results/anemoi_p2_n31_l1_a3_mFCICO_o2.txt

Model: FCICO. Use final LL: True.
====================================================================================================
ANEMOI GF(2^31), alpha = 3, QUAD = 3. With final LL. Model: FCICO
rmax = 10, tmax = 3600.
====================================================================================================
====================================================================================================
n_r: 1, n_v: 2, n_e: 2, mdeg: 3
degs = [3, 3]
Multivariate Polynomial Ring in Y0000, Y0100 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=1)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 2
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 2
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 1

*******
STEP 1
Basis length: 2, queue length: 1, step degree: 3, num pairs: 1
Basis total mons: 9, average length: 4.500
Number of pair polynomials: 1, at 5 column(s), 0.000
Average length for reductees: 5.00 [1], reductors: 4.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 5 columns out of 10 (50.000%)
Density: 90% / 90% (4.5/r), total: 9 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 1 [1], av deg: 1.0
Degree counts: 1:1
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 3, queue length: 1, step degree: 3, num pairs: 1
Basis total mons: 12, average length: 4.000
Number of pair polynomials: 1, at 6 column(s), 0.000
Average length for reductees: 3.00 [1], reductors: 3.33 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 10 columns out of 10 (100.000%)
Density: 32.857% / 51.548% (3.2857/r), total: 23 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 2)
INTERREDUCE 2 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
2 + 0 = 2 rows / 5 columns
Density: 70% / 90% (3.5/r), total: 7 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [2]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 2
Number of pairs: 2
Max step: 1, time: 0.000
Max num entries matrix: 7 by 10
Max num rows matrix: 7 by 10
Approx mat cost: 35.4286, sym red cost: 32
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.001
Time: 0.000
dregs = [ 3, 3 ]
====================================================================================================
n_r: 2, n_v: 4, n_e: 4, mdeg: 3
degs = [3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, Y0000, Y0100, Y0200 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=2)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 4
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 4
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 2

*******
STEP 1
Basis length: 4, queue length: 2, step degree: 3, num pairs: 2
Basis total mons: 38, average length: 9.500
Number of pair polynomials: 2, at 15 column(s), 0.000
Average length for reductees: 10.00 [2], reductors: 9.00 [2]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 2 = 4 rows / 15 columns out of 35 (42.857%)
Density: 63.333% / 65.595% (9.5/r), total: 38 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 1 [1], av deg: 2.0
Degree counts: 1:1 3:1
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 6, queue length: 1, step degree: 3, num pairs: 1
Basis total mons: 49, average length: 8.167
Number of pair polynomials: 1, at 10 column(s), 0.000
Average length for reductees: 8.00 [1], reductors: 3.00 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 20 columns out of 35 (57.143%)
Density: 17.273% / 32.316% (3.4545/r), total: 38 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 7, queue length: 1, step degree: 4, num pairs: 1
Basis total mons: 58, average length: 8.286
Number of pair polynomials: 1, at 17 column(s), 0.000
Average length for reductees: 9.00 [1], reductors: 4.25 [20]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 20 = 21 rows / 33 columns out of 70 (47.143%)
Density: 13.564% / 25.493% (4.4762/r), total: 94 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 4 [1], av deg: 4.0
Degree counts: 4:1
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 8, queue length: 1, step degree: 5, num pairs: 1
Basis total mons: 71, average length: 8.875
Number of pair polynomials: 1, at 18 column(s), 0.000
Average length for reductees: 13.00 [1], reductors: 5.75 [16]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 16 = 17 rows / 32 columns out of 126 (25.397%)
Density: 19.301% / 32.995% (6.1765/r), total: 105 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 5 [1], av deg: 5.0
Degree counts: 5:1
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 9, queue length: 1, step degree: 6, num pairs: 1
Basis total mons: 87, average length: 9.667
Number of pair polynomials: 1, at 23 column(s), 0.000
Average length for reductees: 16.00 [1], reductors: 5.87 [30]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 30 = 31 rows / 48 columns out of 210 (22.857%)
Density: 12.903% / 23.282% (6.1935/r), total: 192 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 7)
INTERREDUCE 6 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
6 + 13 = 19 rows / 36 columns
Density: 14.62% / 27.51% (5.2632/r), total: 100 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [6]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 6
Number of pairs: 6
Max step: 1, time: 0.000
Max num entries matrix: 31 by 48
Max num rows matrix: 31 by 48
Approx mat cost: 776.445, sym red cost: 467
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.001
Time: 0.010
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 3, n_v: 6, n_e: 6, mdeg: 3
degs = [3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, Y0000, Y0100, Y0200, Y0300 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=3)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 6
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 6
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 3

