,A7: 8.. / A4 = 8  => 13 pairs (_) / A7 = 8  => 13 pairs (_)
D5,F5: 9.. / D5 = 9  => 14 pairs (_) / F5 = 9  => 12 pairs (_)
H8,H9: 9.. / H8 = 9  =>  0 pairs (X) / H9 = 9  => 12 pairs (_)
A2,A7: 9.. / A2 = 9  => 13 pairs (_) / A7 = 9  => 13 pairs (_)
* DURATION: 0:00:35.820489  START: 03:40:27.380043  END: 03:41:03.200532 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,B2,B9,E1,F5,F6,H6,H9,I3,I6)
* 3.1...9.......3.8127..1..3.....41.7941..7..6279.68.1...3..6..1556.1.....1.4......
* PAIR A2: 6,9 BLK 1
C2: 6,9,5                                # reduction candidate for 6,9
C2: 6,9                                  # 18 pairs
C3: 6,9,5,8                              # reduction candidate for 6,9
C3: 6,9                                  # 17 pairs
* PAIR B2: 4,5 BLK 1
B1: 4,5,8                                # reduction candidate for 4,5
B1: 4,5 => CTR
* 3.1...9.......3.81278914536...541379415379862793682154.3.46..1556.1.....1.42.5697
B1: 8                                    # 15 pairs
* PAIR B2: 4,5 ROW 2
D2: 4,5,2,7,9                            # reduction candidate for 4,5
D2: 4,5 => CTR
* 3.1...92.....2378127..1.53.....41.7941..7..6279.68.154.3..6..1556.1...4.1.4...69.
D2: 2,7,9                                # 12 pairs
G2: 4,5,2,6,7                            # reduction candidate for 4,5
G2: 4,5 => SOLVED
* 381456927946723581275819436652341879418975362793682154839264715567198243124537698
G2: 2,6,7                                # 12 pairs
* PAIR E1: 2,5 BLK 2
D1: 2,5,4,7,8                            # reduction candidate for 2,5
D1: 2,5 => CTR
* 381..6947645793281279.1.536856241.7941..7..6279.68.15493..6..1556.1.....124...69.
D1: 4,7,8                                # 12 pairs
F1: 2,5,4,6,7,8                          # reduction candidate for 2,5
F1: 2,5 => CTR
* 3.1...9.6.....378127..16.34....41.7941..7..6279.68.143.3..6..1556.1.....1.4...6..
F1: 4,6,7,8                              # 12 pairs
D2: 2,5,4,7,9                            # reduction candidate for 2,5
D2: 2,5 => CTR
* 3.1...92..4...378127..1.53.....41.7941..7..6279.68.154.3..6..1556.1...4.1.4...69.
D2: 4,7,9                                # 12 pairs
E2: 2,5,9                                # reduction candidate for 2,5
E2: 2,5                                  # 15 pairs
* PAIR E1: 2,5 ROW 1
H1: 2,5,4                                # reduction candidate for 2,5
H1: 4 => CTR
* 381..694794.7.328127..1.536...34187941897536279368215483..6..1556.1.....124..769.
H1: 2,5                                  # 14 pairs
* PAIR E1: 2,5 COL E
E9: 2,5,3,9                              # reduction candidate for 2,5
E9: 2,5 => CTR
* 381...9..645.93.81279.1..3.856241379413.7..6279.68.1..93..6..1556.13....1.4......
E9: 3,9                                  # 13 pairs
* PAIR I3: 4,6 BLK 3
I1: 4,6,7                                # reduction candidate for 4,6
I1: 4,6 => CTR
* 3.1...92......378127..1.53.....41.7941..7..6279.68.154.3..6..1556.1...4.1.4...69.
I1: 7                                    # 12 pairs
G2: 4,6,2,5,7                            # reduction candidate for 4,6
G2: 4,6 => CTR
* 341856927.5.723481278.1.536.82541379415379.62793682154.3..6..1556.19..4.1.4.3.698
G2: 2,5,7                                # 12 pairs
G3: 4,6,5                                # reduction candidate for 4,6
G3: 4,6                                  # 21 pairs
* PAIR I3: 4,6 ROW 3
F3: 4,6,5,8,9                            # reduction candidate for 4,6
F3: 4,6 => CTR
* 3.1..69.7...7.3.8127..14536...34187941897536279368215483.469.155691.....1.4..76..
