Analysis of zz-www.sudokuoftheday.co.uk-20060413-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006

position: .....5..8..54..7...1..3.....4....9..38.1.......6....516..5..1.4.9.7..52.1.324..9. initial

Autosolve

position: .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 3,6 => CTR => H1: 1,4
* PRF # F2: 2,8 => SOL
* DIS # H2: 1 => CTR => H2: 3,6
* DIS # E1: 6,9 => CTR => E1: 1,2,7
* DIS # G1: 4,6 => CTR => G1: 2,3
* DIS # H1: 4,6 => CTR => H1: 1,3
* DIS # G3: 4,6 => CTR => G3: 2
* DIS # H5: 4,6 => CTR => H5: 7
* DIS # F6: 2,7 => CTR => F6: 4,8,9
* DIS # H5: 4,6 => CTR => H5: 7
* DIS # G1: 4,6 => CTR => G1: 2,3
* DIS # G3: 4,6 => CTR => G3: 2
* PRF # I4: 2,6 => SOL
* DIS # I4: 3 => CTR => I4: 2,6
* DIS # F7: 8,9 => CTR => F7: 3
* PRF # F7: 3 => SOL
* PRF # F8: 1,6 => SOL
* DIS # F8: 3 => CTR => F8: 1,6
* DIS # E1: 1,6 => CTR => E1: 2,7,9
* PRF # E2: 1,6 => SOL
* DIS # F2: 6,8 => CTR => F2: 1,2
* DIS # F7: 9 => CTR => F7: 3,8
* DIS # H4: 6,7 => CTR => H4: 3,8
* PRF # F8: 1 => SOL
* PRF # I4: 2 => SOL
* CNT  25 HDP CHAINS /  68 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 # H1: 3,6 => CTR => H1: 1,4
* DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6
* PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL
* STA H1: 1,4 + G1: 3,6 + F2: 2,8
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

.....5..8..54..7...1..3.....4....9..38.1.......6....516..5..1.4.9.7..52.1.324..9. initial
.....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97 autosolve
264975318835412769719836245541687932382159476976324851627593184498761523153248697 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
B1: 3,6
A2: 2,8
B2: 3,6
D1: 6,9
H3: 4,6
B6: 2,7
G5: 4,6
I5: 2,6
B7: 2,7
C7: 2,7
A8: 4,8
C8: 4,8
E7: 8,9
E8: 1,6
F9: 6,8
H7: 3,8
I8: 3,6
G9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 1.. / H1 = 1  => 19 pairs (_) / H2 = 1  =>  0 pairs (X)
E8,F8: 1.. / E8 = 1  => 21 pairs (_) / F8 = 1  =>  0 pairs (*)
E1,H1: 1.. / E1 = 1  =>  0 pairs (X) / H1 = 1  => 19 pairs (_)
F2,F8: 1.. / F2 = 1  => 21 pairs (_) / F8 = 1  =>  0 pairs (*)
G1,G3: 2.. / G1 = 2  =>  0 pairs (X) / G3 = 2  => 18 pairs (_)
I4,I5: 2.. / I4 = 2  =>  0 pairs (*) / I5 = 2  =>  0 pairs (X)
B7,C7: 2.. / B7 = 2  => 17 pairs (_) / C7 = 2  => 17 pairs (_)
B6,B7: 2.. / B6 = 2  => 17 pairs (_) / B7 = 2  => 17 pairs (_)
B1,B2: 3.. / B1 = 3  =>  0 pairs (X) / B2 = 3  => 18 pairs (_)
D4,D6: 3.. / D4 = 3  =>  0 pairs (X) / D6 = 3  => 22 pairs (_)
F7,F8: 3.. / F7 = 3  =>  0 pairs (*) / F8 = 3  =>  0 pairs (X)
H7,I8: 3.. / H7 = 3  =>  0 pairs (X) / I8 = 3  =>  0 pairs (_)
B2,H2: 3.. / B2 = 3  => 18 pairs (_) / H2 = 3  =>  0 pairs (X)
D6,G6: 3.. / D6 = 3  => 22 pairs (_) / G6 = 3  =>  0 pairs (X)
F7,H7: 3.. / F7 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
F8,I8: 3.. / F8 = 3  =>  0 pairs (X) / I8 = 3  =>  0 pairs (_)
G1,G6: 3.. / G1 = 3  => 22 pairs (_) / G6 = 3  =>  0 pairs (X)
I4,I8: 3.. / I4 = 3  =>  0 pairs (X) / I8 = 3  =>  0 pairs (_)
F5,F6: 4.. / F5 = 4  =>  0 pairs (X) / F6 = 4  => 19 pairs (_)
A8,C8: 4.. / A8 = 4  => 16 pairs (_) / C8 = 4  => 26 pairs (_)
F6,G6: 4.. / F6 = 4  => 19 pairs (_) / G6 = 4  =>  0 pairs (X)
B1,B2: 6.. / B1 = 6  => 18 pairs (_) / B2 = 6  =>  0 pairs (X)
I8,G9: 6.. / I8 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
F9,G9: 6.. / F9 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
E1,F3: 7.. / E1 = 7  => 19 pairs (_) / F3 = 7  => 18 pairs (_)