*******
STEP 1
Basis length: 6, queue length: 3, step degree: 3, num pairs: 3
Basis total mons: 71, average length: 11.833
Number of pair polynomials: 3, at 27 column(s), 0.000
Average length for reductees: 12.33 [3], reductors: 11.33 [3]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 3 = 6 rows / 27 columns out of 84 (32.143%)
Density: 43.827% / 45.217% (11.833/r), total: 71 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 1 [1], av deg: 2.3
Degree counts: 1:1 3:2
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 9, queue length: 2, step degree: 3, num pairs: 1
Basis total mons: 92, average length: 10.222
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 84 (34.524%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 10, queue length: 2, step degree: 4, num pairs: 2
Basis total mons: 105, average length: 10.500
Number of pair polynomials: 2, at 40 column(s), 0.000
Average length for reductees: 10.50 [2], reductors: 5.39 [31]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 31 = 33 rows / 66 columns out of 210 (31.429%)
Density: 8.6318% / 17.176% (5.697/r), total: 188 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 4 [2], av deg: 4.0
Degree counts: 4:2
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 12, queue length: 2, step degree: 5, num pairs: 2
Basis total mons: 134, average length: 11.167
Number of pair polynomials: 2, at 43 column(s), 0.000
Average length for reductees: 14.50 [2], reductors: 12.82 [11]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 11 = 13 rows / 55 columns out of 462 (11.905%)
Density: 23.776% / 29.584% (13.077/r), total: 170 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 3
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 5 [2], av deg: 5.0
Degree counts: 5:2
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 14, queue length: 2, step degree: 6, num pairs: 2
Basis total mons: 171, average length: 12.214
Number of pair polynomials: 2, at 55 column(s), 0.000
Average length for reductees: 18.50 [2], reductors: 7.07 [59]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 59 = 61 rows / 113 columns out of 924 (12.229%)
Density: 6.5864% / 12.797% (7.4426/r), total: 454 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 3
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 11)
INTERREDUCE 10 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
10 + 17 = 27 rows / 65 columns
Density: 10.142% / 19.734% (6.5926/r), total: 178 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [10]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 10
Number of pairs: 10
Max step: 1, time: 0.000
Max num entries matrix: 61 by 113
Max num rows matrix: 61 by 113
Approx mat cost: 2975.44, sym red cost: 935
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.002
Time: 0.000
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 4, n_v: 8, n_e: 8, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, Y0000, Y0100, Y0200, Y0300, Y0400 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=4)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 8
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 8
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 4

