results/anemoi_p65537_n1_l1_a11_mFCICO_o3.txt

Model: FCICO. Use final LL: True.
====================================================================================================
ANEMOI GF(65537^1), alpha = 11, QUAD = 2. With final LL. Model: FCICO
rmax = 10, tmax = 3600.
====================================================================================================
====================================================================================================
n_r: 1, n_v: 2, n_e: 2, mdeg: 11
degs = [11, 11]
Multivariate Polynomial Ring in Y0100, Y0000 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=1)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 2
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
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: 11, num pairs: 1
Basis total mons: 156, average length: 78.000
Number of pair polynomials: 1, at 78 column(s), 0.000
Average length for reductees: 78.00 [1], reductors: 78.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 78 columns out of 78 (100.000%)
Density: 100% / 100% (78/r), total: 156 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 2 [1], av deg: 2.0
Degree counts: 2:1
Queue insertion time: 0.000
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: 3, queue length: 1, step degree: 11, num pairs: 1
Basis total mons: 161, average length: 53.667
Number of pair polynomials: 1, at 78 column(s), 0.000
Average length for reductees: 5.00 [1], reductors: 6.33 [55]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 55 = 56 rows / 78 columns out of 78 (100.000%)
Density: 8.0815% / 17.638% (6.3036/r), total: 353 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 4, queue length: 1, step degree: 12, num pairs: 1
Basis total mons: 184, average length: 46.000
Number of pair polynomials: 1, at 26 column(s), 0.000
Average length for reductees: 23.00 [1], reductors: 7.77 [13]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 13 = 14 rows / 36 columns out of 91 (39.560%)
Density: 24.603% / 39.43% (8.8571/r), total: 124 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 3 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 5, queue length: 2, step degree: 11, num pairs: 2
Basis total mons: 205, average length: 41.000
Number of pair polynomials: 2, at 33 column(s), 0.000
Average length for reductees: 21.00 [2], reductors: 7.83 [12]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 12 = 14 rows / 33 columns out of 78 (42.308%)
Density: 29.437% / 43.585% (9.7143/r), total: 136 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 4 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 6, queue length: 2, step degree: 10, num pairs: 2
Basis total mons: 224, average length: 37.333
Number of pair polynomials: 2, at 30 column(s), 0.000
Average length for reductees: 19.00 [2], reductors: 7.73 [11]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 11 = 13 rows / 30 columns out of 66 (45.455%)
Density: 31.538% / 45.834% (9.4615/r), total: 123 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 8 [1], av deg: 8.0
Degree counts: 8:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 6
Basis length: 7, queue length: 2, step degree: 9, num pairs: 2
Basis total mons: 241, average length: 34.429
Number of pair polynomials: 2, at 27 column(s), 0.000
Average length for reductees: 17.00 [2], reductors: 7.60 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 10 = 12 rows / 27 columns out of 55 (49.091%)
Density: 33.951% / 48.347% (9.1667/r), total: 110 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 7 [1], av deg: 7.0
Degree counts: 7:1
Queue insertion time: 0.000
Step 6 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 8, queue length: 2, step degree: 8, num pairs: 2
Basis total mons: 256, average length: 32.000
Number of pair polynomials: 2, at 24 column(s), 0.000
Average length for reductees: 15.00 [2], reductors: 7.44 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 9 = 11 rows / 24 columns out of 45 (53.333%)
Density: 36.742% / 51.176% (8.8182/r), total: 97 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 7 [1], av deg: 7.0
Degree counts: 7:1
Queue insertion time: 0.000
Step 7 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 8
Basis length: 9, queue length: 1, step degree: 8, num pairs: 1
Basis total mons: 270, average length: 30.000
Number of pair polynomials: 1, at 22 column(s), 0.000
Average length for reductees: 14.00 [1], reductors: 8.80 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 23 columns out of 45 (51.111%)
Density: 40.316% / 54.899% (9.2727/r), total: 102 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 8 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Reduce 9 final polynomial(s) by 9
0 redundant polynomial(s) removed; time: 0.000
Interreduce 3 (out of range [0 .. 8] = 9) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
3 + 0 = 3 rows / 16 columns
Density: 70.833% / 90.139% (11.333/r), total: 34 (0.0MB)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [3]
Total reduction time: 0.000
Reduction time: 0.000
Final number of polynomials: 9

Final basis length: 3
Number of pairs: 12
Max step: 1, time: 0.000
Max num entries matrix: 56 by 78
Max num rows matrix: 56 by 78
Approx mat cost: 2275.31, sym red cost: 1235
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 = [ 11, 11, 12, 11, 10, 9, 8, 8 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=1)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 2
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 3
Try rep mat lex method; E: Y0000
Get rep mat (dim: 13)
Rep mat time: 0.000
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 0.000
Get kernel for min poly
Kernel mat time: 0.000
Nullity: 1
Get relations for all variables
REDUCE 2 polynomial(s) by 3 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
2 + 8 = 10 rows / 21 columns
Density: 40% / 53.607% (8.4/r), total: 84 (0.0MB)
Row sort time: 0.000
0.000 = 0.000 [2]
Total reduction time: 0.000
Reduction time: 0.000
Relations time: 0.000
Time: 0.000
unideg = 13
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=1)
Time: 0.000
nsols = 0
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=1)
nsols_mult = 0
====================================================================================================
n_r: 2, n_v: 4, n_e: 4, mdeg: 11
degs = [11, 11, 11, 11]
Multivariate Polynomial Ring in Y0200, Y0100, Y0000, X0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=2)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 4
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
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: 11, num pairs: 2
Basis total mons: 885, average length: 221.250
Number of pair polynomials: 2, at 430 column(s), 0.000
Average length for reductees: 221.50 [2], reductors: 221.00 [2]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 2 = 4 rows / 430 columns out of 1365 (31.502%)
Density: 51.453% / 51.693% (221.25/r), total: 885 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 2 [2], av deg: 2.0
Degree counts: 2:2
Queue insertion time: 0.000
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: 6, queue length: 2, step degree: 11, num pairs: 2
Basis total mons: 899, average length: 149.833
Number of pair polynomials: 2, at 432 column(s), 0.000
Average length for reductees: 7.00 [2], reductors: 6.85 [965]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 965 = 967 rows / 1210 columns out of 1365 (88.645%)
Density: 0.56646% / 1.9871% (6.8542/r), total: 6628 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 11 [2], av deg: 11.0
Degree counts: 11:2
Queue insertion time: 0.000
Step 2 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 8, queue length: 3, step degree: 12, num pairs: 3
Basis total mons: 1221, average length: 152.625
Number of pair polynomials: 3, at 434 column(s), 0.000
Average length for reductees: 188.67 [3], reductors: 11.34 [229]
Symbolic reduction time: 0.000, column sort time: 0.000[r]
3 + 229 = 232 rows / 535 columns out of 1820 (29.396%)
Density: 2.5491% / 5.7633% (13.638/r), total: 3164 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 11 [2], av deg: 11.3
Degree counts: 11:2 12:1
Queue insertion time: 0.000
New max step: 3, time: 0.001[r]
Step 3 time: 0.000[r], [0.001], mat/total: 0.000/0.003[r], mem: 32.1MB (=max)

*******
STEP 4
Basis length: 11, queue length: 6, step degree: 12, num pairs: 6
Basis total mons: 1851, average length: 168.273
Number of pair polynomials: 6, at 529 column(s), 0.000
Average length for reductees: 199.50 [6], reductors: 12.76 [229]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 229 = 235 rows / 529 columns out of 1820 (29.066%)
Density: 3.3126% / 6.5152% (17.523/r), total: 4118 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [4]
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (66.7%), min deg: 11 [2], av deg: 11.5
Degree counts: 11:2 12:2
Queue insertion time: 0.000
Step 4 time: 0.000, [0.001], mat/total: 0.000/0.005[r], mem: 32.1MB (=max)

*******
STEP 5
Basis length: 15, queue length: 10, step degree: 12, num pairs: 6
Basis total mons: 2767, average length: 184.467
Number of pair polynomials: 6, at 513 column(s), 0.000
Average length for reductees: 173.83 [6], reductors: 15.02 [220]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 220 = 226 rows / 513 columns out of 1820 (28.187%)
Density: 3.7503% / 7.0386% (19.239/r), total: 4348 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [4]
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (66.7%), min deg: 11 [2], av deg: 11.5
Degree counts: 11:2 12:2
Queue insertion time: 0.000
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.006[r], mem: 32.1MB (=max)

