Analysis of xx-ph-00013023-kz0-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Appendix: Full HDP Chains

Original Sudoku

level: very deep

position: 98.7..6..5..9..4......8....7..4..5...5..3......2....1.4....9.65...6....7....4.9.. initial

Autosolve

position: 98.7..6..5..9..4......8....7..4..5...5..3......2....1.4....9.65...6...47....4.9.. autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:28.997818

The following important HDP chains were detected:

* DIS # F6: 5,8 # F5: 1,2 => CTR => F5: 6,7
* CNT   1 HDP CHAINS /  69 HYP OPENED

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

Deep Constraint Pair Analysis

Time used: 0:00:00.000018

List of important HDP chains detected for E6,E7: 7..:

* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* CNT   1 HDP CHAINS /  54 HYP OPENED

List of important HDP chains detected for E7,F9: 7..:

* DIS # F9: 7 # E8: 1,2 => CTR => E8: 5
* CNT   1 HDP CHAINS /  54 HYP OPENED

List of important HDP chains detected for H3,I3: 9..:

* DIS # H3: 9 # E2: 1,2 => CTR => E2: 6
* CNT   1 HDP CHAINS /  58 HYP OPENED

List of important HDP chains detected for C8,C9: 5..:

* DIS # C8: 5 # E7: 1,2 => CTR => E7: 7
* CNT   1 HDP CHAINS /  40 HYP OPENED

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

Very Deep Constraint Pair Analysis

Time used: 0:00:40.627562

List of important HDP chains detected for E6,E7: 7..:

* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* PRF # E6: 7 + E8: 5 # F1: 1,2 # C7: 1,7 => SOL
* STA # E6: 7 + E8: 5 # F1: 1,2 + C7: 1,7
* CNT   2 HDP CHAINS /  53 HYP OPENED

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

Details

This sudoku is very deep. Here is some information that may be helpful on how to proceed.

Positions

`98.7..6..5..9..4......8....7..4..5...5..3......2....1.4....9.65...6....7....4.9..`	initial
`98.7..6..5..9..4......8....7..4..5...5..3......2....1.4....9.65...6...47....4.9..`	autosolve