*******
STEP 1
Basis length: 8, queue length: 4, step degree: 3, num pairs: 4
Basis total mons: 104, average length: 13.000
Number of pair polynomials: 4, at 39 column(s), 0.000
Average length for reductees: 13.50 [4], reductors: 12.50 [4]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 4 = 8 rows / 39 columns out of 165 (23.636%)
Density: 33.333% / 34.448% (13/r), total: 104 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (100.0%), min deg: 1 [1], av deg: 2.5
Degree counts: 1:1 3:3
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 12, queue length: 3, step degree: 3, num pairs: 1
Basis total mons: 135, average length: 11.250
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 165 (17.576%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 13, queue length: 3, step degree: 4, num pairs: 3
Basis total mons: 148, average length: 11.385
Number of pair polynomials: 3, at 61 column(s), 0.000
Average length for reductees: 10.33 [3], reductors: 6.11 [35]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 35 = 38 rows / 89 columns out of 495 (17.980%)
Density: 7.2442% / 14.497% (6.4474/r), total: 245 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 3
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 4 [3], av deg: 4.0
Degree counts: 4:3
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 16, queue length: 3, step degree: 5, num pairs: 3
Basis total mons: 191, average length: 11.938
Number of pair polynomials: 3, at 64 column(s), 0.000
Average length for reductees: 14.33 [3], reductors: 12.87 [15]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 15 = 18 rows / 84 columns out of 1287 (6.527%)
Density: 15.608% / 19.35% (13.111/r), total: 236 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 5 [3], av deg: 5.0
Degree counts: 5:3
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 19, queue length: 3, step degree: 6, num pairs: 3
Basis total mons: 247, average length: 13.000
Number of pair polynomials: 3, at 82 column(s), 0.000
Average length for reductees: 18.67 [3], reductors: 8.20 [69]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 69 = 72 rows / 157 columns out of 3003 (5.228%)
Density: 5.5025% / 10.553% (8.6389/r), total: 622 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 15)
INTERREDUCE 14 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
14 + 17 = 31 rows / 90 columns
Density: 8.5305% / 16.669% (7.6774/r), total: 238 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [14]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 14
Number of pairs: 14
Max step: 1, time: 0.000
Max num entries matrix: 72 by 157
Max num rows matrix: 72 by 157
Approx mat cost: 5829.29, sym red cost: 1259
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.002
Time: 0.000
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 5, n_v: 10, n_e: 10, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=5)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 10
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 10
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 5

*******
STEP 1
Basis length: 10, queue length: 5, step degree: 3, num pairs: 5
Basis total mons: 137, average length: 13.700
Number of pair polynomials: 5, at 51 column(s), 0.000
Average length for reductees: 14.20 [5], reductors: 13.20 [5]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 5 = 10 rows / 51 columns out of 286 (17.832%)
Density: 26.863% / 27.806% (13.7/r), total: 137 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [5]
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (100.0%), min deg: 1 [1], av deg: 2.6
Degree counts: 1:1 3:4
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 15, queue length: 4, step degree: 3, num pairs: 1
Basis total mons: 178, average length: 11.867
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 286 (10.140%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 16, queue length: 4, step degree: 4, num pairs: 4
Basis total mons: 191, average length: 11.938
Number of pair polynomials: 4, at 82 column(s), 0.000
Average length for reductees: 10.25 [4], reductors: 6.69 [39]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 39 = 43 rows / 112 columns out of 1001 (11.189%)
Density: 6.2708% / 12.553% (7.0233/r), total: 302 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (100.0%), min deg: 4 [4], av deg: 4.0
Degree counts: 4:4
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 20, queue length: 4, step degree: 5, num pairs: 4
Basis total mons: 248, average length: 12.400
Number of pair polynomials: 4, at 85 column(s), 0.000
Average length for reductees: 14.25 [4], reductors: 12.89 [19]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 19 = 23 rows / 113 columns out of 3003 (3.763%)
Density: 11.62% / 14.318% (13.13/r), total: 302 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 5
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (100.0%), min deg: 5 [4], av deg: 5.0
Degree counts: 5:4
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 24, queue length: 4, step degree: 6, num pairs: 4
Basis total mons: 323, average length: 13.458
Number of pair polynomials: 4, at 109 column(s), 0.000
Average length for reductees: 18.75 [4], reductors: 9.05 [79]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 79 = 83 rows / 201 columns out of 8008 (2.510%)
Density: 4.7354% / 8.9599% (9.5181/r), total: 790 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 5
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 19)
INTERREDUCE 18 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
18 + 17 = 35 rows / 115 columns
Density: 7.4037% / 14.387% (8.5143/r), total: 298 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [18]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 18
Number of pairs: 18
Max step: 1, time: 0.000
Max num entries matrix: 83 by 201
Max num rows matrix: 83 by 201
Approx mat cost: 9566.76, sym red cost: 1583
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.002
Time: 0.000
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 6, n_v: 12, n_e: 12, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, X0500, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500, Y0600 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=6)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 12
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 12
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 6