F3: 5,8,9                                # 13 pairs
* PAIR A4: 6,8 BLK 4
C4: 6,8,2,3,5                            # reduction candidate for 6,8
C4: 6,8                                  # 16 pairs
C4: 2,3,5                                # 13 pairs
* PAIR F5: 5,9 BLK 5
D5: 5,9,3                                # reduction candidate for 5,9
D5: 5,9                                  # 16 pairs
D5: 3                                    # 14 pairs
* PAIR F5: 5,9 COL F
F3: 5,9,4,6,8                            # reduction candidate for 5,9
F3: 5,9                                  # 20 pairs
F9: 5,9,2,7,8                            # reduction candidate for 5,9
F9: 5,9                                  # 14 pairs
* PAIR F6: 2,5 BLK 5
D4: 2,5,3                                # reduction candidate for 2,5
D4: 3                                    # 16 pairs
D4: 2,5                                  # 14 pairs
* PAIR F6: 2,5 ROW 6
C6: 2,5,3                                # reduction candidate for 2,5
C6: 2,5 => CTR
* 381426957946753281275918.3.65324187941837956279268514383..6..1556.1.....124....9.
C6: 3                                    # 16 pairs
* PAIR F6: 2,5 COL F
F1: 2,5,4,6,7,8                          # reduction candidate for 2,5
F1: 2,5 => CTR
* 3.1...9.6.....378127..16.34....41.7941..7..6279.68.143.3..6..1556.1.....1.4...6..
F1: 4,6,7,8                              # 12 pairs
F9: 2,5,7,8,9                            # reduction candidate for 2,5
F9: 2,5                                  # 13 pairs
* PAIR H6: 4,5 COL H
H1: 4,5,2                                # reduction candidate for 4,5
H1: 2 => SOLVED
* 381456927946723581275819436652341879418975362793682154839264715567198243124537698
H1: 4,5                                  # 16 pairs
* PAIR I6: 3,4 COL I
I8: 3,4,7,8                              # reduction candidate for 3,4
I8: 3,4                                  # 16 pairs
I8: 7,8                                  # 13 pairs
* PAIR A7: 8,9 BLK 7
C7: 8,9,2,7                              # reduction candidate for 8,9
C7: 8,9                                  # 14 pairs
C8: 8,9,2,7                              # reduction candidate for 8,9
C8: 8,9                                  # 16 pairs
* PAIR A7: 8,9 ROW 7
D7: 8,9,2,4,7                            # reduction candidate for 8,9
D7: 8,9                                  # 14 pairs
F7: 8,9,2,4,7                            # reduction candidate for 8,9
F7: 8,9                                  # 14 pairs
* PAIR B9: 2,8 BLK 7
C7: 2,8,7,9                              # reduction candidate for 2,8
C7: 2,8                                  # 14 pairs
C8: 2,8,7,9                              # reduction candidate for 2,8
C8: 2,8                                  # 16 pairs
* PAIR B9: 2,8 ROW 9
D9: 2,8,5,7,9                            # reduction candidate for 2,8
D9: 2,8                                  # 15 pairs
F9: 2,8,5,7,9                            # reduction candidate for 2,8
F9: 2,8                                  # 15 pairs
* PAIR B9: 2,8 COL B
B4: 2,8,5                                # reduction candidate for 2,8
B4: 2,8 => CTR
* 3.1...9.......3.81278914536...541379415379862793682154.3.46..1556.1.....1.42.5697
B4: 5                                    # 15 pairs
* PAIR H9: 2,9 BLK 9
H8: 2,9,4                                # reduction candidate for 2,9
H8: 4 => SOLVED
* 381456927946723581275819436652341879418975362793682154839264715567198243124537698
H8: 2,9                                  # 16 pairs
* PAIR H9: 2,9 ROW 9
D9: 2,9,5,7,8                            # reduction candidate for 2,9
D9: 2,9 => CTR
* 3.1...9..6.9..3.81278.1..3.82634157941357986279568214393..6.41556.194328184235.9.
D9: 5,7,8                                # 12 pairs
E9: 2,9,3,5                              # reduction candidate for 2,9
E9: 2,9 => CTR
* 3.1..69.7...7.3.81278.1.53682..41.7941..7..6279.6821...3..6..1556.13...81845.7...
E9: 3,5                                  # 13 pairs
F9: 2,9,5,7,8                            # reduction candidate for 2,9
F9: 2,9 => CTR
* 3.1...9......9328127..1..3..2..41.7941..7..6279.6821...3..6..1556.1....8184..9.2.