*******
STEP 6
Basis length: 19, queue length: 14, step degree: 12, num pairs: 7
Basis total mons: 3651, average length: 192.158
Number of pair polynomials: 7, at 499 column(s), 0.000
Average length for reductees: 176.14 [7], reductors: 15.42 [212]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 212 = 219 rows / 499 columns out of 1820 (27.418%)
Density: 4.1187% / 7.4766% (20.553/r), total: 4501 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [5]
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (71.4%), min deg: 11 [2], av deg: 11.6
Degree counts: 11:2 12:3
Queue insertion time: 0.000
Step 6 time: 0.000, [0.001], mat/total: 0.000/0.006[r], mem: 32.1MB (=max)

*******
STEP 7
Basis length: 24, queue length: 21, step degree: 12, num pairs: 6
Basis total mons: 4785, average length: 199.375
Number of pair polynomials: 6, at 473 column(s), 0.000
Average length for reductees: 164.33 [6], reductors: 18.31 [194]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 194 = 200 rows / 473 columns out of 1820 (25.989%)
Density: 4.7981% / 8.3801% (22.695/r), total: 4539 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000[r] + 0.000 = 0.000[r] [4]
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (66.7%), min deg: 11 [2], av deg: 11.5
Degree counts: 11:2 12:2
Queue insertion time: 0.000
Step 7 time: 0.000[r], [0.001], mat/total: 0.010/0.007[r], mem: 32.1MB (=max)

*******
STEP 8
Basis length: 28, queue length: 29, step degree: 12, num pairs: 7
Basis total mons: 5596, average length: 199.857
Number of pair polynomials: 7, at 456 column(s), 0.000
Average length for reductees: 148.14 [7], reductors: 19.30 [183]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 183 = 190 rows / 456 columns out of 1820 (25.055%)
Density: 5.2735% / 8.9895% (24.047/r), total: 4569 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [5]
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (71.4%), min deg: 11 [3], av deg: 11.4
Degree counts: 11:3 12:2
Queue insertion time: 0.000
Step 8 time: 0.000, [0.001], mat/total: 0.010/0.009[r], mem: 32.1MB (=max)

*******
STEP 9
Basis length: 33, queue length: 36, step degree: 12, num pairs: 10
Basis total mons: 6646, average length: 201.394
Number of pair polynomials: 10, at 536 column(s), 0.000
Average length for reductees: 190.80 [10], reductors: 33.30 [267]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 267 = 277 rows / 538 columns out of 1820 (29.560%)
Density: 7.2464% / 10.522% (38.986/r), total: 10799 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [6]
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (60.0%), min deg: 11 [6], av deg: 11.0
Degree counts: 11:6
Queue insertion time: 0.000
Step 9 time: 0.000, [0.002], mat/total: 0.010/0.010[r], mem: 32.1MB (=max)

*******
STEP 10
Basis length: 39, queue length: 49, step degree: 12, num pairs: 23
Basis total mons: 7893, average length: 202.385
Number of pair polynomials: 23, at 533 column(s), 0.000
Average length for reductees: 212.70 [23], reductors: 35.30 [270]
Symbolic reduction time: 0.000, column sort time: 0.000
23 + 270 = 293 rows / 533 columns out of 1820 (29.286%)
Density: 9.2355% / 12.512% (49.225/r), total: 14423 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [10]
After ech memory: 32.1MB (=max)
Num new polynomials: 10 (43.5%), min deg: 10 [2], av deg: 10.9
Degree counts: 10:2 11:7 12:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.001], mat/total: 0.010/0.012[r], mem: 32.1MB (=max)

*******
STEP 11
Basis length: 49, queue length: 61, step degree: 11, num pairs: 8
Basis total mons: 10037, average length: 204.837
Number of pair polynomials: 8, at 465 column(s), 0.000
Average length for reductees: 220.00 [8], reductors: 30.26 [230]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 230 = 238 rows / 465 columns out of 1365 (34.066%)
Density: 7.8793% / 11.316% (36.639/r), total: 8720 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [8]
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (100.0%), min deg: 10 [4], av deg: 10.5
Degree counts: 10:4 11:4
Queue insertion time: 0.000
Step 11 time: 0.000, [0.002], mat/total: 0.010/0.013[r], mem: 32.1MB (=max)

*******
STEP 12
Basis length: 57, queue length: 81, step degree: 11, num pairs: 14
Basis total mons: 11771, average length: 206.509
Number of pair polynomials: 14, at 462 column(s), 0.000
Average length for reductees: 216.00 [14], reductors: 38.03 [237]
Symbolic reduction time: 0.000, column sort time: 0.000
14 + 237 = 251 rows / 462 columns out of 1365 (33.846%)
Density: 10.381% / 13.951% (47.96/r), total: 12038 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [11]
After ech memory: 32.1MB (=max)
Num new polynomials: 11 (78.6%), min deg: 10 [9], av deg: 10.2
Degree counts: 10:9 11:2
Queue insertion time: 0.000
Step 12 time: 0.000, [0.002], mat/total: 0.010/0.016[r], mem: 32.1MB (=max)

*******
STEP 13
Basis length: 68, queue length: 104, step degree: 11, num pairs: 36
Basis total mons: 14063, average length: 206.809
Number of pair polynomials: 36, at 454 column(s), 0.000
Average length for reductees: 207.39 [36], reductors: 44.22 [240]
Symbolic reduction time: 0.000, column sort time: 0.000
36 + 240 = 276 rows / 454 columns out of 1365 (33.260%)
Density: 14.428% / 18.082% (65.504/r), total: 18079 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [10]
After ech memory: 32.1MB (=max)
Num new polynomials: 10 (27.8%), min deg: 10 [8], av deg: 10.2
Degree counts: 10:8 11:2
Queue insertion time: 0.000
Step 13 time: 0.000, [0.003], mat/total: 0.010/0.019[r], mem: 32.1MB (=max)

*******
STEP 14
Basis length: 78, queue length: 101, step degree: 11, num pairs: 32
Basis total mons: 16065, average length: 205.962
Number of pair polynomials: 32, at 436 column(s), 0.000
Average length for reductees: 199.38 [32], reductors: 46.88 [232]
Symbolic reduction time: 0.000, column sort time: 0.000[r]
32 + 232 = 264 rows / 436 columns out of 1365 (31.941%)
Density: 14.991% / 18.844% (65.36/r), total: 17255 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [11]
After ech memory: 32.1MB (=max)
Num new polynomials: 11 (34.4%), min deg: 10 [9], av deg: 10.2
Degree counts: 10:9 11:2
Queue insertion time: 0.000
New max step: 14, time: 0.002[r]
Step 14 time: 0.001[r], [0.002], mat/total: 0.010/0.020[r], mem: 32.1MB (=max)

*******
STEP 15
Basis length: 89, queue length: 106, step degree: 11, num pairs: 35
Basis total mons: 18163, average length: 204.079
Number of pair polynomials: 35, at 420 column(s), 0.000
Average length for reductees: 190.23 [35], reductors: 51.02 [228]
Symbolic reduction time: 0.000, column sort time: 0.000
35 + 228 = 263 rows / 420 columns out of 1365 (30.769%)
Density: 16.558% / 20.592% (69.544/r), total: 18290 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [11]
After ech memory: 32.1MB (=max)
Num new polynomials: 11 (31.4%), min deg: 9 [3], av deg: 9.8
Degree counts: 9:3 10:7 11:1
Queue insertion time: 0.000
Step 15 time: 0.000, [0.002], mat/total: 0.010/0.023[r], mem: 32.1MB (=max)

*******
STEP 16
Basis length: 100, queue length: 111, step degree: 10, num pairs: 12
Basis total mons: 20142, average length: 201.420
Number of pair polynomials: 12, at 383 column(s), 0.000
Average length for reductees: 179.00 [12], reductors: 46.07 [204]
Symbolic reduction time: 0.000, column sort time: 0.000
12 + 204 = 216 rows / 383 columns out of 1001 (38.262%)
Density: 13.958% / 18.188% (53.458/r), total: 11547 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (58.3%), min deg: 9 [6], av deg: 9.1
Degree counts: 9:6 10:1
Queue insertion time: 0.000
Step 16 time: 0.000, [0.002], mat/total: 0.010/0.025[r], mem: 32.1MB (=max)

*******
STEP 17
Basis length: 107, queue length: 126, step degree: 10, num pairs: 24
Basis total mons: 21353, average length: 199.561
Number of pair polynomials: 24, at 378 column(s), 0.000
Average length for reductees: 173.00 [24], reductors: 49.43 [206]
Symbolic reduction time: 0.000, column sort time: 0.000
24 + 206 = 230 rows / 378 columns out of 1001 (37.762%)
Density: 16.487% / 20.776% (62.322/r), total: 14334 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (12.5%), min deg: 9 [3], av deg: 9.0
Degree counts: 9:3
Queue insertion time: 0.000
Step 17 time: 0.000, [0.001], mat/total: 0.010/0.026[r], mem: 32.1MB (=max)