*******
STEP 1
Basis length: 12, queue length: 6, step degree: 3, num pairs: 6
Basis total mons: 170, average length: 14.167
Number of pair polynomials: 6, at 63 column(s), 0.000
Average length for reductees: 14.67 [6], reductors: 13.67 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 6 = 12 rows / 63 columns out of 455 (13.846%)
Density: 22.487% / 23.306% (14.167/r), total: 170 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [6]
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (100.0%), min deg: 1 [1], av deg: 2.7
Degree counts: 1:1 3:5
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 18, queue length: 5, step degree: 3, num pairs: 1
Basis total mons: 221, average length: 12.278
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 455 (6.374%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 19, queue length: 5, step degree: 4, num pairs: 5
Basis total mons: 234, average length: 12.316
Number of pair polynomials: 5, at 103 column(s), 0.000
Average length for reductees: 10.20 [5], reductors: 7.16 [43]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 43 = 48 rows / 135 columns out of 1820 (7.418%)
Density: 5.5401% / 11.069% (7.4792/r), total: 359 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [5]
Number of unused reductors: 5
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (100.0%), min deg: 4 [5], av deg: 4.0
Degree counts: 4:5
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 24, queue length: 5, step degree: 5, num pairs: 5
Basis total mons: 305, average length: 12.708
Number of pair polynomials: 5, at 106 column(s), 0.000
Average length for reductees: 14.20 [5], reductors: 12.91 [23]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 23 = 28 rows / 142 columns out of 6188 (2.295%)
Density: 9.2555% / 11.34% (13.143/r), total: 368 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [5]
Number of unused reductors: 6
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (100.0%), min deg: 5 [5], av deg: 5.0
Degree counts: 5:5
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 29, queue length: 5, step degree: 6, num pairs: 5
Basis total mons: 399, average length: 13.759
Number of pair polynomials: 5, at 136 column(s), 0.000
Average length for reductees: 18.80 [5], reductors: 9.71 [89]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 89 = 94 rows / 245 columns out of 18564 (1.320%)
Density: 4.1598% / 7.7748% (10.191/r), total: 958 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 6
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 23)
INTERREDUCE 22 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
22 + 17 = 39 rows / 140 columns
Density: 6.5568% / 12.637% (9.1795/r), total: 358 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [22]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 22
Number of pairs: 22
Max step: 1, time: 0.000
Max num entries matrix: 94 by 245
Max num rows matrix: 94 by 245
Approx mat cost: 14168.1, sym red cost: 1907
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.003
Time: 0.000
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 7, n_v: 14, n_e: 14, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, X0500, X0600, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500, Y0600, Y0700 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=7)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 14
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 14
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 7

