Analysis of xx-top500-028-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .8...4.5....7..3............1..85...6.....2......4....3.26............417........ initial

Autosolve

position: .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 2,9 => CTR => B3: 3,6,7
* DIS # I1: 2,9 => CTR => I1: 6,7
* DIS # A6: 8 => CTR => A6: 2,9
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # F3: 3,9 => CTR => F3: 1,2
* DIS # C1: 3,9 => CTR => C1: 6,7
* DIS # I1: 2,6 => CTR => I1: 7,9
* PRF # H3: 2,6 => SOL
* DIS # H3: 7 => CTR => H3: 2,6
* DIS # I3: 2,6 => CTR => I3: 7,9
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # C6: 3,7 => CTR => C6: 8,9
* DIS # I4: 3,7 => CTR => I4: 6
* PRF # C3: 3,7 => SOL
* DIS # B6: 3,9 => CTR => B6: 2,7
* DIS # C6: 3,9 => CTR => C6: 7,8
* DIS # F5: 7 => CTR => F5: 3,9
* PRF # B3: 3,9 => SOL
* DIS # B3: 2,6,7 => CTR => B3: 3,9
* DIS # F5: 9 => CTR => F5: 3,7
* DIS # F5: 7 => CTR => F5: 3,9
* DIS # B6: 3,9 => CTR => B6: 2,7
* DIS # C6: 3,9 => CTR => C6: 7,8
* DIS # I4: 3,7 => CTR => I4: 6
* DIS # C6: 3,7 => CTR => C6: 8,9
* DIS # C8: 6 => CTR => C8: 8,9
* DIS # A6: 8,9 => CTR => A6: 2
* DIS # C8: 8 => CTR => C8: 6,9
* DIS # B2: 6,9 => CTR => B2: 2
* DIS # B3: 6,9 => CTR => B3: 2,3,7
* CNT  30 HDP CHAINS /  69 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 # B3: 2,9 => CTR => B3: 3,6,7
* DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9
* DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7
* DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9
* PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL
* STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5
* CNT   5 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

.8...4.5....7..3............1..85...6.....2......4....3.26............417........ initial
.8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986.. autosolve
986324157124759368537861429413285976695173284278946513342617895869532741751498632 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 2,9
A2: 1,5
A3: 1,5
D1: 3,9
H2: 2,6
C4: 3,7
B5: 3,9
E5: 3,7
D6: 3,9
I6: 3,7
A8: 8,9
B8: 6,9
E7: 1,7
F7: 1,7
E8: 2,3
F8: 2,3
H9: 2,3
I9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 17 pairs (_) / A3 = 1  => 16 pairs (_)
E7,F7: 1.. / E7 = 1  => 16 pairs (_) / F7 = 1  =>  0 pairs (X)
A6,B6: 2.. / A6 = 2  => 21 pairs (_) / B6 = 2  =>  0 pairs (X)
E8,F8: 2.. / E8 = 2  => 18 pairs (_) / F8 = 2  => 16 pairs (_)
H9,I9: 2.. / H9 = 2  =>  0 pairs (X) / I9 = 2  => 17 pairs (_)
A1,A6: 2.. / A1 = 2  =>  0 pairs (X) / A6 = 2  => 21 pairs (_)
E8,F8: 3.. / E8 = 3  => 16 pairs (_) / F8 = 3  => 18 pairs (_)
H9,I9: 3.. / H9 = 3  => 17 pairs (_) / I9 = 3  =>  0 pairs (X)
D1,D6: 3.. / D1 = 3  => 21 pairs (_) / D6 = 3  =>  0 pairs (X)
H4,H9: 3.. / H4 = 3  =>  0 pairs (X) / H9 = 3  => 17 pairs (_)
A2,A3: 5.. / A2 = 5  => 16 pairs (_) / A3 = 5  => 17 pairs (_)
E2,E3: 5.. / E2 = 5  => 17 pairs (_) / E3 = 5  => 16 pairs (_)
A2,E2: 5.. / A2 = 5  => 16 pairs (_) / E2 = 5  => 17 pairs (_)