*******
STEP 18
Basis length: 110, queue length: 114, step degree: 10, num pairs: 12
Basis total mons: 21863, average length: 198.755
Number of pair polynomials: 12, at 365 column(s), 0.000
Average length for reductees: 170.00 [12], reductors: 46.92 [196]
Symbolic reduction time: 0.000, column sort time: 0.000
12 + 196 = 208 rows / 365 columns out of 1001 (36.464%)
Density: 14.801% / 19.207% (54.024/r), total: 11237 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 18 time: 0.000, [0.001], mat/total: 0.010/0.026[r], mem: 32.1MB (=max)

*******
STEP 19
Basis length: 110, queue length: 102, step degree: 11, num pairs: 30
Basis total mons: 21863, average length: 198.755
Number of pair polynomials: 30, at 396 column(s), 0.000
Average length for reductees: 179.37 [30], reductors: 58.60 [227]
Symbolic reduction time: 0.000, column sort time: 0.000
30 + 227 = 257 rows / 396 columns out of 1365 (29.011%)
Density: 18.358% / 22.951% (72.696/r), total: 18683 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 19 time: 0.000, [0.001], mat/total: 0.010/0.029[r], mem: 32.1MB (=max)

*******
STEP 20
Basis length: 110, queue length: 72, step degree: 12, num pairs: 42
Basis total mons: 21863, average length: 198.755
39 pairs eliminated
Number of pair polynomials: 3, at 278 column(s), 0.000
Average length for reductees: 229.33 [3], reductors: 192.07 [109]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 109 = 112 rows / 278 columns out of 1820 (15.275%)
Density: 69.45% / 87.048% (193.07/r), total: 21624 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000[r] + 0.000 = 0.000[r] [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 20 time: 0.001[r], [0.002], mat/total: 0.020/0.030[r], mem: 32.1MB (=max)

*******
STEP 21
Basis length: 110, queue length: 30, step degree: 13, num pairs: 28
Basis total mons: 21863, average length: 198.755
28 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 22
Basis length: 110, queue length: 2, step degree: 14, num pairs: 2
Basis total mons: 21863, average length: 198.755
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 110 final polynomial(s) by 110
3 redundant polynomial(s) removed; time: 0.000
Interreduce 38 (out of range [0 .. 109] = 110) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
38 + 0 = 38 rows / 207 columns
Density: 84.35% / 94.552% (174.61/r), total: 6635 (0.0MB)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [38]
Total reduction time: 0.000
Reduction time: 0.000
Final number of polynomials: 107

Final basis length: 38
Number of pairs: 278
Max step: 14, time: 0.002
Max num entries matrix: 967 by 1210
Max num rows matrix: 967 by 1210
Approx mat cost: 4.62462e+06, sym red cost: 216416
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.020
Total row sort time: 0.000
Total matrix time: 0.020
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.032[r], real time: 0.032
Time: 0.040
dregs = [ 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 11, 11, 11, 11, 11, 10, 10, 10, 11, 12, 13, 14 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=2)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 4
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 38
Try rep mat lex method; E: X0100
Get rep mat (dim: 169)
Rep mat time: 0.000
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 0.049[r]
Get kernel for min poly
Kernel mat time: 0.009[r]
Nullity: 1
Get relations for all variables
REDUCE 4 polynomial(s) by 38 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
4 + 190 = 194 rows / 359 columns
Density: 12.242% / 16.657% (43.948/r), total: 8526 (0.0MB)
Row sort time: 0.001[r]
0.000 = 0.000 [4]
Total reduction time: 0.003[r]
Reduction time: 0.004[r]
Relations time: 0.016[r]
Time: 0.090
unideg = 169
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=2)
Time: 0.000
nsols = 0
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=2)
nsols_mult = 0
====================================================================================================
n_r: 3, n_v: 6, n_e: 6, mdeg: 11
degs = [11, 11, 11, 11, 11, 11]
Multivariate Polynomial Ring in Y0300, Y0200, Y0100, Y0000, X0200, X0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=3)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 6
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
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: 11, num pairs: 3
Basis total mons: 1614, average length: 269.000
Number of pair polynomials: 3, at 782 column(s), 0.000
Average length for reductees: 269.33 [3], reductors: 268.67 [3]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 3 = 6 rows / 782 columns out of 12376 (6.319%)
Density: 34.399% / 34.718% (269/r), total: 1614 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 2 [3], av deg: 2.0
Degree counts: 2:3
Queue insertion time: 0.000
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: 9, queue length: 3, step degree: 11, num pairs: 3
Basis total mons: 1641, average length: 182.333
Number of pair polynomials: 3, at 790 column(s), 0.000
Average length for reductees: 9.00 [3], reductors: 9.05 [5379]
Symbolic reduction time: 0.005[r], column sort time: 0.000
3 + 5379 = 5382 rows / 7006 columns out of 12376 (56.610%)
Density: 0.12921% / 0.52129% (9.0522/r), total: 48719 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.007[r] + 0.000 = 0.007[r] [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 11 [3], av deg: 11.0
Degree counts: 11:3
Queue insertion time: 0.000
New max step: 2, time: 0.018[r]
Step 2 time: 0.018[r], [0.018], mat/total: 0.010/0.019[r], mem: 32.1MB (=max)

*******
STEP 3
Basis length: 12, queue length: 6, step degree: 12, num pairs: 6
Basis total mons: 3909, average length: 325.750
Number of pair polynomials: 6, at 3930 column(s), 0.000
Average length for reductees: 1010.67 [6], reductors: 13.44 [2136]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 2136 = 2142 rows / 4626 columns out of 18564 (24.919%)
Density: 0.35093% / 1.0264% (16.234/r), total: 34773 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.002[r] + 0.000 = 0.003[r] [6]
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (100.0%), min deg: 11 [3], av deg: 11.5
Degree counts: 11:3 12:3
Queue insertion time: 0.000[r]
Step 3 time: 0.009[r], [0.010], mat/total: 0.020/0.029[r], mem: 32.1MB (=max)

*******
STEP 4
Basis length: 18, queue length: 13, step degree: 12, num pairs: 10
Basis total mons: 11662, average length: 647.889
Number of pair polynomials: 10, at 4540 column(s), 0.000
Average length for reductees: 1158.70 [10], reductors: 16.39 [2112]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 2112 = 2122 rows / 4588 columns out of 18564 (24.715%)
Density: 0.47458% / 1.1586% (21.774/r), total: 46204 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:4
Queue insertion time: 0.000
Step 4 time: 0.000, [0.011], mat/total: 0.020/0.039[r], mem: 32.1MB (=max)

*******
STEP 5
Basis length: 25, queue length: 22, step degree: 12, num pairs: 10
Basis total mons: 21694, average length: 867.760
Number of pair polynomials: 10, at 4383 column(s), 0.000[r]
Average length for reductees: 1097.20 [10], reductors: 19.21 [1940]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 1940 = 1950 rows / 4410 columns out of 18564 (23.756%)
Density: 0.56087% / 1.2924% (24.734/r), total: 48232 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:4
Queue insertion time: 0.000
Step 5 time: 0.009[r], [0.010], mat/total: 0.020/0.049[r], mem: 32.1MB (=max)

*******
STEP 6
Basis length: 32, queue length: 31, step degree: 12, num pairs: 11
Basis total mons: 31336, average length: 979.250
Number of pair polynomials: 11, at 4199 column(s), 0.000
Average length for reductees: 1056.09 [11], reductors: 19.23 [1818]
Symbolic reduction time: 0.002[r], column sort time: 0.000
11 + 1818 = 1829 rows / 4236 columns out of 18564 (22.818%)
Density: 0.60127% / 1.3638% (25.47/r), total: 46584 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [8]
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (72.7%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:5
Queue insertion time: 0.000
Step 6 time: 0.009[r], [0.010], mat/total: 0.020/0.059[r], mem: 32.1MB (=max)

*******
STEP 7
Basis length: 40, queue length: 43, step degree: 12, num pairs: 10
Basis total mons: 43319, average length: 1082.975
Number of pair polynomials: 10, at 3960 column(s), 0.000
Average length for reductees: 1072.20 [10], reductors: 23.62 [1543]
Symbolic reduction time: 0.000, column sort time: 0.001[r]
10 + 1543 = 1553 rows / 3972 columns out of 18564 (21.396%)
Density: 0.76459% / 1.6245% (30.37/r), total: 47164 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:4
Queue insertion time: 0.000
Step 7 time: 0.008[r], [0.010], mat/total: 0.020/0.069[r], mem: 32.1MB (=max)