*******
STEP 1
Basis length: 14, queue length: 7, step degree: 3, num pairs: 7
Basis total mons: 203, average length: 14.500
Number of pair polynomials: 7, at 75 column(s), 0.000
Average length for reductees: 15.00 [7], reductors: 14.00 [7]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 7 = 14 rows / 75 columns out of 680 (11.029%)
Density: 19.333% / 20.057% (14.5/r), total: 203 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (100.0%), min deg: 1 [1], av deg: 2.7
Degree counts: 1:1 3:6
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 21, queue length: 6, step degree: 3, num pairs: 1
Basis total mons: 264, average length: 12.571
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 680 (4.265%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 22, queue length: 6, step degree: 4, num pairs: 6
Basis total mons: 277, average length: 12.591
Number of pair polynomials: 6, at 124 column(s), 0.000
Average length for reductees: 10.17 [6], reductors: 7.55 [47]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 47 = 53 rows / 158 columns out of 3060 (5.163%)
Density: 4.9678% / 9.8985% (7.8491/r), total: 416 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [6]
Number of unused reductors: 6
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (100.0%), min deg: 4 [6], av deg: 4.0
Degree counts: 4:6
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 28, queue length: 6, step degree: 5, num pairs: 6
Basis total mons: 362, average length: 12.929
Number of pair polynomials: 6, at 127 column(s), 0.000
Average length for reductees: 14.17 [6], reductors: 12.93 [27]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 27 = 33 rows / 171 columns out of 11628 (1.471%)
Density: 7.6909% / 9.378% (13.152/r), total: 434 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [6]
Number of unused reductors: 7
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (100.0%), min deg: 5 [6], av deg: 5.0
Degree counts: 5:6
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 34, queue length: 6, step degree: 6, num pairs: 6
Basis total mons: 475, average length: 13.971
Number of pair polynomials: 6, at 163 column(s), 0.000
Average length for reductees: 18.83 [6], reductors: 10.23 [99]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 99 = 105 rows / 289 columns out of 38760 (0.746%)
Density: 3.7107% / 6.8614% (10.724/r), total: 1126 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 7
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 27)
INTERREDUCE 26 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
26 + 17 = 43 rows / 165 columns
Density: 5.8915% / 11.258% (9.7209/r), total: 418 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [26]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 26
Number of pairs: 26
Max step: 1, time: 0.000
Max num entries matrix: 105 by 289
Max num rows matrix: 105 by 289
Approx mat cost: 19622.5, sym red cost: 2231
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.000, real time: 0.003
Time: 0.000
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 8, n_v: 16, n_e: 16, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, X0500, X0600, X0700, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500, Y0600, Y0700, Y0800 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=8)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 16
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 16
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 8

*******
STEP 1
Basis length: 16, queue length: 8, step degree: 3, num pairs: 8
Basis total mons: 236, average length: 14.750
Number of pair polynomials: 8, at 87 column(s), 0.000
Average length for reductees: 15.25 [8], reductors: 14.25 [8]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 8 = 16 rows / 87 columns out of 969 (8.978%)
Density: 16.954% / 17.601% (14.75/r), total: 236 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [8]
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (100.0%), min deg: 1 [1], av deg: 2.8
Degree counts: 1:1 3:7
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 24, queue length: 7, step degree: 3, num pairs: 1
Basis total mons: 307, average length: 12.792
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 969 (2.993%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 25, queue length: 7, step degree: 4, num pairs: 7
Basis total mons: 320, average length: 12.800
Number of pair polynomials: 7, at 145 column(s), 0.000
Average length for reductees: 10.14 [7], reductors: 7.88 [51]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 51 = 58 rows / 181 columns out of 4845 (3.736%)
Density: 4.5056% / 8.9515% (8.1552/r), total: 473 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [7]
Number of unused reductors: 7
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (100.0%), min deg: 4 [7], av deg: 4.0
Degree counts: 4:7
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 32, queue length: 7, step degree: 5, num pairs: 7
Basis total mons: 419, average length: 13.094
Number of pair polynomials: 7, at 148 column(s), 0.000
Average length for reductees: 14.14 [7], reductors: 12.94 [31]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 31 = 38 rows / 200 columns out of 20349 (0.983%)
Density: 6.5789% / 7.9899% (13.158/r), total: 500 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [7]
Number of unused reductors: 8
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (100.0%), min deg: 5 [7], av deg: 5.0
Degree counts: 5:7
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 39, queue length: 7, step degree: 6, num pairs: 7
Basis total mons: 551, average length: 14.128
Number of pair polynomials: 7, at 190 column(s), 0.000
Average length for reductees: 18.86 [7], reductors: 10.66 [109]
Symbolic reduction time: 0.000[r], column sort time: 0.000
7 + 109 = 116 rows / 333 columns out of 74613 (0.446%)
Density: 3.3499% / 6.1371% (11.155/r), total: 1294 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 8
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
New max step: 5, time: 0.001[r]
Step 5 time: 0.001[r], [0.001], mat/total: 0.000/0.003[r], mem: 32.1MB (=max)