H4,H5: 7.. / H4 = 7  =>  0 pairs (X) / H5 = 7  => 20 pairs (_)
B7,C7: 7.. / B7 = 7  => 17 pairs (_) / C7 = 7  => 17 pairs (_)
B6,B7: 7.. / B6 = 7  => 17 pairs (_) / B7 = 7  => 17 pairs (_)
H4,G6: 8.. / H4 = 8  =>  0 pairs (X) / G6 = 8  =>  0 pairs (_)
A8,C8: 8.. / A8 = 8  => 26 pairs (_) / C8 = 8  => 16 pairs (_)
H7,G9: 8.. / H7 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
F9,G9: 8.. / F9 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
C3,C8: 8.. / C3 = 8  => 26 pairs (_) / C8 = 8  => 16 pairs (_)
G6,G9: 8.. / G6 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
H4,H7: 8.. / H4 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
C5,A6: 9.. / C5 = 9  => 20 pairs (_) / A6 = 9  => 24 pairs (_)
E7,F7: 9.. / E7 = 9  => 18 pairs (_) / F7 = 9  =>  0 pairs (X)
C5,F5: 9.. / C5 = 9  => 20 pairs (_) / F5 = 9  => 24 pairs (_)
* DURATION: 0:00:42.308233  START: 22:21:26.052902  END: 22:22:08.361135 2019-04-30
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,B2,B6,B7,C7,C8,D1,E7,E8,F9,G5,G9,H3,H7,I5,I8)
* .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97
* PAIR B1: 3,6 ROW 1
G1: 3,6,2,4                              # reduction candidate for 3,6
G1: 3,6                                  # 22 pairs
H1: 3,6,1,4                              # reduction candidate for 3,6
H1: 3,6 => CTR
* ....15..8.354.6719.1..37.655416.29..38.15......6....516..5..1.4.9.761523153248697
H1: 1,4                                  # 19 pairs
* PAIR A2: 2,8 BLK 1
A3: 2,8,4,7,9                            # reduction candidate for 2,8
A3: 2,8                                  # 19 pairs
C3: 2,8,4,7,9                            # reduction candidate for 2,8
C3: 2,8                                  # 19 pairs
* PAIR A2: 2,8 ROW 2
E2: 2,8,1,6                              # reduction candidate for 2,8
E2: 2,8                                  # 20 pairs
F2: 2,8,1,6                              # reduction candidate for 2,8
F2: 2,8 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
F2: 1,6                                  # 20 pairs
* PAIR B2: 3,6 ROW 2
H2: 3,6,1                                # reduction candidate for 3,6
H2: 1 => CTR
* .6.915..8.354..719.1..37.655416..93238.15.476..63.48516..5.3184.9.761523153248697
H2: 3,6                                  # 19 pairs
* PAIR D1: 6,9 BLK 2
E1: 6,9,1,2,7                            # reduction candidate for 6,9
E1: 6,9 => CTR
* .....5.188.54..739.1.837..5541...9..38.15......6...3516..5.31844987..523153248697
E1: 1,2,7                                # 18 pairs
D3: 6,9,8                                # reduction candidate for 6,9
D3: 6,9                                  # 24 pairs
F3: 6,9,2,7,8                            # reduction candidate for 6,9
F3: 6,9                                  # 22 pairs
* PAIR H3: 4,6 BLK 3
G1: 4,6,2,3                              # reduction candidate for 4,6
G1: 4,6 => CTR
* .....5..8..54..7.9.1..3.2.5541...9..38.15......6...3516..5..1.4.9.7..52315324..97
G1: 2,3                                  # 19 pairs
H1: 4,6,1,3                              # reduction candidate for 4,6
H1: 4,6 => CTR
* ....153.8.354.6719.1..372655416.29..38.15......6....516..5..1.4.9.761523153248697
H1: 1,3                                  # 19 pairs
G3: 4,6,2                                # reduction candidate for 4,6
G3: 4,6 => CTR