*******
STEP 8
Basis length: 47, queue length: 56, step degree: 12, num pairs: 11
Basis total mons: 52444, average length: 1115.830
Number of pair polynomials: 11, at 3723 column(s), 0.000
Average length for reductees: 822.64 [11], reductors: 25.87 [1390]
Symbolic reduction time: 0.000, column sort time: 0.000
11 + 1390 = 1401 rows / 3744 columns out of 18564 (20.168%)
Density: 0.85806% / 1.7777% (32.126/r), total: 45008 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.003[r] + 0.000 = 0.003[r] [8]
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (72.7%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:5
Queue insertion time: 0.000
Step 8 time: 0.009[r], [0.010], mat/total: 0.030/0.079[r], mem: 32.1MB (=max)

*******
STEP 9
Basis length: 55, queue length: 70, step degree: 12, num pairs: 10
Basis total mons: 64089, average length: 1165.255
Number of pair polynomials: 10, at 3676 column(s), 0.000
Average length for reductees: 1017.90 [10], reductors: 29.62 [1318]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 1318 = 1328 rows / 3697 columns out of 18564 (19.915%)
Density: 1.0024% / 1.9862% (37.06/r), total: 49216 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.003[r] + 0.000 = 0.003[r] [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:4
Queue insertion time: 0.000
Step 9 time: 0.009[r], [0.009], mat/total: 0.040/0.088[r], mem: 32.1MB (=max)

*******
STEP 10
Basis length: 62, queue length: 88, step degree: 12, num pairs: 11
Basis total mons: 73206, average length: 1180.742
Number of pair polynomials: 11, at 3716 column(s), 0.000
Average length for reductees: 846.27 [11], reductors: 30.97 [1434]
Symbolic reduction time: 0.000, column sort time: 0.000
11 + 1434 = 1445 rows / 3733 columns out of 18564 (20.109%)
Density: 0.99581% / 1.927% (37.174/r), total: 53716 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [8]
After ech memory: 32.1MB (=max)
Num new polynomials: 8 (72.7%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:5
Queue insertion time: 0.000
Step 10 time: 0.000, [0.009], mat/total: 0.040/0.090, mem: 32.1MB (=max)

*******
STEP 11
Basis length: 70, queue length: 106, step degree: 12, num pairs: 10
Basis total mons: 84757, average length: 1210.814
Number of pair polynomials: 10, at 3966 column(s), 0.000[r]
Average length for reductees: 1027.00 [10], reductors: 36.73 [1743]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 1743 = 1753 rows / 4064 columns out of 18564 (21.892%)
Density: 1.0428% / 1.8659% (42.38/r), total: 74293 (0.3MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 11 [3], av deg: 11.6
Degree counts: 11:3 12:4
Queue insertion time: 0.000
Step 11 time: 0.009[r], [0.010], mat/total: 0.040/0.100, mem: 32.1MB (=max)

*******
STEP 12
Basis length: 77, queue length: 130, step degree: 12, num pairs: 10
Basis total mons: 94894, average length: 1232.390
Number of pair polynomials: 10, at 4330 column(s), 0.000[r]
Average length for reductees: 731.50 [10], reductors: 68.35 [1994]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 1994 = 2004 rows / 4407 columns out of 18564 (23.739%)
Density: 1.6259% / 2.3957% (71.655/r), total: 143596 (0.5MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.004[r] + 0.000 = 0.004[r] [7]
After ech memory: 32.1MB (=max)
Num new polynomials: 7 (70.0%), min deg: 12 [7], av deg: 12.0
Degree counts: 12:7
Queue insertion time: 0.000
Step 12 time: 0.015[r], [0.015], mat/total: 0.050/0.120, mem: 32.1MB (=max)

*******
STEP 13
Basis length: 84, queue length: 157, step degree: 13, num pairs: 107
Basis total mons: 108182, average length: 1287.881
17 pairs eliminated
Number of pair polynomials: 90, at 6404 column(s), 0.000
Average length for reductees: 1780.98 [90], reductors: 109.31 [3514]
Symbolic reduction time: 0.010, column sort time: 0.002[r]
90 + 3514 = 3604 rows / 6418 columns out of 27132 (23.655%)
Density: 2.3536% / 3.0359% (151.06/r), total: 544406 (2.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.039[r] + 0.000 = 0.039 [27]
After ech memory: 32.1MB (=max)
Num new polynomials: 27 (30.0%), min deg: 13 [27], av deg: 13.0
Degree counts: 13:27
Queue insertion time: 0.000
New max step: 13, time: 0.060
Step 13 time: 0.059, [0.066], mat/total: 0.090/0.180, mem: 32.1MB (=max)

*******
STEP 14
Basis length: 111, queue length: 196, step degree: 14, num pairs: 141
Basis total mons: 173613, average length: 1564.081
9 pairs eliminated
Number of pair polynomials: 132, at 7737 column(s), 0.013[r]
Average length for reductees: 2410.05 [132], reductors: 186.79 [4607]
Symbolic reduction time: 0.020, column sort time: 0.000
132 + 4607 = 4739 rows / 7870 columns out of 38760 (20.304%)
Density: 3.1604% / 4.0203% (248.72/r), total: 1178690 (4.5MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.113[r] + 0.000 = 0.115[r] [38]
After ech memory: 32.1MB, max: 40.5MB
Num new polynomials: 38 (28.8%), min deg: 13 [11], av deg: 13.7
Degree counts: 13:11 14:27
Queue insertion time: 0.000
New max step: 14, time: 0.160
Step 14 time: 0.160, [0.164], mat/total: 0.210/0.340, mem: 32.1MB, max: 40.5MB

*******
STEP 15
Basis length: 149, queue length: 244, step degree: 14, num pairs: 64
Basis total mons: 281552, average length: 1889.611
Number of pair polynomials: 64, at 7723 column(s), 0.007[r]
Average length for reductees: 2671.31 [64], reductors: 205.41 [4683]
Symbolic reduction time: 0.028[r], column sort time: 0.000
64 + 4683 = 4747 rows / 7906 columns out of 38760 (20.397%)
Density: 3.0186% / 3.8985% (238.65/r), total: 1132890 (4.3MB)
Before ech memory: 32.1MB, max: 40.5MB
Row sort time: 0.000
[5 threads]
0.065[r] + 0.000 = 0.067[r] [26]
After ech memory: 32.1MB, max: 40.6MB
Num new polynomials: 26 (40.6%), min deg: 13 [8], av deg: 13.7
Degree counts: 13:8 14:18
Queue insertion time: 0.003[r]
Step 15 time: 0.111[r], [0.112], mat/total: 0.280/0.460, mem: 32.1MB, max: 40.6MB

*******
STEP 16
Basis length: 175, queue length: 323, step degree: 14, num pairs: 48
Basis total mons: 356544, average length: 2037.394
Number of pair polynomials: 48, at 7609 column(s), 0.000
Average length for reductees: 2706.25 [48], reductors: 202.15 [4570]
Symbolic reduction time: 0.026[r], column sort time: 0.000
48 + 4570 = 4618 rows / 7755 columns out of 38760 (20.008%)
Density: 2.9423% / 3.8194% (228.18/r), total: 1053723 (4.0MB)
Before ech memory: 32.1MB, max: 40.6MB
Row sort time: 0.000
[5 threads]
0.047[r] + 0.000 = 0.049[r] [24]
After ech memory: 32.1MB, max: 40.6MB
Num new polynomials: 24 (50.0%), min deg: 13 [4], av deg: 13.8
Degree counts: 13:4 14:20
Queue insertion time: 0.000
Step 16 time: 0.079, [0.088], mat/total: 0.330/0.540, mem: 32.1MB, max: 40.6MB

*******
STEP 17
Basis length: 199, queue length: 411, step degree: 14, num pairs: 24
Basis total mons: 427213, average length: 2146.799
Number of pair polynomials: 24, at 7513 column(s), 0.000
Average length for reductees: 2764.71 [24], reductors: 198.62 [4481]
Symbolic reduction time: 0.028[r], column sort time: 0.000
24 + 4481 = 4505 rows / 7630 columns out of 38760 (19.685%)
Density: 2.7823% / 3.6543% (212.29/r), total: 956357 (3.6MB)
Before ech memory: 32.1MB, max: 40.6MB
Row sort time: 0.000
[5 threads]
0.029[r] + 0.000[r] = 0.030[r] [13]
After ech memory: 32.1MB, max: 40.6MB
Num new polynomials: 13 (54.2%), min deg: 14 [13], av deg: 14.0
Degree counts: 14:13
Queue insertion time: 0.000
Step 17 time: 0.069[r], [0.069], mat/total: 0.370/0.610, mem: 32.1MB, max: 40.6MB