A3,E3: 5.. / A3 = 5  => 17 pairs (_) / E3 = 5  => 16 pairs (_)
H4,I4: 6.. / H4 = 6  =>  0 pairs (X) / I4 = 6  => 19 pairs (_)
B8,C8: 6.. / B8 = 6  => 21 pairs (_) / C8 = 6  =>  0 pairs (X)
E5,F5: 7.. / E5 = 7  => 16 pairs (_) / F5 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  =>  0 pairs (X) / F7 = 7  => 16 pairs (_)
C1,I1: 7.. / C1 = 7  =>  0 pairs (X) / I1 = 7  =>  0 pairs (_)
B3,B6: 7.. / B3 = 7  =>  0 pairs (X) / B6 = 7  =>  0 pairs (_)
E5,E7: 7.. / E5 = 7  => 16 pairs (_) / E7 = 7  =>  0 pairs (X)
F5,F7: 7.. / F5 = 7  =>  0 pairs (X) / F7 = 7  => 16 pairs (_)
H3,H4: 7.. / H3 = 7  =>  0 pairs (X) / H4 = 7  =>  0 pairs (_)
A6,C6: 8.. / A6 = 8  =>  0 pairs (X) / C6 = 8  => 19 pairs (_)
A8,C8: 8.. / A8 = 8  => 19 pairs (_) / C8 = 8  =>  0 pairs (X)
A6,A8: 8.. / A6 = 8  =>  0 pairs (X) / A8 = 8  => 19 pairs (_)
C6,C8: 8.. / C6 = 8  => 19 pairs (_) / C8 = 8  =>  0 pairs (X)
I1,I3: 9.. / I1 = 9  =>  0 pairs (X) / I3 = 9  => 18 pairs (_)
F5,D6: 9.. / F5 = 9  =>  0 pairs (X) / D6 = 9  => 21 pairs (_)
B2,F2: 9.. / B2 = 9  =>  0 pairs (X) / F2 = 9  => 21 pairs (_)
B5,F5: 9.. / B5 = 9  => 21 pairs (_) / F5 = 9  =>  0 pairs (X)
D1,D6: 9.. / D1 = 9  =>  0 pairs (X) / D6 = 9  => 21 pairs (_)
* DURATION: 0:01:10.859583  START: 03:34:11.934740  END: 03:35:22.794323 2017-05-04
* CP COUNT: (32)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A8,B5,B8,C4,D1,D6,E5,E7,E8,F7,F8,H2,H9,I6,I9)
* .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986..
* PAIR A1: 2,9 BLK 1
B2: 2,9,6                                # reduction candidate for 2,9
B2: 2,9                                  # 21 pairs
B3: 2,9,3,6,7                            # reduction candidate for 2,9
B3: 2,9 => CTR
* .8.3.415...47..3.8..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632
B3: 3,6,7                                # 18 pairs
* PAIR A1: 2,9 ROW 1
I1: 2,9,6,7                              # reduction candidate for 2,9
I1: 2,9 => CTR
* .87.6415...47..3.8...8..4..4132859..6951..284.789465133426..8958695..741751498632
I1: 6,7                                  # 18 pairs
* PAIR A1: 2,9 COL A
A6: 2,9,8                                # reduction candidate for 2,9
A6: 8 => CTR
* 28...415..947..3.8.7.8..4..41.2859766351..28482..4651.3426..8959685..7417514986..
A6: 2,9                                  # 19 pairs
* PAIR A2: 1,5 ROW 2
E2: 1,5,2,6                              # reduction candidate for 1,5
E2: 2,6 => CTR
* 287..415.5947.13.81..85.4..41.2859..635179284...346517342617895.6.5..7417514986..
E2: 1,5                                  # 20 pairs
* PAIR A3: 1,5 ROW 3
E3: 1,5,2,3,6                            # reduction candidate for 1,5
E3: 1,5                                  # 19 pairs
E3: 2,3,6                                # 15 pairs
* PAIR D1: 3,9 BLK 2
F3: 3,9,1,2                              # reduction candidate for 3,9
F3: 3,9 => CTR
* .8...415..947..3.8...8..4..41.2859..635179284...346517342617895.6.5327417514986..