Do extern interreduction (length 31)
INTERREDUCE 30 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
30 + 17 = 47 rows / 190 columns
Density: 5.3527% / 10.144% (10.17/r), total: 478 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [30]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 30
Number of pairs: 30
Max step: 5, time: 0.001
Max num entries matrix: 116 by 333
Max num rows matrix: 116 by 333
Approx mat cost: 25923.3, sym red cost: 2555
Total pair setup time: 0.000
Total symbolic reduction time: 0.010
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.003[r], real time: 0.004
Time: 0.010
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 9, n_v: 18, n_e: 18, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, X0500, X0600, X0700, X0800, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500, Y0600, Y0700, Y0800, Y0900 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=9)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 18
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 18
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 9

*******
STEP 1
Basis length: 18, queue length: 9, step degree: 3, num pairs: 9
Basis total mons: 269, average length: 14.944
Number of pair polynomials: 9, at 99 column(s), 0.000
Average length for reductees: 15.44 [9], reductors: 14.44 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 9 = 18 rows / 99 columns out of 1330 (7.444%)
Density: 15.095% / 15.681% (14.944/r), total: 269 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000[r] + 0.000 + 0.000 = 0.000[r] [9]
After ech memory: 32.1MB (=max)
Num new polynomials: 9 (100.0%), min deg: 1 [1], av deg: 2.8
Degree counts: 1:1 3:8
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000[r]
Step 1 time: 0.000[r], [0.000], mat/total: 0.010/0.000[r], mem: 32.1MB (=max)

*******
STEP 2
Basis length: 27, queue length: 8, step degree: 3, num pairs: 1
Basis total mons: 350, average length: 12.963
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 1330 (2.180%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.010/0.000[r], mem: 32.1MB (=max)

*******
STEP 3
Basis length: 28, queue length: 8, step degree: 4, num pairs: 8
Basis total mons: 363, average length: 12.964
Number of pair polynomials: 8, at 166 column(s), 0.000
Average length for reductees: 10.12 [8], reductors: 8.16 [55]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 55 = 63 rows / 204 columns out of 7315 (2.789%)
Density: 4.1239% / 8.1695% (8.4127/r), total: 530 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [8]
Number of unused reductors: 8
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (100.0%), min deg: 4 [8], av deg: 4.0
Degree counts: 4:8
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.010/0.001[r], mem: 32.1MB (=max)

*******
STEP 4
Basis length: 36, queue length: 8, step degree: 5, num pairs: 8
Basis total mons: 476, average length: 13.222
Number of pair polynomials: 8, at 169 column(s), 0.000
Average length for reductees: 14.12 [8], reductors: 12.94 [35]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 35 = 43 rows / 229 columns out of 33649 (0.681%)
Density: 5.7479% / 6.9572% (13.163/r), total: 566 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [8]
Number of unused reductors: 9
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (100.0%), min deg: 5 [8], av deg: 5.0
Degree counts: 5:8
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.001], mat/total: 0.010/0.002[r], mem: 32.1MB (=max)

*******
STEP 5
Basis length: 44, queue length: 8, step degree: 6, num pairs: 8
Basis total mons: 627, average length: 14.250
Number of pair polynomials: 8, at 217 column(s), 0.000
Average length for reductees: 18.88 [8], reductors: 11.02 [119]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 119 = 127 rows / 377 columns out of 134596 (0.280%)
Density: 3.0535% / 5.5492% (11.512/r), total: 1462 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 9
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
Step 5 time: 0.000, [0.001], mat/total: 0.010/0.003[r], mem: 32.1MB (=max)

Do extern interreduction (length 35)
INTERREDUCE 34 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
34 + 17 = 51 rows / 215 columns
Density: 4.9065% / 9.2282% (10.549/r), total: 538 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [34]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 34
Number of pairs: 34
Max step: 1, time: 0.000
Max num entries matrix: 127 by 377
Max num rows matrix: 127 by 377
Approx mat cost: 33066, sym red cost: 2879
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.010
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.003[r], real time: 0.003
Time: 0.010
dregs = [ 3, 3, 4, 5, 6 ]
====================================================================================================
n_r: 10, n_v: 20, n_e: 20, mdeg: 3
degs = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
Multivariate Polynomial Ring in X0100, X0200, X0300, X0400, X0500, X0600, X0700, X0800, X0900, Y0000, Y0100, Y0200, Y0300, Y0400, Y0500, Y0600, Y0700, Y0800, Y0900, Y1000 over Finite Field in z31 of size 2^31
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=10)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^31)
Rank: 20
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 4
No queue sort
Initial length: 20
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 10