*******
STEP 18
Basis length: 212, queue length: 460, step degree: 15, num pairs: 367
Basis total mons: 465793, average length: 2197.137
44 pairs eliminated
Number of pair polynomials: 323, at 8989 column(s), 0.040
Average length for reductees: 2952.45 [323], reductors: 321.23 [5932]
Symbolic reduction time: 0.060, column sort time: 0.003[r]
323 + 5932 = 6255 rows / 9385 columns out of 54264 (17.295%)
Density: 4.8706% / 6.1089% (457.11/r), total: 2859205 (10.9MB)
Before ech memory: 32.1MB, max: 40.6MB
Row sort time: 0.000
[5 threads]
0.510 + 0.000 = 0.510 [76]
After ech memory: 32.1MB, max: 42.1MB
Num new polynomials: 76 (23.5%), min deg: 13 [2], av deg: 14.5
Degree counts: 13:2 14:34 15:40
Queue insertion time: 0.010
New max step: 18, time: 0.630
Step 18 time: 0.629, [0.644], mat/total: 0.880/1.240, mem: 32.1MB, max: 42.1MB

*******
STEP 19
Basis length: 288, queue length: 424, step degree: 14, num pairs: 12
Basis total mons: 701323, average length: 2435.149
Number of pair polynomials: 12, at 7597 column(s), 0.003[r]
Average length for reductees: 2888.50 [12], reductors: 260.46 [4732]
Symbolic reduction time: 0.040, column sort time: 0.000
12 + 4732 = 4744 rows / 7856 columns out of 38760 (20.268%)
Density: 3.4001% / 4.3323% (267.11/r), total: 1267179 (4.8MB)
Before ech memory: 32.1MB, max: 42.1MB
Row sort time: 0.000
[5 threads]
0.037[r] + 0.000 = 0.039[r] [4]
After ech memory: 32.1MB, max: 42.1MB
Num new polynomials: 4 (33.3%), min deg: 14 [4], av deg: 14.0
Degree counts: 14:4
Queue insertion time: 0.000
Step 19 time: 0.090[r], [0.090], mat/total: 0.930/1.340, mem: 32.1MB, max: 42.1MB

*******
STEP 20
Basis length: 292, queue length: 436, step degree: 15, num pairs: 206
Basis total mons: 713235, average length: 2442.586
Number of pair polynomials: 206, at 8791 column(s), 0.029[r]
Average length for reductees: 3023.19 [206], reductors: 368.38 [5893]
Symbolic reduction time: 0.060, column sort time: 0.005[r]
206 + 5893 = 6099 rows / 9253 columns out of 54264 (17.052%)
Density: 4.9502% / 6.2102% (458.05/r), total: 2793620 (10.7MB)
Before ech memory: 32.1MB, max: 42.1MB
Row sort time: 0.000
[5 threads]
0.359 + 0.000 = 0.359 [74]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 74 (35.9%), min deg: 14 [37], av deg: 14.5
Degree counts: 14:37 15:37
Queue insertion time: 0.009
Step 20 time: 0.480, [0.488], mat/total: 1.300/1.820, mem: 64.1MB, max: 74.0MB

*******
STEP 21
Basis length: 366, queue length: 583, step degree: 15, num pairs: 208
Basis total mons: 939924, average length: 2568.098
Number of pair polynomials: 208, at 8717 column(s), 0.029
Average length for reductees: 3002.36 [208], reductors: 405.27 [5900]
Symbolic reduction time: 0.075[r], column sort time: 0.000
208 + 5900 = 6108 rows / 9172 columns out of 54264 (16.903%)
Density: 5.3828% / 6.6856% (493.71/r), total: 3015583 (11.5MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.450[r] + 0.000 = 0.456[r] [81]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 81 (38.9%), min deg: 14 [50], av deg: 14.4
Degree counts: 14:50 15:31
Queue insertion time: 0.016[r]
Step 21 time: 0.588[r], [0.589], mat/total: 1.760/2.409, mem: 64.1MB, max: 74.0MB

*******
STEP 22
Basis length: 447, queue length: 746, step degree: 15, num pairs: 287
Basis total mons: 1182987, average length: 2646.503
Number of pair polynomials: 287, at 8555 column(s), 0.040
Average length for reductees: 2964.12 [287], reductors: 443.32 [5879]
Symbolic reduction time: 0.078[r], column sort time: 0.000
287 + 5879 = 6166 rows / 9055 columns out of 54264 (16.687%)
Density: 6.1916% / 7.5551% (560.65/r), total: 3456990 (13.2MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.001[r]
[5 threads]
0.629[r] + 0.009 = 0.639 [110]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 110 (38.3%), min deg: 13 [30], av deg: 13.9
Degree counts: 13:30 14:64 15:16
Queue insertion time: 0.020
New max step: 22, time: 0.790
Step 22 time: 0.790, [0.794], mat/total: 2.410/3.199, mem: 64.1MB, max: 74.0MB

*******
STEP 23
Basis length: 557, queue length: 1011, step degree: 14, num pairs: 177
Basis total mons: 1496612, average length: 2686.916
Number of pair polynomials: 177, at 7725 column(s), 0.023[r]
Average length for reductees: 2820.54 [177], reductors: 361.97 [4925]
Symbolic reduction time: 0.049, column sort time: 0.003[r]
177 + 4925 = 5102 rows / 7861 columns out of 38760 (20.281%)
Density: 5.6897% / 6.7649% (447.27/r), total: 2281952 (8.7MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.349 + 0.008[r] = 0.359 [145]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 145 (81.9%), min deg: 13 [125], av deg: 13.1
Degree counts: 13:125 14:20
Queue insertion time: 0.030
Step 23 time: 0.480, [0.482], mat/total: 2.770/3.679, mem: 64.1MB, max: 74.0MB

*******
STEP 24
Basis length: 702, queue length: 1645, step degree: 14, num pairs: 733
Basis total mons: 1887049, average length: 2688.104
Number of pair polynomials: 733, at 7555 column(s), 0.083[r]
Average length for reductees: 2687.69 [733], reductors: 424.86 [4972]
Symbolic reduction time: 0.050, column sort time: 0.000
733 + 4972 = 5705 rows / 7746 columns out of 38760 (19.985%)
Density: 9.2383% / 10.571% (715.6/r), total: 4082486 (15.6MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.002[r]
[5 threads]
1.399 + 0.010 = 1.410 [152]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 152 (20.7%), min deg: 13 [126], av deg: 13.2
Degree counts: 13:126 14:26
Queue insertion time: 0.039[r]
New max step: 24, time: 1.600
Step 24 time: 1.600, [1.606], mat/total: 4.190/5.280, mem: 64.1MB, max: 74.0MB

*******
STEP 25
Basis length: 854, queue length: 1723, step degree: 14, num pairs: 748
Basis total mons: 2275885, average length: 2664.971
Number of pair polynomials: 748, at 7248 column(s), 0.079
Average length for reductees: 2553.49 [748], reductors: 481.71 [4784]
Symbolic reduction time: 0.058[r], column sort time: 0.000
748 + 4784 = 5532 rows / 7398 columns out of 38760 (19.087%)
Density: 10.298% / 11.773% (761.85/r), total: 4214532 (16.1MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000[r]
[5 threads]
1.350 + 0.009[r] = 1.360 [151]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 151 (20.2%), min deg: 12 [59], av deg: 12.7
Degree counts: 12:59 13:77 14:15
Queue insertion time: 0.040
Step 25 time: 1.549, [1.555], mat/total: 5.560/6.830, mem: 64.1MB, max: 74.0MB

*******
STEP 26
Basis length: 1005, queue length: 1809, step degree: 13, num pairs: 354
Basis total mons: 2640890, average length: 2627.751
Number of pair polynomials: 354, at 6571 column(s), 0.037[r]
Average length for reductees: 2410.93 [354], reductors: 381.18 [4162]
Symbolic reduction time: 0.046[r], column sort time: 0.000
354 + 4162 = 4516 rows / 6597 columns out of 27132 (24.314%)
Density: 8.1899% / 9.4462% (540.29/r), total: 2439948 (9.3MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.448[r] + 0.000 = 0.450 [106]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 106 (29.9%), min deg: 12 [91], av deg: 12.1
Degree counts: 12:91 13:15
Queue insertion time: 0.029[r]
Step 26 time: 0.569[r], [0.570], mat/total: 6.010/7.399, mem: 64.1MB, max: 74.0MB