* .....52.8..54..7.9.1..3...5541...9..38.15......6...3516..5..1.4.9.7..52315324..97
G3: 2                                    # 18 pairs
* PAIR H3: 4,6 COL H
H5: 4,6,7                                # reduction candidate for 4,6
H5: 4,6 => CTR
* .....5..8..54..7.9.1..3...5541...97.38.15......6...8516..5..184.9.7..523153248697
H5: 7                                    # 20 pairs
* PAIR B6: 2,7 BLK 4
C5: 2,7,9                                # reduction candidate for 2,7
C5: 2,7                                  # 24 pairs
A6: 2,7,9                                # reduction candidate for 2,7
A6: 2,7                                  # 20 pairs
* PAIR B6: 2,7 ROW 6
E6: 2,7,8,9                              # reduction candidate for 2,7
E6: 2,7                                  # 24 pairs
F6: 2,7,4,8,9                            # reduction candidate for 2,7
F6: 2,7 => CTR
* .....53.8.354..7.9.1..3.2.5541...983389154672..63..4516..5..1.4.9.7..526153246897
F6: 4,8,9                                # 18 pairs
* PAIR G5: 4,6 BLK 6
H5: 4,6,7                                # reduction candidate for 4,6
H5: 4,6 => CTR
* .....5..8..54..7.9.1..3...5541...97.38.15......6...8516..5..184.9.7..523153248697
H5: 7                                    # 20 pairs
* PAIR G5: 4,6 ROW 5
F5: 4,6,2,7,9                            # reduction candidate for 4,6
F5: 4,6                                  # 24 pairs
F5: 2,7,9                                # 20 pairs
* PAIR G5: 4,6 COL G
G1: 4,6,2,3                              # reduction candidate for 4,6
G1: 4,6 => CTR
* .....5..8..54..7.9.1..3.2.5541...9..38.15......6...3516..5..1.4.9.7..52315324..97
G1: 2,3                                  # 19 pairs
G3: 4,6,2                                # reduction candidate for 4,6
G3: 4,6 => CTR
* .....52.8..54..7.9.1..3...5541...9..38.15......6...3516..5..1.4.9.7..52315324..97
G3: 2                                    # 18 pairs
* PAIR I5: 2,6 BLK 6
I4: 2,6,3                                # reduction candidate for 2,6
I4: 2,6 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
I4: 3 => CTR
* .....53.8.354.1769.1.63.24554186297338.15...2..63...516..5..134.9.7.3526153246897
* PAIR I5: 2,6 ROW 5
F5: 2,6,4,7,9                            # reduction candidate for 2,6
F5: 2,6                                  # 22 pairs
F5: 4,7,9                                # 19 pairs
* PAIR C7: 2,7 COL C
C1: 2,7,4,9                              # reduction candidate for 2,7
C1: 2,7                                  # 22 pairs
C3: 2,7,4,8,9                            # reduction candidate for 2,7
C3: 2,7                                  # 19 pairs
C5: 2,7,9                                # reduction candidate for 2,7
C5: 2,7                                  # 24 pairs
* PAIR A8: 4,8 COL A
A3: 4,8,2,7,9                            # reduction candidate for 4,8
A3: 4,8                                  # 29 pairs
A3: 2,7,9                                # 18 pairs
* PAIR C8: 4,8 COL C
C3: 4,8,2,7,9                            # reduction candidate for 4,8
C3: 4,8                                  # 19 pairs
C3: 2,7,9                                # 16 pairs
* PAIR E7: 8,9 BLK 8
F7: 8,9,3                                # reduction candidate for 8,9
F7: 8,9 => CTR
* .....53.8.354.1769.1.63.245541.6.98338.15......6....516..5..134.9.7.3526153246897
F7: 3 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
* PAIR E7: 8,9 COL E