F3: 1,2                                  # 19 pairs
* PAIR D1: 3,9 ROW 1
C1: 3,9,6,7                              # reduction candidate for 3,9
C1: 3,9 => CTR
* 28.364157..47.93.8...8..4.94132859766951..284...9465133426..895.6.5..741751498632
C1: 6,7                                  # 19 pairs
* PAIR H2: 2,6 BLK 3
I1: 2,6,7,9                              # reduction candidate for 2,6
I1: 2,6 => CTR
* 987324156.247..3.8...8..4.94132859..6951..284.789465133426..8958695..741751498632
I1: 7,9                                  # 19 pairs
H3: 2,6,7                                # reduction candidate for 2,6
H3: 2,6 => SOLVED
* 986324157124759368537861429413285976695173284278946513342617895869532741751498632
H3: 7 => CTR
* .873.415...47..328.238..47.41.2859..6.51..284.7..465133426..895...5..741751498632
I3: 2,6,7,9                              # reduction candidate for 2,6
I3: 2,6 => CTR
* .8...4159..47..3.8...8..47.41.2859..6.51..284.7.9465133426..8959685..7417514986..
I3: 7,9                                  # 19 pairs
* PAIR H2: 2,6 ROW 2
B2: 2,6,9                                # reduction candidate for 2,6
B2: 2,6                                  # 21 pairs
E2: 2,6,1,5                              # reduction candidate for 2,6
E2: 2,6 => CTR
* 287..415.5947.13.81..85.4..41.2859..635179284...346517342617895.6.5..7417514986..
E2: 1,5                                  # 20 pairs
* PAIR C4: 3,7 BLK 4
B6: 3,7,2,9                              # reduction candidate for 3,7
B6: 3,7                                  # 21 pairs
C6: 3,7,8,9                              # reduction candidate for 3,7
C6: 3,7 => CTR
* 28.36415..947..368.7.8..4..41.2859..6.51..28482.94651.3426..8959685..7417514986..
C6: 8,9                                  # 19 pairs
* PAIR C4: 3,7 ROW 4
H4: 3,7,6                                # reduction candidate for 3,7
H4: 3,7                                  # 19 pairs
I4: 3,7,6                                # reduction candidate for 3,7
I4: 3,7 => CTR
* .873.415...47..328.238..47.41.28596.6.51..284.7..465133426..895...5..741751498632
I4: 6                                    # 19 pairs
* PAIR C4: 3,7 COL C
C1: 3,7,6,9                              # reduction candidate for 3,7
C1: 3,7                                  # 22 pairs
C3: 3,7,6,9                              # reduction candidate for 3,7
C3: 3,7 => SOLVED
* 986324157124759368537861429413285976695173284278946513342617895869532741751498632
C3: 6,9                                  # 22 pairs
* PAIR B5: 3,9 BLK 4
B6: 3,9,2,7                              # reduction candidate for 3,9
B6: 3,9 => CTR
* .8...415...47..3.8.7.8..4..41.2859766.51..2842...4651.3426..895...5..7417514986..
B6: 2,7                                  # 19 pairs
C6: 3,9,7,8                              # reduction candidate for 3,9
C6: 3,9 => CTR
* 287..415..947..3.8.3.8..4..41.2859..6.51..28482..465173426..8959685..7417514986..
C6: 7,8                                  # 19 pairs
* PAIR B5: 3,9 ROW 5
F5: 3,9,7                                # reduction candidate for 3,9
F5: 7 => CTR
* .8.36415..247.9368..68.247941.28593669513728427.94651.342671895.6.5237417514986..
F5: 3,9                                  # 16 pairs
* PAIR B5: 3,9 COL B
B3: 3,9,2,6,7                            # reduction candidate for 3,9
B3: 3,9 => SOLVED
* 986324157124759368537861429413285976695173284278946513342617895869532741751498632
B3: 2,6,7 => CTR
* .8...415...47..3.8...8..4..4172859..6.51..284....465173426..895...5..7417514986..