F9: 5,7,8                                # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0016-base-pr-000.dot
* REASONING
* DIS # B1: 4,5 => CTR => B1: 8
* DIS # D2: 4,5 => CTR => D2: 2,7,9
* PRF # G2: 4,5 => SOL
* DIS # D1: 2,5 => CTR => D1: 4,7,8
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* DIS # D2: 2,5 => CTR => D2: 4,7,9
* DIS # H1: 4 => CTR => H1: 2,5
* DIS # E9: 2,5 => CTR => E9: 3,9
* DIS # I1: 4,6 => CTR => I1: 7
* DIS # G2: 4,6 => CTR => G2: 2,5,7
* DIS # F3: 4,6 => CTR => F3: 5,8,9
* DIS # C6: 2,5 => CTR => C6: 3
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* PRF # H1: 2 => SOL
* DIS # B4: 2,8 => CTR => B4: 5
* PRF # H8: 4 => SOL
* DIS # D9: 2,9 => CTR => D9: 5,7,8
* DIS # E9: 2,9 => CTR => E9: 3,5
* DIS # F9: 2,9 => CTR => F9: 5,7,8
* CNT  19 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A7,B2,B9,E1,F5,F6,H6,H9,I3,I6)
* 3.1...9.......3.8127..1..3.....41.7941..7..6279.68.1...3..6..1556.1.....1.4......
* PAIR A2: 6,9 BLK 1
C2: 6,9,5                                # reduction candidate for 6,9
C2: 6,9                                  # 18 pairs
C3: 6,9,5,8                              # reduction candidate for 6,9
C3: 6,9                                  # 17 pairs
* PAIR B2: 4,5 BLK 1
B1: 4,5,8                                # reduction candidate for 4,5
B1: 4,5 => CTR
* 3.1...9.......3.81278914536...541379415379862793682154.3.46..1556.1.....1.42.5697
* PAIR E1: 2,5 BLK 2
D1: 2,5,4,7                              # reduction candidate for 2,5
D1: 2,5 => CTR
* 381.26947645793281279.1.536856241.7941..7..6279.68.15493..6..1556.1.942.124...69.
F1: 2,5,4,6,7                            # reduction candidate for 2,5
F1: 2,5 => CTR
* 381...9.6.4...378127..16.34.5..41.7941..7..6279.68.143.3..6..1556.1...2.124....9.
D2: 2,5,7,9                              # reduction candidate for 2,5
D2: 2,5 => CTR
* 381...92..4...378127..1.53..5..41.7941..7..6279.68.154.3..6..1556.1...4.124...69.
E2: 2,5,9                                # reduction candidate for 2,5
E2: 2,5                                  # 20 pairs
* RESTART
* PAIR E1: 2,5 BLK 2
E2: 2,5,9                                # reduction candidate for 2,5
E2: 9 => CTR
* 381.2.95..45.93281279.1..3..5624137941.37..6279.68.1...3..6..1556.1.....124....9.
* PAIR I3: 4,6 BLK 3
I1: 4,6,7                                # reduction candidate for 4,6
I1: 4,6 => CTR
* 381...92..4.923781279.1.53..5..41.7941..79.6279.68.15493..6..1556.19..43124.3569.
G3: 4,6,5                                # reduction candidate for 4,6
G3: 4,6                                  # 26 pairs
* RESTART
* PAIR I3: 4,6 BLK 3
G3: 4,6,5                                # reduction candidate for 4,6
G3: 5 => CTR
* 3814.69.7.4.7.3.8127..1.534.5..41.7941..7..6279.68.1...3..6..1556.19....124.3..9.
* PAIR A4: 6,8 BLK 4
C4: 6,8,2,3                              # reduction candidate for 6,8
C4: 6,8 => CTR
* 3814.69.7.4.7.3.81275.1..3..5.24137941.379.6279.68.1...3..6..1556.19....124.3..9.