*******
STEP 27
Basis length: 1111, queue length: 2090, step degree: 13, num pairs: 546
Basis total mons: 2886849, average length: 2598.424
Number of pair polynomials: 546, at 6314 column(s), 0.050
Average length for reductees: 2319.97 [546], reductors: 401.08 [4013]
Symbolic reduction time: 0.040[r], column sort time: 0.000
546 + 4013 = 4559 rows / 6342 columns out of 27132 (23.375%)
Density: 9.9478% / 11.293% (630.89/r), total: 2876232 (11.0MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.835[r] + 0.000 = 0.837[r] [80]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 80 (14.7%), min deg: 12 [73], av deg: 12.1
Degree counts: 12:73 13:7
Queue insertion time: 0.019
Step 27 time: 0.960, [0.961], mat/total: 6.850/8.359, mem: 64.1MB, max: 74.0MB

*******
STEP 28
Basis length: 1191, queue length: 2023, step degree: 13, num pairs: 438
Basis total mons: 3066608, average length: 2574.818
Number of pair polynomials: 438, at 6068 column(s), 0.046[r]
Average length for reductees: 2246.96 [438], reductors: 405.59 [3848]
Symbolic reduction time: 0.039, column sort time: 0.000
438 + 3848 = 4286 rows / 6097 columns out of 27132 (22.472%)
Density: 9.7387% / 11.112% (593.77/r), total: 2544881 (9.7MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000[r]
[5 threads]
0.610 + 0.000 = 0.610 [52]
After ech memory: 64.1MB, max: 74.0MB
Num new polynomials: 52 (11.9%), min deg: 12 [49], av deg: 12.1
Degree counts: 12:49 13:3
Queue insertion time: 0.016[r]
Step 28 time: 0.730, [0.733], mat/total: 7.470/9.089, mem: 64.1MB, max: 74.0MB

*******
STEP 29
Basis length: 1243, queue length: 1897, step degree: 13, num pairs: 294
Basis total mons: 3180903, average length: 2559.053
Number of pair polynomials: 294, at 5869 column(s), 0.029
Average length for reductees: 2197.98 [294], reductors: 395.67 [3700]
Symbolic reduction time: 0.046[r], column sort time: 0.000
294 + 3700 = 3994 rows / 5897 columns out of 27132 (21.734%)
Density: 8.9594% / 10.328% (528.34/r), total: 2110176 (8.0MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.388[r] + 0.000 = 0.388[r] [0]
After ech memory: 64.1MB, max: 74.0MB
No new polynomials
Queue insertion time: 0.000
Step 29 time: 0.470, [0.472], mat/total: 7.860/9.560, mem: 64.1MB, max: 74.0MB

*******
STEP 30
Basis length: 1243, queue length: 1603, step degree: 14, num pairs: 584
Basis total mons: 3180903, average length: 2559.053
55 pairs eliminated
Number of pair polynomials: 529, at 6768 column(s), 0.088[r]
Average length for reductees: 2390.10 [529], reductors: 560.86 [4680]
Symbolic reduction time: 0.089, column sort time: 0.000
529 + 4680 = 5209 rows / 6877 columns out of 38760 (17.743%)
Density: 10.857% / 12.869% (746.63/r), total: 3889181 (14.8MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
1.058[r] + 0.000 = 1.059[r] [0]
After ech memory: 64.1MB, max: 74.0MB
No new polynomials
Queue insertion time: 0.000
Step 30 time: 1.240, [1.245], mat/total: 8.920/10.800, mem: 64.1MB, max: 74.0MB

*******
STEP 31
Basis length: 1243, queue length: 1019, step degree: 15, num pairs: 457
Basis total mons: 3180903, average length: 2559.053
411 pairs eliminated
Number of pair polynomials: 46, at 6943 column(s), 0.009[r]
Average length for reductees: 2846.91 [46], reductors: 755.97 [6557]
Symbolic reduction time: 0.165[r], column sort time: 0.000
46 + 6557 = 6603 rows / 8754 columns out of 54264 (16.132%)
Density: 8.8021% / 11.924% (770.53/r), total: 5087835 (19.4MB)
Before ech memory: 64.1MB, max: 74.0MB
Row sort time: 0.000
[5 threads]
0.209 + 0.000 = 0.209 [0]
After ech memory: 64.1MB, max: 74.0MB
No new polynomials
Queue insertion time: 0.000
Step 31 time: 0.389, [0.397], mat/total: 9.130/11.189, mem: 64.1MB, max: 74.0MB

*******
STEP 32
Basis length: 1243, queue length: 562, step degree: 16, num pairs: 363
Basis total mons: 3180903, average length: 2559.053
363 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 33
Basis length: 1243, queue length: 199, step degree: 17, num pairs: 64
Basis total mons: 3180903, average length: 2559.053
64 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 34
Basis length: 1243, queue length: 135, step degree: 18, num pairs: 42
Basis total mons: 3180903, average length: 2559.053
42 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 35
Basis length: 1243, queue length: 93, step degree: 19, num pairs: 30
Basis total mons: 3180903, average length: 2559.053
30 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 36
Basis length: 1243, queue length: 63, step degree: 20, num pairs: 19
Basis total mons: 3180903, average length: 2559.053
19 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 37
Basis length: 1243, queue length: 44, step degree: 21, num pairs: 17
Basis total mons: 3180903, average length: 2559.053
17 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 38
Basis length: 1243, queue length: 27, step degree: 22, num pairs: 12
Basis total mons: 3180903, average length: 2559.053
12 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 39
Basis length: 1243, queue length: 15, step degree: 23, num pairs: 7
Basis total mons: 3180903, average length: 2559.053
7 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 40
Basis length: 1243, queue length: 8, step degree: 24, num pairs: 6
Basis total mons: 3180903, average length: 2559.053
6 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 41
Basis length: 1243, queue length: 2, step degree: 25, num pairs: 1
Basis total mons: 3180903, average length: 2559.053
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 42
Basis length: 1243, queue length: 1, step degree: 26, num pairs: 1
Basis total mons: 3180903, average length: 2559.053
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 1243 final polynomial(s) by 1243
28 redundant polynomial(s) removed; time: 0.000
Interreduce 488 (out of range [0 .. 1242] = 1243) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
488 + 21 = 509 rows / 2706 columns
Density: 79.671% / 87.813% (2155.9/r), total: 1097347 (4.2MB)
Row sort time: 0.000
[5 threads]
0.398[r] + 0.000 = 0.400 [488]
Total reduction time: 0.419
Reduction time: 0.490
Final number of polynomials: 1215

Final basis length: 488
Number of pairs: 5364
Max step: 24, time: 1.600
Max num entries matrix: 6255 by 9385
Max num rows matrix: 6603 by 8754
Approx mat cost: 1.75623e+10, sym red cost: 4.95223e+07
Total pair setup time: 0.680
Total symbolic reduction time: 1.070
Total column sort time: 0.050
Total row sort time: 0.040
Total matrix time: 9.130
Total new polys time: 0.040
Total queue update time: 0.220
Total Faugere F4 time: 11.730, real time: 11.790
Time: 11.730
dregs = [ 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 14, 15, 15, 15, 14, 14, 14, 13, 13, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=3)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 6
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 488
Try rep mat lex method; E: X0100
Get rep mat (dim: 2197)
Rep mat time: 0.315[r]
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 26.100
Get kernel for min poly
Kernel mat time: 2.509
Nullity: 1
Get relations for all variables
REDUCE 6 polynomial(s) by 488 polynomial(s)
Symbolic reduction time: 0.078[r]
Column sort time: 0.000
6 + 3572 = 3578 rows / 5769 columns
Density: 6.2452% / 7.5554% (360.29/r), total: 1289101 (4.9MB)
Row sort time: 0.000[r]
0.030 = 0.030 [6]
Total reduction time: 0.117[r]
Reduction time: 0.118[r]
Relations time: 2.750
Time: 31.690
unideg = 2197
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=3)
Time: 0.050
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=3)
nsols_mult = 1
====================================================================================================
n_r: 4, n_v: 8, n_e: 8, mdeg: 11
degs = [11, 11, 11, 11, 11, 11, 11, 11]
Multivariate Polynomial Ring in Y0400, Y0300, Y0200, Y0100, Y0000, X0300, X0200, X0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=4)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 8
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
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: 11, num pairs: 4
Basis total mons: 2343, average length: 292.875
Number of pair polynomials: 4, at 1134 column(s), 0.000
Average length for reductees: 293.25 [4], reductors: 292.50 [4]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 4 = 8 rows / 1134 columns out of 75582 (1.500%)
Density: 25.827% / 26.116% (292.88/r), total: 2343 (0.0MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [4]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 4 (100.0%), min deg: 2 [4], av deg: 2.0
Degree counts: 2:4
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.003], mat/total: 0.000/0.000, mem: 64.1MB, max: 228.7MB