* PAIR E5: 3,7 BLK 5
F5: 3,7,9                                # reduction candidate for 3,7
F5: 9 => CTR
* .87934156.9476.328...8524794132859..6.5179284...346517342617895...5..7417514986..
F5: 3,7                                  # 21 pairs
* PAIR D6: 3,9 BLK 5
F5: 3,9,7                                # reduction candidate for 3,9
F5: 7 => CTR
* .8.36415..247.9368..68.247941.28593669513728427.94651.342671895.6.5237417514986..
F5: 3,9                                  # 16 pairs
* PAIR D6: 3,9 ROW 6
B6: 3,9,2,7                              # reduction candidate for 3,9
B6: 3,9 => CTR
* .8...415...47..3.8.7.8..4..41.2859766.51..2842...4651.3426..895...5..7417514986..
B6: 2,7                                  # 19 pairs
C6: 3,9,7,8                              # reduction candidate for 3,9
C6: 3,9 => CTR
* 287..415..947..3.8.3.8..4..41.2859..6.51..28482..465173426..8959685..7417514986..
C6: 7,8                                  # 19 pairs
* PAIR I6: 3,7 BLK 6
H4: 3,7,6                                # reduction candidate for 3,7
H4: 3,7                                  # 19 pairs
I4: 3,7,6                                # reduction candidate for 3,7
I4: 3,7 => CTR
* .873.415...47..328.238..47.41.28596.6.51..284.7..465133426..895...5..741751498632
I4: 6                                    # 19 pairs
* PAIR I6: 3,7 ROW 6
B6: 3,7,2,9                              # reduction candidate for 3,7
B6: 3,7                                  # 21 pairs
C6: 3,7,8,9                              # reduction candidate for 3,7
C6: 3,7 => CTR
* 28.36415..947..368.7.8..4..41.2859..6.51..28482.94651.3426..8959685..7417514986..
C6: 8,9                                  # 19 pairs
* PAIR A8: 8,9 BLK 7
C8: 8,9,6                                # reduction candidate for 8,9
C8: 6 => CTR
* .8...415...47.93.8...8..4..41.2859..63517.284..8.4651.3426..8958965..7417514986..
C8: 8,9                                  # 21 pairs
* PAIR A8: 8,9 COL A
A6: 8,9,2                                # reduction candidate for 8,9
A6: 8,9 => CTR
* 28...415...47..3.8.7.8..4..41.2859766351..284.2..4651.3426..895...5..7417514986..
A6: 2                                    # 21 pairs
* PAIR B8: 6,9 BLK 7
C8: 6,9,8                                # reduction candidate for 6,9
C8: 8 => CTR
* 28...415..947..3.8.7.8..4..41.2859766351..28482..4651.3426..8959685..7417514986..
C8: 6,9                                  # 19 pairs
* PAIR B8: 6,9 COL B
B2: 6,9,2                                # reduction candidate for 6,9
B2: 6,9 => CTR
* .87..415...47..3.8...8..4..41.2859..635179284...346517342617895...5..7417514986..