Classification

level: very deep

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
D6: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F3: 4.. / F1 = 4  =>  2 pairs (_) / F3 = 4  =>  1 pairs (_)
C5,B6: 4.. / C5 = 4  =>  2 pairs (_) / B6 = 4  =>  1 pairs (_)
I5,I6: 4.. / I5 = 4  =>  1 pairs (_) / I6 = 4  =>  2 pairs (_)
C1,F1: 4.. / C1 = 4  =>  1 pairs (_) / F1 = 4  =>  2 pairs (_)
C5,I5: 4.. / C5 = 4  =>  2 pairs (_) / I5 = 4  =>  1 pairs (_)
B6,I6: 4.. / B6 = 4  =>  1 pairs (_) / I6 = 4  =>  2 pairs (_)
B3,B6: 4.. / B3 = 4  =>  2 pairs (_) / B6 = 4  =>  1 pairs (_)
H1,H3: 5.. / H1 = 5  =>  2 pairs (_) / H3 = 5  =>  2 pairs (_)
C8,C9: 5.. / C8 = 5  =>  2 pairs (_) / C9 = 5  =>  1 pairs (_)
E7,F9: 7.. / E7 = 7  =>  1 pairs (_) / F9 = 7  =>  6 pairs (_)
E6,E7: 7.. / E6 = 7  =>  6 pairs (_) / E7 = 7  =>  1 pairs (_)
H2,I2: 8.. / H2 = 8  =>  2 pairs (_) / I2 = 8  =>  1 pairs (_)
H3,I3: 9.. / H3 = 9  =>  5 pairs (_) / I3 = 9  =>  1 pairs (_)
E4,E6: 9.. / E4 = 9  =>  4 pairs (_) / E6 = 9  =>  1 pairs (_)
B8,C8: 9.. / B8 = 9  =>  1 pairs (_) / C8 = 9  =>  1 pairs (_)
* DURATION: 0:00:09.427475  START: 14:09:36.489994  END: 14:09:45.917469 2020-12-02
* CP COUNT: (15)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
E6,E7: 7.. / E6 = 7 ==>  7 pairs (_) / E7 = 7 ==>  1 pairs (_)
E7,F9: 7.. / E7 = 7 ==>  1 pairs (_) / F9 = 7 ==>  7 pairs (_)
H3,I3: 9.. / H3 = 9 ==>  5 pairs (_) / I3 = 9 ==>  1 pairs (_)
E4,E6: 9.. / E4 = 9 ==>  4 pairs (_) / E6 = 9 ==>  1 pairs (_)
H1,H3: 5.. / H1 = 5 ==>  2 pairs (_) / H3 = 5 ==>  2 pairs (_)
H2,I2: 8.. / H2 = 8 ==>  2 pairs (_) / I2 = 8 ==>  1 pairs (_)
C8,C9: 5.. / C8 = 5 ==>  2 pairs (_) / C9 = 5 ==>  1 pairs (_)
B3,B6: 4.. / B3 = 4 ==>  2 pairs (_) / B6 = 4 ==>  1 pairs (_)
B6,I6: 4.. / B6 = 4 ==>  1 pairs (_) / I6 = 4 ==>  2 pairs (_)
C5,I5: 4.. / C5 = 4 ==>  2 pairs (_) / I5 = 4 ==>  1 pairs (_)
C1,F1: 4.. / C1 = 4 ==>  1 pairs (_) / F1 = 4 ==>  2 pairs (_)
I5,I6: 4.. / I5 = 4 ==>  1 pairs (_) / I6 = 4 ==>  2 pairs (_)
C5,B6: 4.. / C5 = 4 ==>  2 pairs (_) / B6 = 4 ==>  1 pairs (_)
F1,F3: 4.. / F1 = 4 ==>  2 pairs (_) / F3 = 4 ==>  1 pairs (_)
B8,C8: 9.. / B8 = 9 ==>  1 pairs (_) / C8 = 9 ==>  1 pairs (_)
* DURATION: 0:03:11.616067  START: 14:10:17.917611  END: 14:13:29.533678 2020-12-02
* REASONING E6,E7: 7..
* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* CNT   1 HDP CHAINS /  54 HYP OPENED
* REASONING E7,F9: 7..
* DIS # F9: 7 # E8: 1,2 => CTR => E8: 5
* CNT   1 HDP CHAINS /  54 HYP OPENED
* REASONING H3,I3: 9..
* DIS # H3: 9 # E2: 1,2 => CTR => E2: 6
* CNT   1 HDP CHAINS /  58 HYP OPENED
* REASONING C8,C9: 5..
* DIS # C8: 5 # E7: 1,2 => CTR => E7: 7
* CNT   1 HDP CHAINS /  40 HYP OPENED
* DCP COUNT: (15)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
E6,E7: 7.. / E6 = 7 ==>  0 pairs (*) / E7 = 7  =>  0 pairs (X)
* DURATION: 0:00:40.624612  START: 14:13:29.710066  END: 14:14:10.334678 2020-12-02
* REASONING E6,E7: 7..
* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* PRF # E6: 7 + E8: 5 # F1: 1,2 # C7: 1,7 => SOL
* STA # E6: 7 + E8: 5 # F1: 1,2 + C7: 1,7
* CNT   2 HDP CHAINS /  53 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND

Header Info

13023;kz0;GP;23;11.30;1.20;1.20

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # F6: 5,8 => UNS
* INC # F6: 6,7 => UNS
* INC # D9: 5,8 => UNS
* INC # D9: 1,2,3 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F6: 5,8 => UNS
* INC # F6: 6,7 => UNS
* INC # D9: 5,8 => UNS
* INC # D9: 1,2,3 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F6: 5,8 => UNS
* INC # F6: 6,7 => UNS
* INC # D9: 5,8 => UNS
* INC # D9: 1,2,3 => UNS
* INC # F6: 5,8 # B4: 3,6 => UNS
* INC # F6: 5,8 # C4: 3,6 => UNS
* INC # F6: 5,8 # B6: 3,6 => UNS
* INC # F6: 5,8 # I6: 3,6 => UNS
* INC # F6: 5,8 # I6: 4,9 => UNS
* INC # F6: 5,8 # A3: 3,6 => UNS
* INC # F6: 5,8 # A9: 3,6 => UNS
* INC # F6: 5,8 # E4: 1,2 => UNS
* INC # F6: 5,8 # F4: 1,2 => UNS
* DIS # F6: 5,8 # F5: 1,2 => CTR => F5: 6,7
* INC # F6: 5,8 + F5: 6,7 # D3: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D7: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # E4: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # F4: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D3: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D7: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 1,2,3 => UNS
* INC # F6: 5,8 + F5: 6,7 # F8: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # F9: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # G3: 3,7 => UNS
* INC # F6: 5,8 + F5: 6,7 # G3: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # B4: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # C4: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # B6: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # I6: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # I6: 4,9 => UNS
* INC # F6: 5,8 + F5: 6,7 # A3: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # A9: 3,6 => UNS
* INC # F6: 5,8 + F5: 6,7 # E4: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # F4: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D3: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D7: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 # E6: 6,7 => UNS
* INC # F6: 5,8 + F5: 6,7 # E6: 9 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # D9: 1,2,3 => UNS
* INC # F6: 5,8 + F5: 6,7 # F8: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # F9: 5,8 => UNS
* INC # F6: 5,8 + F5: 6,7 # G3: 3,7 => UNS
* INC # F6: 5,8 + F5: 6,7 # G3: 1,2 => UNS
* INC # F6: 5,8 + F5: 6,7 => UNS
* INC # F6: 6,7 # D9: 5,8 => UNS
* INC # F6: 6,7 # D9: 1,2,3 => UNS
* INC # F6: 6,7 # F5: 6,7 => UNS
* INC # F6: 6,7 # E6: 6,7 => UNS
* INC # F6: 6,7 => UNS
* INC # D9: 5,8 # E4: 1,2 => UNS
* INC # D9: 5,8 # F4: 1,2 => UNS
* INC # D9: 5,8 # F5: 1,2 => UNS
* INC # D9: 5,8 # D3: 1,2 => UNS
* INC # D9: 5,8 # D7: 1,2 => UNS
* INC # D9: 5,8 # F6: 5,8 => UNS
* INC # D9: 5,8 # F6: 6,7 => UNS
* INC # D9: 5,8 # F8: 5,8 => UNS
* INC # D9: 5,8 # F9: 5,8 => UNS
* INC # D9: 5,8 # C9: 5,8 => UNS
* INC # D9: 5,8 # C9: 1,3,6,7 => UNS
* INC # D9: 5,8 => UNS
* INC # D9: 1,2,3 # F6: 5,8 => UNS
* INC # D9: 1,2,3 # F6: 6,7 => UNS
* INC # D9: 1,2,3 => UNS
* CNT  69 HDP CHAINS /  69 HYP OPENED

A4. Deep Constraint Pair Analysis

Full list of HDP chains traversed for E6,E7: 7..:

* INC # E6: 7 # I5: 4,9 => UNS
* INC # E6: 7 # I5: 2,6,8 => UNS
* INC # E6: 7 # F6: 5,8 => UNS
* INC # E6: 7 # F6: 6 => UNS
* INC # E6: 7 # D9: 5,8 => UNS
* INC # E6: 7 # D9: 1,2,3 => UNS
* INC # E6: 7 # H4: 3,8 => UNS
* INC # E6: 7 # I4: 3,8 => UNS
* INC # E6: 7 # A6: 3,8 => UNS
* INC # E6: 7 # A6: 6 => UNS
* INC # E6: 7 # G7: 3,8 => UNS
* INC # E6: 7 # G8: 3,8 => UNS
* INC # E6: 7 # I5: 4,9 => UNS
* INC # E6: 7 # I5: 2,6,8 => UNS
* INC # E6: 7 # D7: 1,2 => UNS
* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F1: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F2: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D3: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F3: 1,2 => UNS
* INC # E6: 7 + E8: 5 # I1: 1,2 => UNS
* INC # E6: 7 + E8: 5 # I1: 3 => UNS
* INC # E6: 7 + E8: 5 # I5: 4,9 => UNS
* INC # E6: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # E6: 7 + E8: 5 # F6: 5,8 => UNS
* INC # E6: 7 + E8: 5 # F6: 6 => UNS
* INC # E6: 7 + E8: 5 # H4: 3,8 => UNS
* INC # E6: 7 + E8: 5 # I4: 3,8 => UNS
* INC # E6: 7 + E8: 5 # A6: 3,8 => UNS
* INC # E6: 7 + E8: 5 # A6: 6 => UNS
* INC # E6: 7 + E8: 5 # G7: 3,8 => UNS
* INC # E6: 7 + E8: 5 # G8: 3,8 => UNS
* INC # E6: 7 + E8: 5 # I5: 4,9 => UNS
* INC # E6: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # E6: 7 + E8: 5 # D7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 => UNS
* INC # E7: 7 # F6: 5,8 => UNS
* INC # E7: 7 # F6: 6,7 => UNS
* INC # E7: 7 # D9: 5,8 => UNS
* INC # E7: 7 # D9: 1,2,3 => UNS
* INC # E7: 7 => UNS
* CNT  54 HDP CHAINS /  54 HYP OPENED

Full list of HDP chains traversed for E7,F9: 7..:

* INC # F9: 7 # I5: 4,9 => UNS
* INC # F9: 7 # I5: 2,6,8 => UNS
* INC # F9: 7 # F6: 5,8 => UNS
* INC # F9: 7 # F6: 6 => UNS
* INC # F9: 7 # D9: 5,8 => UNS
* INC # F9: 7 # D9: 1,2,3 => UNS
* INC # F9: 7 # H4: 3,8 => UNS
* INC # F9: 7 # I4: 3,8 => UNS
* INC # F9: 7 # A6: 3,8 => UNS
* INC # F9: 7 # A6: 6 => UNS
* INC # F9: 7 # G7: 3,8 => UNS
* INC # F9: 7 # G8: 3,8 => UNS
* INC # F9: 7 # I5: 4,9 => UNS
* INC # F9: 7 # I5: 2,6,8 => UNS
* INC # F9: 7 # D7: 1,2 => UNS
* DIS # F9: 7 # E8: 1,2 => CTR => E8: 5
* INC # F9: 7 + E8: 5 # F8: 1,2 => UNS
* INC # F9: 7 + E8: 5 # D9: 1,2 => UNS
* INC # F9: 7 + E8: 5 # B7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # G7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # D7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # F8: 1,2 => UNS
* INC # F9: 7 + E8: 5 # D9: 1,2 => UNS
* INC # F9: 7 + E8: 5 # B7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # G7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # F1: 1,2 => UNS
* INC # F9: 7 + E8: 5 # F2: 1,2 => UNS
* INC # F9: 7 + E8: 5 # D3: 1,2 => UNS
* INC # F9: 7 + E8: 5 # F3: 1,2 => UNS
* INC # F9: 7 + E8: 5 # I1: 1,2 => UNS
* INC # F9: 7 + E8: 5 # I1: 3 => UNS
* INC # F9: 7 + E8: 5 # I5: 4,9 => UNS
* INC # F9: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # F9: 7 + E8: 5 # F6: 5,8 => UNS
* INC # F9: 7 + E8: 5 # F6: 6 => UNS
* INC # F9: 7 + E8: 5 # H4: 3,8 => UNS
* INC # F9: 7 + E8: 5 # I4: 3,8 => UNS
* INC # F9: 7 + E8: 5 # A6: 3,8 => UNS
* INC # F9: 7 + E8: 5 # A6: 6 => UNS
* INC # F9: 7 + E8: 5 # G7: 3,8 => UNS
* INC # F9: 7 + E8: 5 # G8: 3,8 => UNS
* INC # F9: 7 + E8: 5 # I5: 4,9 => UNS
* INC # F9: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # F9: 7 + E8: 5 # D7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # F8: 1,2 => UNS
* INC # F9: 7 + E8: 5 # D9: 1,2 => UNS
* INC # F9: 7 + E8: 5 # B7: 1,2 => UNS
* INC # F9: 7 + E8: 5 # G7: 1,2 => UNS
* INC # F9: 7 + E8: 5 => UNS
* INC # E7: 7 # F6: 5,8 => UNS
* INC # E7: 7 # F6: 6,7 => UNS
* INC # E7: 7 # D9: 5,8 => UNS
* INC # E7: 7 # D9: 1,2,3 => UNS
* INC # E7: 7 => UNS
* CNT  54 HDP CHAINS /  54 HYP OPENED

Full list of HDP chains traversed for H3,I3: 9..:

* INC # H3: 9 # F1: 1,2 => UNS
* DIS # H3: 9 # E2: 1,2 => CTR => E2: 6
* INC # H3: 9 + E2: 6 # F2: 1,2 => UNS
* INC # H3: 9 + E2: 6 # D3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 3 => UNS
* INC # H3: 9 + E2: 6 # E4: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E7: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E8: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F1: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F2: 1,2 => UNS
* INC # H3: 9 + E2: 6 # D3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 3 => UNS
* INC # H3: 9 + E2: 6 # E4: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E7: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E8: 1,2 => UNS
* INC # H3: 9 + E2: 6 # B6: 4,9 => UNS
* INC # H3: 9 + E2: 6 # B6: 3,6 => UNS
* INC # H3: 9 + E2: 6 # F6: 5,8 => UNS
* INC # H3: 9 + E2: 6 # F6: 6,7 => UNS
* INC # H3: 9 + E2: 6 # D9: 5,8 => UNS
* INC # H3: 9 + E2: 6 # D9: 1,2,3 => UNS
* INC # H3: 9 + E2: 6 # I6: 6,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 4 => UNS
* INC # H3: 9 + E2: 6 # B4: 6,9 => UNS
* INC # H3: 9 + E2: 6 # C4: 6,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 4,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 6 => UNS
* INC # H3: 9 + E2: 6 # F1: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F2: 1,2 => UNS
* INC # H3: 9 + E2: 6 # D3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # F3: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 1,2 => UNS
* INC # H3: 9 + E2: 6 # I1: 3 => UNS
* INC # H3: 9 + E2: 6 # E4: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E7: 1,2 => UNS
* INC # H3: 9 + E2: 6 # E8: 1,2 => UNS
* INC # H3: 9 + E2: 6 # B6: 4,9 => UNS
* INC # H3: 9 + E2: 6 # B6: 3,6 => UNS
* INC # H3: 9 + E2: 6 # F6: 5,8 => UNS
* INC # H3: 9 + E2: 6 # F6: 6,7 => UNS
* INC # H3: 9 + E2: 6 # D9: 5,8 => UNS
* INC # H3: 9 + E2: 6 # D9: 1,2,3 => UNS
* INC # H3: 9 + E2: 6 # I6: 6,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 4 => UNS
* INC # H3: 9 + E2: 6 # B4: 6,9 => UNS
* INC # H3: 9 + E2: 6 # C4: 6,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 4,9 => UNS
* INC # H3: 9 + E2: 6 # I6: 6 => UNS
* INC # H3: 9 + E2: 6 => UNS
* INC # I3: 9 # F6: 5,8 => UNS
* INC # I3: 9 # F6: 6,7 => UNS
* INC # I3: 9 # D9: 5,8 => UNS
* INC # I3: 9 # D9: 1,2,3 => UNS
* INC # I3: 9 => UNS
* CNT  58 HDP CHAINS /  58 HYP OPENED