*******
STEP 1
Basis length: 20, queue length: 10, step degree: 3, num pairs: 10
Basis total mons: 302, average length: 15.100
Number of pair polynomials: 10, at 111 column(s), 0.000
Average length for reductees: 15.60 [10], reductors: 14.60 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 10 = 20 rows / 111 columns out of 1771 (6.268%)
Density: 13.604% / 14.138% (15.1/r), total: 302 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [10]
After ech memory: 32.1MB (=max)
Num new polynomials: 10 (100.0%), min deg: 1 [1], av deg: 2.8
Degree counts: 1:1 3:9
Queue insertion time: 0.000
Number of linears: 1
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 30, queue length: 9, step degree: 3, num pairs: 1
Basis total mons: 393, average length: 13.100
Number of pair polynomials: 1, at 12 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 3.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 29 columns out of 1771 (1.637%)
Density: 11.954% / 24.241% (3.4667/r), total: 52 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 3 [1], av deg: 3.0
Degree counts: 3:1
Queue insertion time: 0.000
Number of linears: 1
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 31, queue length: 9, step degree: 4, num pairs: 9
Basis total mons: 406, average length: 13.097
Number of pair polynomials: 9, at 187 column(s), 0.000
Average length for reductees: 10.11 [9], reductors: 8.41 [59]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 59 = 68 rows / 227 columns out of 10626 (2.136%)
Density: 3.8028% / 7.5129% (8.6324/r), total: 587 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [9]
Number of unused reductors: 9
After ech memory: 32.1MB (=max)
Num new polynomials: 9 (100.0%), min deg: 4 [9], av deg: 4.0
Degree counts: 4:9
Queue insertion time: 0.000
Number of linears: 1
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 40, queue length: 9, step degree: 5, num pairs: 9
Basis total mons: 533, average length: 13.325
Number of pair polynomials: 9, at 190 column(s), 0.000
Average length for reductees: 14.11 [9], reductors: 12.95 [39]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 39 = 48 rows / 258 columns out of 53130 (0.486%)
Density: 5.1034% / 6.1594% (13.167/r), total: 632 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [9]
Number of unused reductors: 10
After ech memory: 32.1MB (=max)
Num new polynomials: 9 (100.0%), min deg: 5 [9], av deg: 5.0
Degree counts: 5:9
Queue insertion time: 0.000
Number of linears: 1
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 49, queue length: 9, step degree: 6, num pairs: 9
Basis total mons: 703, average length: 14.347
Number of pair polynomials: 9, at 244 column(s), 0.000
Average length for reductees: 18.89 [9], reductors: 11.32 [129]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 129 = 138 rows / 421 columns out of 230230 (0.183%)
Density: 2.8056% / 5.0629% (11.812/r), total: 1630 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000[r] + 0.000 + 0.000 = 0.000[r] [0]
Number of unused reductors: 10
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Number of linears: 1
New max step: 5, time: 0.002[r]
Step 5 time: 0.002[r], [0.002], mat/total: 0.010/0.003[r], mem: 32.1MB (=max)

Do extern interreduction (length 39)
INTERREDUCE 38 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
38 + 17 = 55 rows / 240 columns
Density: 4.5303% / 8.4617% (10.873/r), total: 598 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [38]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 38
Number of pairs: 38
Max step: 5, time: 0.002
Max num entries matrix: 138 by 421
Max num rows matrix: 138 by 421
Approx mat cost: 41047.8, sym red cost: 3203
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.010
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.003[r], real time: 0.004
Time: 0.010
dregs = [ 3, 3, 4, 5, 6 ]
3.60user 0.53system 0:04.60elapsed 89%CPU (0avgtext+0avgdata 237504maxresident)k
0inputs+1152outputs (0major+93646minor)pagefaults 0swaps