*******
STEP 2
Basis length: 12, queue length: 4, step degree: 11, num pairs: 4
Basis total mons: 2387, average length: 198.917
Number of pair polynomials: 4, at 1152 column(s), 0.000
Average length for reductees: 11.00 [4], reductors: 11.48 [20561]
Symbolic reduction time: 0.025[r], column sort time: 0.010
4 + 20561 = 20565 rows / 28250 columns out of 75582 (37.377%)
Density: 0.040639% / 0.17625% (11.481/r), total: 236098 (0.9MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.006[r]
[5 threads]
0.065[r] + 0.000 = 0.066[r] [4]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 4 (100.0%), min deg: 11 [4], av deg: 11.0
Degree counts: 11:4
Queue insertion time: 0.000
New max step: 2, time: 0.115[r]
Step 2 time: 0.115[r], [0.115], mat/total: 0.080/0.119[r], mem: 64.1MB, max: 228.7MB

*******
STEP 3
Basis length: 16, queue length: 10, step degree: 12, num pairs: 10
Basis total mons: 13599, average length: 849.938
Number of pair polynomials: 10, at 23229 column(s), 0.003[r]
Average length for reductees: 4038.00 [10], reductors: 15.53 [12732]
Symbolic reduction time: 0.010, column sort time: 0.013[r]
10 + 12732 = 12742 rows / 27027 columns out of 125970 (21.455%)
Density: 0.069123% / 0.24293% (18.682/r), total: 238046 (0.9MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.055[r] + 0.000 = 0.058[r] [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (100.0%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 3 time: 0.100, [0.102], mat/total: 0.140/0.219, mem: 64.1MB, max: 228.7MB

*******
STEP 4
Basis length: 26, queue length: 26, step degree: 12, num pairs: 14
Basis total mons: 72897, average length: 2803.731
Number of pair polynomials: 14, at 25733 column(s), 0.005[r]
Average length for reductees: 5159.64 [14], reductors: 19.30 [12240]
Symbolic reduction time: 0.020, column sort time: 0.009
14 + 12240 = 12254 rows / 26441 columns out of 125970 (20.990%)
Density: 0.095203% / 0.27496% (25.173/r), total: 308465 (1.2MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.063[r] + 0.000 = 0.065[r] [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 4 time: 0.109, [0.113], mat/total: 0.210/0.329, mem: 64.1MB, max: 228.7MB

*******
STEP 5
Basis length: 36, queue length: 44, step degree: 12, num pairs: 14
Basis total mons: 138928, average length: 3859.111
Number of pair polynomials: 14, at 24763 column(s), 0.006[r]
Average length for reductees: 5048.86 [14], reductors: 22.04 [10879]
Symbolic reduction time: 0.020, column sort time: 0.009
14 + 10879 = 10893 rows / 25215 columns out of 125970 (20.017%)
Density: 0.11301% / 0.31007% (28.496/r), total: 310407 (1.2MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.060 + 0.000 = 0.060 [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 5 time: 0.109, [0.111], mat/total: 0.270/0.439, mem: 64.1MB, max: 228.7MB

*******
STEP 6
Basis length: 46, queue length: 58, step degree: 12, num pairs: 15
Basis total mons: 201689, average length: 4384.543
Number of pair polynomials: 15, at 22234 column(s), 0.000
Average length for reductees: 4629.07 [15], reductors: 21.63 [9304]
Symbolic reduction time: 0.016[r], column sort time: 0.009
15 + 9304 = 9319 rows / 22925 columns out of 125970 (18.199%)
Density: 0.1267% / 0.34647% (29.046/r), total: 270684 (1.0MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.049[r] + 0.000[r] = 0.050[r] [11]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 11 (73.3%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:7
Queue insertion time: 0.000
Step 6 time: 0.089, [0.091], mat/total: 0.330/0.529, mem: 64.1MB, max: 228.7MB

*******
STEP 7
Basis length: 57, queue length: 78, step degree: 12, num pairs: 14
Basis total mons: 277297, average length: 4864.860
Number of pair polynomials: 14, at 21135 column(s), 0.000
Average length for reductees: 4810.93 [14], reductors: 27.44 [7610]
Symbolic reduction time: 0.016[r], column sort time: 0.009
14 + 7610 = 7624 rows / 21468 columns out of 125970 (17.042%)
Density: 0.16872% / 0.42093% (36.22/r), total: 276142 (1.1MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.039 + 0.000 = 0.039 [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 7 time: 0.070, [0.081], mat/total: 0.370/0.599, mem: 64.1MB, max: 228.7MB

*******
STEP 8
Basis length: 67, queue length: 97, step degree: 12, num pairs: 15
Basis total mons: 336595, average length: 5023.806
Number of pair polynomials: 15, at 18386 column(s), 0.004[r]
Average length for reductees: 3433.80 [15], reductors: 31.06 [5858]
Symbolic reduction time: 0.009, column sort time: 0.009[r]
15 + 5858 = 5873 rows / 18888 columns out of 125970 (14.994%)
Density: 0.21044% / 0.51546% (39.747/r), total: 233435 (0.9MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.037[r] + 0.000 = 0.038[r] [11]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 11 (73.3%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:7
Queue insertion time: 0.000
Step 8 time: 0.070[r], [0.070], mat/total: 0.420/0.679, mem: 64.1MB, max: 228.7MB

*******
STEP 9
Basis length: 78, queue length: 120, step degree: 12, num pairs: 14
Basis total mons: 409473, average length: 5249.654
Number of pair polynomials: 14, at 18676 column(s), 0.000
Average length for reductees: 4390.86 [14], reductors: 35.78 [5715]
Symbolic reduction time: 0.015[r], column sort time: 0.009[r]
14 + 5715 = 5729 rows / 19035 columns out of 125970 (15.111%)
Density: 0.2439% / 0.56871% (46.426/r), total: 265976 (1.0MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.029 + 0.000 = 0.029 [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 9 time: 0.059, [0.071], mat/total: 0.450/0.739, mem: 64.1MB, max: 228.7MB

*******
STEP 10
Basis length: 88, queue length: 147, step degree: 12, num pairs: 15
Basis total mons: 468518, average length: 5324.068
Number of pair polynomials: 15, at 18656 column(s), 0.005[r]
Average length for reductees: 3520.53 [15], reductors: 36.46 [6269]
Symbolic reduction time: 0.016[r], column sort time: 0.000
15 + 6269 = 6284 rows / 18956 columns out of 125970 (15.048%)
Density: 0.23622% / 0.54566% (44.777/r), total: 281380 (1.1MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.002[r]
[5 threads]
0.038[r] + 0.000 = 0.038[r] [11]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 11 (73.3%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:7
Queue insertion time: 0.000
Step 10 time: 0.075[r], [0.075], mat/total: 0.500/0.820, mem: 64.1MB, max: 228.7MB

*******
STEP 11
Basis length: 99, queue length: 177, step degree: 12, num pairs: 14
Basis total mons: 539491, average length: 5449.404
Number of pair polynomials: 14, at 20947 column(s), 0.000
Average length for reductees: 4375.64 [14], reductors: 38.12 [8993]
Symbolic reduction time: 0.024[r], column sort time: 0.010
14 + 8993 = 9007 rows / 21885 columns out of 125970 (17.373%)
Density: 0.20497% / 0.4393% (44.858/r), total: 404038 (1.5MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.049[r] + 0.000 = 0.049[r] [10]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:6
Queue insertion time: 0.000
Step 11 time: 0.089, [0.097], mat/total: 0.550/0.909, mem: 64.1MB, max: 228.7MB

*******
STEP 12
Basis length: 109, queue length: 216, step degree: 12, num pairs: 15
Basis total mons: 601638, average length: 5519.615
Number of pair polynomials: 15, at 24471 column(s), 0.006[r]
Average length for reductees: 3210.73 [15], reductors: 69.88 [10990]
Symbolic reduction time: 0.046[r], column sort time: 0.009
15 + 10990 = 11005 rows / 25615 columns out of 125970 (20.334%)
Density: 0.28952% / 0.49276% (74.161/r), total: 816140 (3.1MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.000
[5 threads]
0.072[r] + 0.000 = 0.074[r] [11]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 11 (73.3%), min deg: 12 [11], av deg: 12.0
Degree counts: 12:11
Queue insertion time: 0.000
New max step: 12, time: 0.149[r]
Step 12 time: 0.148[r], [0.149], mat/total: 0.630/1.059, mem: 64.1MB, max: 228.7MB