Full list of HDP chains traversed for E4,E6: 9..:

* INC # E4: 9 # I5: 4,9 => UNS
* INC # E4: 9 # I5: 2,6,8 => UNS
* INC # E4: 9 # F6: 5,8 => UNS
* INC # E4: 9 # F6: 6,7 => UNS
* INC # E4: 9 # D9: 5,8 => UNS
* INC # E4: 9 # D9: 1,2,3 => UNS
* INC # E4: 9 # I5: 4,9 => UNS
* INC # E4: 9 # I5: 2,6,8 => UNS
* INC # E4: 9 => UNS
* INC # E6: 9 # F6: 5,8 => UNS
* INC # E6: 9 # F6: 6,7 => UNS
* INC # E6: 9 # D9: 5,8 => UNS
* INC # E6: 9 # D9: 1,2,3 => UNS
* INC # E6: 9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

Full list of HDP chains traversed for H1,H3: 5..:

* INC # H1: 5 # F1: 1,2 => UNS
* INC # H1: 5 # E2: 1,2 => UNS
* INC # H1: 5 # F2: 1,2 => UNS
* INC # H1: 5 # D3: 1,2 => UNS
* INC # H1: 5 # F3: 1,2 => UNS
* INC # H1: 5 # I1: 1,2 => UNS
* INC # H1: 5 # I1: 3 => UNS
* INC # H1: 5 # E4: 1,2 => UNS
* INC # H1: 5 # E7: 1,2 => UNS
* INC # H1: 5 # E8: 1,2 => UNS
* INC # H1: 5 # F6: 5,8 => UNS
* INC # H1: 5 # F6: 6,7 => UNS
* INC # H1: 5 # D9: 5,8 => UNS
* INC # H1: 5 # D9: 1,2,3 => UNS
* INC # H1: 5 => UNS
* INC # H3: 5 # I1: 2,3 => UNS
* INC # H3: 5 # H2: 2,3 => UNS
* INC # H3: 5 # I2: 2,3 => UNS
* INC # H3: 5 # G3: 2,3 => UNS
* INC # H3: 5 # F1: 2,3 => UNS
* INC # H3: 5 # F1: 1,4,5 => UNS
* INC # H3: 5 # H4: 2,3 => UNS
* INC # H3: 5 # H9: 2,3 => UNS
* INC # H3: 5 # F6: 5,8 => UNS
* INC # H3: 5 # F6: 6,7 => UNS
* INC # H3: 5 # D9: 5,8 => UNS
* INC # H3: 5 # D9: 1,2,3 => UNS
* INC # H3: 5 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

Full list of HDP chains traversed for H2,I2: 8..:

* INC # H2: 8 # F6: 5,8 => UNS
* INC # H2: 8 # F6: 6,7 => UNS
* INC # H2: 8 # D9: 5,8 => UNS
* INC # H2: 8 # D9: 1,2,3 => UNS
* INC # H2: 8 # G7: 2,3 => UNS
* INC # H2: 8 # G8: 2,3 => UNS
* INC # H2: 8 # I9: 2,3 => UNS
* INC # H2: 8 # A9: 2,3 => UNS
* INC # H2: 8 # B9: 2,3 => UNS
* INC # H2: 8 # D9: 2,3 => UNS
* INC # H2: 8 # F9: 2,3 => UNS
* INC # H2: 8 # H1: 2,3 => UNS
* INC # H2: 8 # H3: 2,3 => UNS
* INC # H2: 8 # H4: 2,3 => UNS
* INC # H2: 8 => UNS
* INC # I2: 8 # F6: 5,8 => UNS
* INC # I2: 8 # F6: 6,7 => UNS
* INC # I2: 8 # D9: 5,8 => UNS
* INC # I2: 8 # D9: 1,2,3 => UNS
* INC # I2: 8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for C8,C9: 5..:

* INC # C8: 5 # F6: 5,8 => UNS
* INC # C8: 5 # F6: 6,7 => UNS
* INC # C8: 5 # D9: 5,8 => UNS
* INC # C8: 5 # D9: 1,2,3 => UNS
* INC # C8: 5 # D7: 1,2 => UNS
* DIS # C8: 5 # E7: 1,2 => CTR => E7: 7
* INC # C8: 5 + E7: 7 # F8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # D9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # A8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # G8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E1: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E2: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E4: 1,2 => UNS
* INC # C8: 5 + E7: 7 # D7: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # D9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # A8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # G8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E1: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E2: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E4: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F6: 5,8 => UNS
* INC # C8: 5 + E7: 7 # F6: 6,7 => UNS
* INC # C8: 5 + E7: 7 # D9: 5,8 => UNS
* INC # C8: 5 + E7: 7 # D9: 1,2,3 => UNS
* INC # C8: 5 + E7: 7 # D7: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # D9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # F9: 1,2 => UNS
* INC # C8: 5 + E7: 7 # A8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # G8: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E1: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E2: 1,2 => UNS
* INC # C8: 5 + E7: 7 # E4: 1,2 => UNS
* INC # C8: 5 + E7: 7 => UNS
* INC # C9: 5 # F6: 5,8 => UNS
* INC # C9: 5 # F6: 6,7 => UNS
* INC # C9: 5 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

Full list of HDP chains traversed for B3,B6: 4..:

* INC # B3: 4 # B2: 1,3 => UNS
* INC # B3: 4 # C2: 1,3 => UNS
* INC # B3: 4 # A3: 1,3 => UNS
* INC # B3: 4 # C3: 1,3 => UNS
* INC # B3: 4 # I1: 1,3 => UNS
* INC # B3: 4 # I1: 2 => UNS
* INC # B3: 4 # C4: 1,3 => UNS
* INC # B3: 4 # C7: 1,3 => UNS
* INC # B3: 4 # C8: 1,3 => UNS
* INC # B3: 4 # C9: 1,3 => UNS
* INC # B3: 4 # F6: 5,8 => UNS
* INC # B3: 4 # F6: 6,7 => UNS
* INC # B3: 4 # D9: 5,8 => UNS
* INC # B3: 4 # D9: 1,2,3 => UNS
* INC # B3: 4 => UNS
* INC # B6: 4 # F6: 5,8 => UNS
* INC # B6: 4 # F6: 6,7 => UNS
* INC # B6: 4 # D9: 5,8 => UNS
* INC # B6: 4 # D9: 1,2,3 => UNS
* INC # B6: 4 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for B6,I6: 4..:

* INC # I6: 4 # B2: 1,3 => UNS
* INC # I6: 4 # C2: 1,3 => UNS
* INC # I6: 4 # A3: 1,3 => UNS
* INC # I6: 4 # C3: 1,3 => UNS
* INC # I6: 4 # I1: 1,3 => UNS
* INC # I6: 4 # I1: 2 => UNS
* INC # I6: 4 # C4: 1,3 => UNS
* INC # I6: 4 # C7: 1,3 => UNS
* INC # I6: 4 # C8: 1,3 => UNS
* INC # I6: 4 # C9: 1,3 => UNS
* INC # I6: 4 # F6: 5,8 => UNS
* INC # I6: 4 # F6: 6,7 => UNS
* INC # I6: 4 # D9: 5,8 => UNS
* INC # I6: 4 # D9: 1,2,3 => UNS
* INC # I6: 4 => UNS
* INC # B6: 4 # F6: 5,8 => UNS
* INC # B6: 4 # F6: 6,7 => UNS
* INC # B6: 4 # D9: 5,8 => UNS
* INC # B6: 4 # D9: 1,2,3 => UNS
* INC # B6: 4 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for C5,I5: 4..:

* INC # C5: 4 # B2: 1,3 => UNS
* INC # C5: 4 # C2: 1,3 => UNS
* INC # C5: 4 # A3: 1,3 => UNS
* INC # C5: 4 # C3: 1,3 => UNS
* INC # C5: 4 # I1: 1,3 => UNS
* INC # C5: 4 # I1: 2 => UNS
* INC # C5: 4 # C4: 1,3 => UNS
* INC # C5: 4 # C7: 1,3 => UNS
* INC # C5: 4 # C8: 1,3 => UNS
* INC # C5: 4 # C9: 1,3 => UNS
* INC # C5: 4 # F6: 5,8 => UNS
* INC # C5: 4 # F6: 6,7 => UNS
* INC # C5: 4 # D9: 5,8 => UNS
* INC # C5: 4 # D9: 1,2,3 => UNS
* INC # C5: 4 => UNS
* INC # I5: 4 # F6: 5,8 => UNS
* INC # I5: 4 # F6: 6,7 => UNS
* INC # I5: 4 # D9: 5,8 => UNS
* INC # I5: 4 # D9: 1,2,3 => UNS
* INC # I5: 4 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for C1,F1: 4..:

* INC # F1: 4 # B2: 1,3 => UNS
* INC # F1: 4 # C2: 1,3 => UNS
* INC # F1: 4 # A3: 1,3 => UNS
* INC # F1: 4 # B3: 1,3 => UNS
* INC # F1: 4 # C3: 1,3 => UNS
* INC # F1: 4 # I1: 1,3 => UNS
* INC # F1: 4 # I1: 2 => UNS
* INC # F1: 4 # C4: 1,3 => UNS
* INC # F1: 4 # C7: 1,3 => UNS
* INC # F1: 4 # C8: 1,3 => UNS
* INC # F1: 4 # C9: 1,3 => UNS
* INC # F1: 4 # F6: 5,8 => UNS
* INC # F1: 4 # F6: 6,7 => UNS
* INC # F1: 4 # D9: 5,8 => UNS
* INC # F1: 4 # D9: 1,2,3 => UNS
* INC # F1: 4 => UNS
* INC # C1: 4 # F6: 5,8 => UNS
* INC # C1: 4 # F6: 6,7 => UNS
* INC # C1: 4 # D9: 5,8 => UNS
* INC # C1: 4 # D9: 1,2,3 => UNS
* INC # C1: 4 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

Full list of HDP chains traversed for I5,I6: 4..:

* INC # I6: 4 # B2: 1,3 => UNS
* INC # I6: 4 # C2: 1,3 => UNS
* INC # I6: 4 # A3: 1,3 => UNS
* INC # I6: 4 # C3: 1,3 => UNS
* INC # I6: 4 # I1: 1,3 => UNS
* INC # I6: 4 # I1: 2 => UNS
* INC # I6: 4 # C4: 1,3 => UNS
* INC # I6: 4 # C7: 1,3 => UNS
* INC # I6: 4 # C8: 1,3 => UNS
* INC # I6: 4 # C9: 1,3 => UNS
* INC # I6: 4 # F6: 5,8 => UNS
* INC # I6: 4 # F6: 6,7 => UNS
* INC # I6: 4 # D9: 5,8 => UNS
* INC # I6: 4 # D9: 1,2,3 => UNS
* INC # I6: 4 => UNS
* INC # I5: 4 # F6: 5,8 => UNS
* INC # I5: 4 # F6: 6,7 => UNS
* INC # I5: 4 # D9: 5,8 => UNS
* INC # I5: 4 # D9: 1,2,3 => UNS
* INC # I5: 4 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for C5,B6: 4..:

* INC # C5: 4 # B2: 1,3 => UNS
* INC # C5: 4 # C2: 1,3 => UNS
* INC # C5: 4 # A3: 1,3 => UNS
* INC # C5: 4 # C3: 1,3 => UNS
* INC # C5: 4 # I1: 1,3 => UNS
* INC # C5: 4 # I1: 2 => UNS
* INC # C5: 4 # C4: 1,3 => UNS
* INC # C5: 4 # C7: 1,3 => UNS
* INC # C5: 4 # C8: 1,3 => UNS
* INC # C5: 4 # C9: 1,3 => UNS
* INC # C5: 4 # F6: 5,8 => UNS
* INC # C5: 4 # F6: 6,7 => UNS
* INC # C5: 4 # D9: 5,8 => UNS
* INC # C5: 4 # D9: 1,2,3 => UNS
* INC # C5: 4 => UNS
* INC # B6: 4 # F6: 5,8 => UNS
* INC # B6: 4 # F6: 6,7 => UNS
* INC # B6: 4 # D9: 5,8 => UNS
* INC # B6: 4 # D9: 1,2,3 => UNS
* INC # B6: 4 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