B2: 2                                    # 21 pairs
B3: 6,9,2,3,7                            # reduction candidate for 6,9
B3: 6,9 => CTR
* .8.3.415..247.9368..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632
B3: 2,3,7                                # 18 pairs
* PAIR E8: 2,3 COL E
E1: 2,3,6                                # reduction candidate for 2,3
E1: 2,3                                  # 24 pairs
E3: 2,3,1,5,6                            # reduction candidate for 2,3
E3: 2,3                                  # 16 pairs
* PAIR F8: 2,3 COL F
F3: 2,3,1,9                              # reduction candidate for 2,3
F3: 2,3                                  # 22 pairs
F3: 1,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-028-base-pr-000.dot
* REASONING
* DIS # B3: 2,9 => CTR => B3: 3,6,7
* DIS # I1: 2,9 => CTR => I1: 6,7
* DIS # A6: 8 => CTR => A6: 2,9
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # F3: 3,9 => CTR => F3: 1,2
* DIS # C1: 3,9 => CTR => C1: 6,7
* DIS # I1: 2,6 => CTR => I1: 7,9
* PRF # H3: 2,6 => SOL
* DIS # H3: 7 => CTR => H3: 2,6
* DIS # I3: 2,6 => CTR => I3: 7,9
* DIS # E2: 2,6 => CTR => E2: 1,5
* DIS # C6: 3,7 => CTR => C6: 8,9
* DIS # I4: 3,7 => CTR => I4: 6
* PRF # C3: 3,7 => SOL
* DIS # B6: 3,9 => CTR => B6: 2,7
* DIS # C6: 3,9 => CTR => C6: 7,8
* DIS # F5: 7 => CTR => F5: 3,9
* PRF # B3: 3,9 => SOL
* DIS # B3: 2,6,7 => CTR => B3: 3,9
* DIS # F5: 9 => CTR => F5: 3,7
* DIS # F5: 7 => CTR => F5: 3,9
* DIS # B6: 3,9 => CTR => B6: 2,7
* DIS # C6: 3,9 => CTR => C6: 7,8
* DIS # I4: 3,7 => CTR => I4: 6
* DIS # C6: 3,7 => CTR => C6: 8,9
* DIS # C8: 6 => CTR => C8: 8,9
* DIS # A6: 8,9 => CTR => A6: 2
* DIS # C8: 8 => CTR => C8: 6,9
* DIS # B2: 6,9 => CTR => B2: 2
* DIS # B3: 6,9 => CTR => B3: 2,3,7
* CNT  30 HDP CHAINS /  69 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A8,B5,B8,C4,D1,D6,E5,E7,E8,F7,F8,H2,H9,I6,I9)
* .8...415...47..3.8...8..4..41.2859..6.51..284....4651.3426..895...5..7417514986..
* PAIR A1: 2,9 BLK 1
B2: 2,9,6                                # reduction candidate for 2,9
B2: 2,9                                  # 21 pairs
B3: 2,9,3,6,7                            # reduction candidate for 2,9
B3: 2,9 => CTR
* .8.3.415...47..3.8..38..4..41.2859..6.51..284.7..465133426..895...5..741751498632
* RESTART
* PAIR A1: 2,9 BLK 1
B2: 2,9,6                                # reduction candidate for 2,9
B2: 6 => CTR
* 28...415..647.9328...8..4..41.2859..6951..284....4651.3426..895...5..7417514986..
* PAIR A1: 2,9 ROW 1
I1: 2,9,6,7                              # reduction candidate for 2,9
I1: 2,9 => CTR
* .87.6415...47..368.368..4..4132859766951..284.789465133426..8958695..741751498632
* PAIR A1: 2,9 COL A
A6: 2,9,8                                # reduction candidate for 2,9
A6: 8 => CTR
* 2879.415..947..3.8...8..4.941.2859..6351792848293465173426178959685..741751498632
* PAIR RESTART
* PAIR A2: 1,5 ROW 2
E2: 1,5,2,6                              # reduction candidate for 1,5
E2: 1,5 => SOLVED
* 986324157124759368537861429413285976695173284278946513342617895869532741751498632
* DURATION: 0:00:12.518720  START: 03:36:43.469372  END: 03:36:55.988092 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-028-base-pr-001.dot