E6: 8,9,2,7                              # reduction candidate for 8,9
E6: 2,7                                  # 24 pairs
E6: 8,9                                  # 19 pairs
* PAIR E8: 1,6 BLK 8
F8: 1,6,3                                # reduction candidate for 1,6
F8: 1,6 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
F8: 3 => CTR
* .....5318.354.1769.1..3...5541...98338.15..72..63..4516..5..134.9.713526153246897
* PAIR E8: 1,6 COL E
E1: 1,6,2,7,9                            # reduction candidate for 1,6
E1: 1,6 => CTR
* .6.9153488354..7199148372655416..9..38915..7...63...516..5..1.4498761523153248697
E1: 2,7,9                                # 19 pairs
E2: 1,6,2,8                              # reduction candidate for 1,6
E2: 1,6 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
E2: 2,8                                  # 20 pairs
* PAIR F9: 6,8 COL F
F2: 6,8,1,2                              # reduction candidate for 6,8
F2: 6,8 => CTR
* .....53.8.354.6719.1..3.26554168.93238.152476..63948516..5.3184.9.761523153248697
F2: 1,2                                  # 19 pairs
F3: 6,8,2,7,9                            # reduction candidate for 6,8
F3: 6,8                                  # 25 pairs
F4: 6,8,2,7                              # reduction candidate for 6,8
F4: 6,8                                  # 23 pairs
* PAIR H7: 3,8 ROW 7
F7: 3,8,9                                # reduction candidate for 3,8
F7: 9 => CTR
* .....53.8.354.1769.1.63.245541.6.98338.15......6....516..5.9134.9.7.3526153246897
F7: 3,8                                  # 18 pairs
* PAIR H7: 3,8 COL H
H4: 3,8,6,7                              # reduction candidate for 3,8
H4: 6,7 => CTR
* .....5..8..54..7.9.1..3...5541...9..38.15......6...8516..5..184.9.7..523153248697
H4: 3,8                                  # 22 pairs
* PAIR I8: 3,6 ROW 8
F8: 3,6,1                                # reduction candidate for 3,6
F8: 1 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
F8: 3,6                                  # 21 pairs
* PAIR I8: 3,6 COL I
I4: 3,6,2                                # reduction candidate for 3,6
I4: 2 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
I4: 3,6                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060413-absurd-base-pr-000.dot
* REASONING
* DIS # H1: 3,6 => CTR => H1: 1,4
* PRF # F2: 2,8 => SOL
* DIS # H2: 1 => CTR => H2: 3,6
* DIS # E1: 6,9 => CTR => E1: 1,2,7
* DIS # G1: 4,6 => CTR => G1: 2,3
* DIS # H1: 4,6 => CTR => H1: 1,3
* DIS # G3: 4,6 => CTR => G3: 2
* DIS # H5: 4,6 => CTR => H5: 7
* DIS # F6: 2,7 => CTR => F6: 4,8,9
* DIS # H5: 4,6 => CTR => H5: 7
* DIS # G1: 4,6 => CTR => G1: 2,3
* DIS # G3: 4,6 => CTR => G3: 2
* PRF # I4: 2,6 => SOL
* DIS # I4: 3 => CTR => I4: 2,6
* DIS # F7: 8,9 => CTR => F7: 3
* PRF # F7: 3 => SOL
* PRF # F8: 1,6 => SOL
* DIS # F8: 3 => CTR => F8: 1,6
* DIS # E1: 1,6 => CTR => E1: 2,7,9
* PRF # E2: 1,6 => SOL
* DIS # F2: 6,8 => CTR => F2: 1,2
* DIS # F7: 9 => CTR => F7: 3,8
* DIS # H4: 6,7 => CTR => H4: 3,8
* PRF # F8: 1 => SOL
* PRF # I4: 2 => SOL
* CNT  25 HDP CHAINS /  68 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,B2,B6,B7,C7,C8,D1,E7,E8,F9,G5,G9,H3,H7,I5,I8)
* .....5..8..54..7.9.1..3...5541...9..38.15......6....516..5..1.4.9.7..52.15324..97
* PAIR B1: 3,6 ROW 1
G1: 3,6,2,4                              # reduction candidate for 3,6
G1: 3,6                                  # 22 pairs