Full list of HDP chains traversed for F1,F3: 4..:

* INC # F1: 4 # B2: 1,3 => UNS
* INC # F1: 4 # C2: 1,3 => UNS
* INC # F1: 4 # A3: 1,3 => UNS
* INC # F1: 4 # B3: 1,3 => UNS
* INC # F1: 4 # C3: 1,3 => UNS
* INC # F1: 4 # I1: 1,3 => UNS
* INC # F1: 4 # I1: 2 => UNS
* INC # F1: 4 # C4: 1,3 => UNS
* INC # F1: 4 # C7: 1,3 => UNS
* INC # F1: 4 # C8: 1,3 => UNS
* INC # F1: 4 # C9: 1,3 => UNS
* INC # F1: 4 # F6: 5,8 => UNS
* INC # F1: 4 # F6: 6,7 => UNS
* INC # F1: 4 # D9: 5,8 => UNS
* INC # F1: 4 # D9: 1,2,3 => UNS
* INC # F1: 4 => UNS
* INC # F3: 4 # F6: 5,8 => UNS
* INC # F3: 4 # F6: 6,7 => UNS
* INC # F3: 4 # D9: 5,8 => UNS
* INC # F3: 4 # D9: 1,2,3 => UNS
* INC # F3: 4 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

Full list of HDP chains traversed for B8,C8: 9..:

* INC # B8: 9 # F6: 5,8 => UNS
* INC # B8: 9 # F6: 6,7 => UNS
* INC # B8: 9 # D9: 5,8 => UNS
* INC # B8: 9 # D9: 1,2,3 => UNS
* INC # B8: 9 => UNS
* INC # C8: 9 # F6: 5,8 => UNS
* INC # C8: 9 # F6: 6,7 => UNS
* INC # C8: 9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A5. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for E6,E7: 7..:

* INC # E6: 7 # I5: 4,9 => UNS
* INC # E6: 7 # I5: 2,6,8 => UNS
* INC # E6: 7 # F6: 5,8 => UNS
* INC # E6: 7 # F6: 6 => UNS
* INC # E6: 7 # D9: 5,8 => UNS
* INC # E6: 7 # D9: 1,2,3 => UNS
* INC # E6: 7 # H4: 3,8 => UNS
* INC # E6: 7 # I4: 3,8 => UNS
* INC # E6: 7 # A6: 3,8 => UNS
* INC # E6: 7 # A6: 6 => UNS
* INC # E6: 7 # G7: 3,8 => UNS
* INC # E6: 7 # G8: 3,8 => UNS
* INC # E6: 7 # I5: 4,9 => UNS
* INC # E6: 7 # I5: 2,6,8 => UNS
* INC # E6: 7 # D7: 1,2 => UNS
* DIS # E6: 7 # E8: 1,2 => CTR => E8: 5
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F1: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F2: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D3: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F3: 1,2 => UNS
* INC # E6: 7 + E8: 5 # I1: 1,2 => UNS
* INC # E6: 7 + E8: 5 # I1: 3 => UNS
* INC # E6: 7 + E8: 5 # I5: 4,9 => UNS
* INC # E6: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # E6: 7 + E8: 5 # F6: 5,8 => UNS
* INC # E6: 7 + E8: 5 # F6: 6 => UNS
* INC # E6: 7 + E8: 5 # H4: 3,8 => UNS
* INC # E6: 7 + E8: 5 # I4: 3,8 => UNS
* INC # E6: 7 + E8: 5 # A6: 3,8 => UNS
* INC # E6: 7 + E8: 5 # A6: 6 => UNS
* INC # E6: 7 + E8: 5 # G7: 3,8 => UNS
* INC # E6: 7 + E8: 5 # G8: 3,8 => UNS
* INC # E6: 7 + E8: 5 # I5: 4,9 => UNS
* INC # E6: 7 + E8: 5 # I5: 2,6,8 => UNS
* INC # E6: 7 + E8: 5 # D7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F8: 1,2 => UNS
* INC # E6: 7 + E8: 5 # D9: 1,2 => UNS
* INC # E6: 7 + E8: 5 # B7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # G7: 1,2 => UNS
* INC # E6: 7 + E8: 5 # F1: 1,2 # B2: 1,7 => UNS
* INC # E6: 7 + E8: 5 # F1: 1,2 # B3: 1,7 => UNS
* PRF # E6: 7 + E8: 5 # F1: 1,2 # C7: 1,7 => SOL
* STA # E6: 7 + E8: 5 # F1: 1,2 + C7: 1,7
* CNT  51 HDP CHAINS /  53 HYP OPENED