* REASONING
* DIS # B3: 2,9 => CTR => B3: 3,6,7
* DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9
* DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7
* DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9
* PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL
* STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5
* CNT   5 HDP CHAINS /   8 HYP OPENED

Header Info

Top 500 Minimum 17 028

solution: 986324157124759368537861429413285976695173284278946513342617895869532741751498632
info: 1324     FNBTHWX  S8.f     23501

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 986324157124759368537861429413285976695173284278946513342617895869532741751498632 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 # B2: 2,9 => UNS
* DIS # B3: 2,9 => CTR => B3: 3,6,7
* INC # B3: 3,6,7 => UNS
* DIS # I1: 2,9 => CTR => I1: 6,7
* INC # I1: 6,7 => UNS
* INC # A6: 2,9 => UNS
* DIS # A6: 8 => CTR => A6: 2,9
* INC # E2: 1,5 => UNS
* DIS # E2: 2,6 => CTR => E2: 1,5
* INC # E3: 1,5 => UNS
* INC # E3: 2,3,6 => UNS
* DIS # F3: 3,9 => CTR => F3: 1,2
* INC # F3: 1,2 => UNS
* DIS # C1: 3,9 => CTR => C1: 6,7
* INC # C1: 6,7 => UNS
* DIS # I1: 2,6 => CTR => I1: 7,9
* INC # I1: 7,9 => UNS
* PRF # H3: 2,6 => SOL
* DIS # H3: 7 => CTR => H3: 2,6
* DIS # I3: 2,6 => CTR => I3: 7,9
* INC # I3: 7,9 => UNS
* INC # B2: 2,6 => UNS
* DIS # E2: 2,6 => CTR => E2: 1,5
* INC # E2: 1,5 => UNS
* INC # B6: 3,7 => UNS
* DIS # C6: 3,7 => CTR => C6: 8,9
* INC # C6: 8,9 => UNS
* INC # H4: 3,7 => UNS
* DIS # I4: 3,7 => CTR => I4: 6
* INC # I4: 6 => UNS
* INC # C1: 3,7 => UNS
* PRF # C3: 3,7 => SOL
* INC # C3: 6,9 => UNS
* DIS # B6: 3,9 => CTR => B6: 2,7
* INC # B6: 2,7 => UNS
* DIS # C6: 3,9 => CTR => C6: 7,8
* INC # C6: 7,8 => UNS
* INC # F5: 3,9 => UNS
* DIS # F5: 7 => CTR => F5: 3,9
* PRF # B3: 3,9 => SOL
* DIS # B3: 2,6,7 => CTR => B3: 3,9
* INC # F5: 3,7 => UNS
* DIS # F5: 9 => CTR => F5: 3,7
* INC # F5: 3,9 => UNS
* DIS # F5: 7 => CTR => F5: 3,9
* DIS # B6: 3,9 => CTR => B6: 2,7
* INC # B6: 2,7 => UNS
* DIS # C6: 3,9 => CTR => C6: 7,8
* INC # C6: 7,8 => UNS
* INC # H4: 3,7 => UNS
* DIS # I4: 3,7 => CTR => I4: 6
* INC # I4: 6 => UNS
* INC # B6: 3,7 => UNS
* DIS # C6: 3,7 => CTR => C6: 8,9
* INC # C6: 8,9 => UNS
* INC # C8: 8,9 => UNS
* DIS # C8: 6 => CTR => C8: 8,9
* DIS # A6: 8,9 => CTR => A6: 2
* INC # A6: 2 => UNS
* INC # C8: 6,9 => UNS
* DIS # C8: 8 => CTR => C8: 6,9
* DIS # B2: 6,9 => CTR => B2: 2
* INC # B2: 2 => UNS
* DIS # B3: 6,9 => CTR => B3: 2,3,7
* INC # B3: 2,3,7 => UNS
* INC # E1: 2,3 => UNS
* INC # E3: 2,3 => UNS
* INC # F3: 2,3 => UNS
* INC # F3: 1,9 => UNS
* CNT  69 HDP CHAINS /  69 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 2,9 => UNS
* DIS # B3: 2,9 => CTR => B3: 3,6,7
* INC B3: 3,6,7 # B2: 2,9 => UNS
* DIS B3: 3,6,7 # B2: 6 => CTR => B2: 2,9
* DIS B3: 3,6,7 + B2: 2,9 # I1: 2,9 => CTR => I1: 6,7
* INC B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 2,9 => UNS
* DIS B3: 3,6,7 + B2: 2,9 + I1: 6,7 # A6: 8 => CTR => A6: 2,9
* PRF B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 # E2: 1,5 => SOL
* STA B3: 3,6,7 + B2: 2,9 + I1: 6,7 + A6: 2,9 + E2: 1,5
* CNT   8 HDP CHAINS /   8 HYP OPENED