H1: 3,6,1,4                              # reduction candidate for 3,6
H1: 3,6 => CTR
* ....15..8.354.6719.1..37.655416.29..38.15......6....516..5..1.4.9.761523153248697
* RESTART
* PAIR B1: 3,6 ROW 1
G1: 3,6,2,4                              # reduction candidate for 3,6
G1: 2,4 => CTR
* .3...5..8.654..739.1..3...5541...9..38.15......6...3516..5.3184.9.7..523153248697
* PAIR RESTART
* PAIR A2: 2,8 ROW 2
E2: 2,8,1,6                              # reduction candidate for 2,8
E2: 2,8                                  # 24 pairs
F2: 2,8,1,6                              # reduction candidate for 2,8
F2: 2,8 => SOLVED
* 264975318835412769719836245541687932382159476976324851627593184498761523153248697
* DURATION: 0:00:04.785998  START: 22:22:48.881977  END: 22:22:53.667975 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060413-absurd-base-pr-001.dot
* REASONING
* DIS # H1: 3,6 => CTR => H1: 1,4
* DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6
* PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL
* STA H1: 1,4 + G1: 3,6 + F2: 2,8
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060413, absurd

Solution

position: 264975318835412769719836245541687932382159476976324851627593184498761523153248697 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 # G1: 3,6 => UNS
* DIS # H1: 3,6 => CTR => H1: 1,4
* INC # H1: 1,4 => UNS
* INC # A3: 2,8 => UNS
* INC # C3: 2,8 => UNS
* INC # E2: 2,8 => UNS
* PRF # F2: 2,8 => SOL
* INC # F2: 1,6 => UNS
* INC # H2: 3,6 => UNS
* DIS # H2: 1 => CTR => H2: 3,6
* DIS # E1: 6,9 => CTR => E1: 1,2,7
* INC # E1: 1,2,7 => UNS
* INC # D3: 6,9 => UNS
* INC # F3: 6,9 => UNS
* DIS # G1: 4,6 => CTR => G1: 2,3
* INC # G1: 2,3 => UNS
* DIS # H1: 4,6 => CTR => H1: 1,3
* INC # H1: 1,3 => UNS
* DIS # G3: 4,6 => CTR => G3: 2
* INC # G3: 2 => UNS
* DIS # H5: 4,6 => CTR => H5: 7
* INC # H5: 7 => UNS
* INC # C5: 2,7 => UNS
* INC # A6: 2,7 => UNS
* INC # E6: 2,7 => UNS
* DIS # F6: 2,7 => CTR => F6: 4,8,9
* INC # F6: 4,8,9 => UNS
* DIS # H5: 4,6 => CTR => H5: 7
* INC # H5: 7 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 2,7,9 => UNS
* DIS # G1: 4,6 => CTR => G1: 2,3
* INC # G1: 2,3 => UNS
* DIS # G3: 4,6 => CTR => G3: 2
* INC # G3: 2 => UNS
* PRF # I4: 2,6 => SOL
* DIS # I4: 3 => CTR => I4: 2,6
* INC # F5: 2,6 => UNS
* INC # F5: 4,7,9 => UNS
* INC # C1: 2,7 => UNS
* INC # C3: 2,7 => UNS
* INC # C5: 2,7 => UNS
* INC # A3: 4,8 => UNS
* INC # A3: 2,7,9 => UNS
* INC # C3: 4,8 => UNS
* INC # C3: 2,7,9 => UNS
* DIS # F7: 8,9 => CTR => F7: 3
* PRF # F7: 3 => SOL
* INC # E6: 8,9 => UNS
* INC # E6: 2,7 => UNS
* PRF # F8: 1,6 => SOL
* DIS # F8: 3 => CTR => F8: 1,6
* DIS # E1: 1,6 => CTR => E1: 2,7,9
* INC # E1: 2,7,9 => UNS
* PRF # E2: 1,6 => SOL
* INC # E2: 2,8 => UNS
* DIS # F2: 6,8 => CTR => F2: 1,2
* INC # F2: 1,2 => UNS
* INC # F3: 6,8 => UNS
* INC # F4: 6,8 => UNS
* INC # F7: 3,8 => UNS
* DIS # F7: 9 => CTR => F7: 3,8
* INC # H4: 3,8 => UNS
* DIS # H4: 6,7 => CTR => H4: 3,8
* INC # F8: 3,6 => UNS
* PRF # F8: 1 => SOL
* INC # I4: 3,6 => UNS
* PRF # I4: 2 => SOL
* CNT  68 HDP CHAINS /  68 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,6 => UNS
* DIS # H1: 3,6 => CTR => H1: 1,4
* INC H1: 1,4 # G1: 3,6 => UNS
* DIS H1: 1,4 # G1: 2,4 => CTR => G1: 3,6
* INC H1: 1,4 + G1: 3,6 # E2: 2,8 => UNS
* PRF H1: 1,4 + G1: 3,6 # F2: 2,8 => SOL
* STA H1: 1,4 + G1: 3,6 + F2: 2,8
* CNT   6 HDP CHAINS /   6 HYP OPENED