C4: 2,3 => SOLVED
* 381456927946723581275819436652341879418975362793682154839264715567198243124537698
* DURATION: 0:00:16.200266  START: 03:41:49.832266  END: 03:42:06.032532 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0016-base-pr-001.dot
* REASONING
* DIS # B1: 4,5 => CTR => B1: 8
* DIS B1: 8 # D1: 2,5 => CTR => D1: 4,7
* DIS B1: 8 + D1: 4,7 # F1: 2,5 => CTR => F1: 4,6,7
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 # D2: 2,5 => CTR => D2: 7,9
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 # E2: 9 => CTR => E2: 2,5
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 # I1: 4,6 => CTR => I1: 7
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 # G3: 5 => CTR => G3: 4,6
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 # C4: 6,8 => CTR => C4: 2,3
* PRF B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3 => SOL
* STA B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3
* CNT   9 HDP CHAINS /  14 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=16

Solution

position: 381456927946723581275819436652341879418975362793682154839264715567198243124537698 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 # C2: 6,9 => UNS
* INC # C3: 6,9 => UNS
* DIS # B1: 4,5 => CTR => B1: 8
* INC # B1: 8 => UNS
* DIS # D2: 4,5 => CTR => D2: 2,7,9
* INC # D2: 2,7,9 => UNS
* PRF # G2: 4,5 => SOL
* INC # G2: 2,6,7 => UNS
* DIS # D1: 2,5 => CTR => D1: 4,7,8
* INC # D1: 4,7,8 => UNS
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* INC # F1: 4,6,7,8 => UNS
* DIS # D2: 2,5 => CTR => D2: 4,7,9
* INC # D2: 4,7,9 => UNS
* INC # E2: 2,5 => UNS
* INC # H1: 2,5 => UNS
* DIS # H1: 4 => CTR => H1: 2,5
* DIS # E9: 2,5 => CTR => E9: 3,9
* INC # E9: 3,9 => UNS
* DIS # I1: 4,6 => CTR => I1: 7
* INC # I1: 7 => UNS
* DIS # G2: 4,6 => CTR => G2: 2,5,7
* INC # G2: 2,5,7 => UNS
* INC # G3: 4,6 => UNS
* DIS # F3: 4,6 => CTR => F3: 5,8,9
* INC # F3: 5,8,9 => UNS
* INC # C4: 6,8 => UNS
* INC # C4: 2,3,5 => UNS
* INC # D5: 5,9 => UNS
* INC # D5: 3 => UNS
* INC # F3: 5,9 => UNS
* INC # F9: 5,9 => UNS
* INC # D4: 2,5 => UNS
* INC # D4: 3 => UNS
* DIS # C6: 2,5 => CTR => C6: 3
* INC # C6: 3 => UNS
* DIS # F1: 2,5 => CTR => F1: 4,6,7,8
* INC # F1: 4,6,7,8 => UNS
* INC # F9: 2,5 => UNS
* INC # H1: 4,5 => UNS
* PRF # H1: 2 => SOL
* INC # I8: 3,4 => UNS
* INC # I8: 7,8 => UNS
* INC # C7: 8,9 => UNS
* INC # C8: 8,9 => UNS
* INC # D7: 8,9 => UNS
* INC # F7: 8,9 => UNS
* INC # C7: 2,8 => UNS
* INC # C8: 2,8 => UNS
* INC # D9: 2,8 => UNS
* INC # F9: 2,8 => UNS
* DIS # B4: 2,8 => CTR => B4: 5
* INC # B4: 5 => UNS
* INC # H8: 2,9 => UNS
* PRF # H8: 4 => SOL
* DIS # D9: 2,9 => CTR => D9: 5,7,8
* INC # D9: 5,7,8 => UNS
* DIS # E9: 2,9 => CTR => E9: 3,5
* INC # E9: 3,5 => UNS
* DIS # F9: 2,9 => CTR => F9: 5,7,8
* INC # F9: 5,7,8 => UNS
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 6,9 => UNS
* INC # C3: 6,9 => UNS
* DIS # B1: 4,5 => CTR => B1: 8
* DIS B1: 8 # D1: 2,5 => CTR => D1: 4,7
* DIS B1: 8 + D1: 4,7 # F1: 2,5 => CTR => F1: 4,6,7
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 # D2: 2,5 => CTR => D2: 7,9
* INC B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 # E2: 2,5 => UNS
* INC B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 # E2: 2,5 => UNS
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 # E2: 9 => CTR => E2: 2,5
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 # I1: 4,6 => CTR => I1: 7
* INC B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 # G3: 4,6 => UNS
* INC B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 # G3: 4,6 => UNS
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 # G3: 5 => CTR => G3: 4,6
* DIS B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 # C4: 6,8 => CTR => C4: 2,3
* PRF B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3 => SOL
* STA B1: 8 + D1: 4,7 + F1: 4,6,7 + D2: 7,9 + E2: 2,5 + I1: 7 + G3: 4,6 + C4: 2,3
* CNT  15 HDP CHAINS /  14 HYP OPENED