*******
STEP 13
Basis length: 120, queue length: 280, step degree: 13, num pairs: 150
Basis total mons: 694552, average length: 5787.933
17 pairs eliminated
Number of pair polynomials: 133, at 44940 column(s), 0.079[r]
Average length for reductees: 7679.20 [133], reductors: 135.97 [24780]
Symbolic reduction time: 0.219, column sort time: 0.026[r]
133 + 24780 = 24913 rows / 45948 columns out of 203490 (22.580%)
Density: 0.38357% / 0.51602% (176.24/r), total: 4390736 (16.7MB)
Before ech memory: 64.1MB, max: 228.7MB
Row sort time: 0.006[r]
[5 threads]
0.848[r] + 0.000 = 0.850 [42]
After ech memory: 64.1MB, max: 228.7MB
Num new polynomials: 42 (31.6%), min deg: 13 [42], av deg: 13.0
Degree counts: 13:42
Queue insertion time: 0.008[r]
New max step: 13, time: 1.198[r]
Step 13 time: 1.197[r], [1.198], mat/total: 1.490/2.259, mem: 64.1MB, max: 228.7MB

*******
STEP 14
Basis length: 162, queue length: 442, step degree: 14, num pairs: 254
Basis total mons: 1237816, average length: 7640.840
10 pairs eliminated
Number of pair polynomials: 244, at 60586 column(s), 0.200
Average length for reductees: 12662.20 [244], reductors: 273.51 [36632]
Symbolic reduction time: 0.616[r], column sort time: 0.034[r]
244 + 36632 = 36876 rows / 63753 columns out of 319770 (19.937%)
Density: 0.55759% / 0.7103% (355.48/r), total: 13108662 (50.0MB)
Before ech memory: 128.2MB, max: 228.7MB
Row sort time: 0.009
[5 threads]
3.439[r] + 0.009 = 3.450 [87]
After ech memory: 128.2MB, max: 228.7MB
Num new polynomials: 87 (35.7%), min deg: 13 [6], av deg: 13.9
Degree counts: 13:6 14:81
Queue insertion time: 0.019[r]
New max step: 14, time: 4.340
Step 14 time: 4.339, [4.348], mat/total: 4.950/6.599, mem: 128.2MB, max: 228.7MB

*******
STEP 15
Basis length: 249, queue length: 838, step degree: 14, num pairs: 36
Basis total mons: 2886160, average length: 11591.004
Number of pair polynomials: 36, at 52581 column(s), 0.033[r]
Average length for reductees: 13210.64 [36], reductors: 272.18 [31296]
Symbolic reduction time: 0.429, column sort time: 0.029
36 + 31296 = 31332 rows / 57636 columns out of 319770 (18.024%)
Density: 0.49803% / 0.65827% (287.05/r), total: 8993761 (34.3MB)
Before ech memory: 128.2MB, max: 228.7MB
Row sort time: 0.009[r]
[5 threads]
0.780 + 0.000 = 0.789[r] [20]
After ech memory: 128.2MB, max: 228.7MB
Num new polynomials: 20 (55.6%), min deg: 13 [4], av deg: 13.8
Degree counts: 13:4 14:16
Queue insertion time: 0.007[r]
Step 15 time: 1.310, [1.312], mat/total: 5.750/7.909, mem: 128.2MB, max: 228.7MB

*******
STEP 16
Basis length: 269, queue length: 947, step degree: 14, num pairs: 30
Basis total mons: 3226966, average length: 11996.156
Number of pair polynomials: 30, at 52926 column(s), 0.030
Average length for reductees: 12389.80 [30], reductors: 282.02 [31125]
Symbolic reduction time: 0.460, column sort time: 0.029[r]
30 + 31125 = 31155 rows / 57566 columns out of 319770 (18.002%)
Density: 0.51016% / 0.67215% (293.68/r), total: 9149562 (34.9MB)
Before ech memory: 128.2MB, max: 228.7MB
Row sort time: 0.009[r]
[5 threads]
0.789[r] + 0.000 = 0.789 [20]
After ech memory: 128.2MB, max: 228.7MB
Num new polynomials: 20 (66.7%), min deg: 13 [2], av deg: 13.9
Degree counts: 13:2 14:18
Queue insertion time: 0.006[r]
Step 16 time: 1.329, [1.337], mat/total: 6.550/9.239, mem: 128.2MB, max: 228.7MB

*******
STEP 17
Basis length: 289, queue length: 1075, step degree: 14, num pairs: 14
Basis total mons: 3605759, average length: 12476.675
Number of pair polynomials: 14, at 52927 column(s), 0.019[r]
Average length for reductees: 12881.86 [14], reductors: 290.70 [31237]
Symbolic reduction time: 0.429, column sort time: 0.029[r]
14 + 31237 = 31251 rows / 57684 columns out of 319770 (18.039%)
Density: 0.51374% / 0.67634% (296.34/r), total: 9261056 (35.3MB)
Before ech memory: 128.2MB, max: 228.7MB
Row sort time: 0.009[r]
[5 threads]
0.375[r] + 0.000 = 0.378[r] [10]
After ech memory: 128.2MB, max: 228.7MB
Num new polynomials: 10 (71.4%), min deg: 14 [10], av deg: 14.0
Degree counts: 14:10
Queue insertion time: 0.000
Step 17 time: 0.870, [0.877], mat/total: 6.940/10.109, mem: 128.2MB, max: 228.7MB

*******
STEP 18
Basis length: 299, queue length: 1140, step degree: 15, num pairs: 721
Basis total mons: 3795306, average length: 12693.331
71 pairs eliminated
Number of pair polynomials: 650, at 84004 column(s), 0.885[r]
Average length for reductees: 19620.43 [650], reductors: 522.32 [54887]
Symbolic reduction time: 1.739, column sort time: 0.039
650 + 54887 = 55537 rows / 87941 columns out of 490314 (17.936%)
Density: 0.84812% / 1.0501% (745.85/r), total: 41422017 (158.0MB)
Before ech memory: 256.3MB (=max)
Row sort time: 0.016[r]
[5 threads]
21.490 + 0.098[r] = 21.600 [178]
After ech memory: 320.4MB, max: 449.6MB
Num new polynomials: 178 (27.4%), min deg: 14 [14], av deg: 14.9
Degree counts: 14:14 15:164
Queue insertion time: 0.060
New max step: 18, time: 24.350
Step 18 time: 24.350, [24.357], mat/total: 28.560/34.460, mem: 320.4MB, max: 449.6MB

*******
STEP 19
Basis length: 477, queue length: 1721, step degree: 15, num pairs: 86
Basis total mons: 8499930, average length: 17819.560
Number of pair polynomials: 86, at 74526 column(s), 0.129
Average length for reductees: 20359.63 [86], reductors: 615.02 [52102]
Symbolic reduction time: 1.776[r], column sort time: 0.040
86 + 52102 = 52188 rows / 84934 columns out of 490314 (17.322%)
Density: 0.76243% / 0.96304% (647.56/r), total: 33794915 (128.9MB)
Before ech memory: 320.4MB, max: 449.6MB
Row sort time: 0.016[r]
[5 threads]
3.709[r] + 0.005[r] = 3.719[r] [48]
After ech memory: 320.4MB, max: 449.6MB
Num new polynomials: 48 (55.8%), min deg: 14 [6], av deg: 14.9
Degree counts: 14:6 15:42
Queue insertion time: 0.026[r]
Step 19 time: 5.719[r], [5.719], mat/total: 32.300/40.179, mem: 329.3MB, max: 449.6MB

*******
STEP 20
Basis length: 525, queue length: 2026, step degree: 15, num pairs: 41
Basis total mons: 9735488, average length: 18543.787
Number of pair polynomials: 41, at 73990 column(s), 0.069
Average length for reductees: 18927.17 [41], reductors: 567.43 [50287]
Symbolic reduction time: 1.560, column sort time: 0.047[r]
41 + 50287 = 50328 rows / 82745 columns out of 490314 (16.876%)
Density: 0.70383% / 0.8989% (582.39/r), total: 29310279 (111.8MB)
Before ech memory: 329.3MB, max: 449.6MB
Row sort time: 0.016[r]
[5 threads]
2.297[r] + 0.000 = 2.299 [25]
After ech memory: 329.3MB, max: 452.4MB
Num new polynomials: 25 (61.0%), min deg: 15 [25], av deg: 15.0
Degree counts: 15:25
Queue insertion time: 0.013[r]
Step 20 time: 4.019, [4.027], mat/total: 34.620/44.199, mem: 330.2MB, max: 452.4MB

*******
STEP 21
Basis length: 550, queue length: 2202, step degree: 16, num pairs: 1416
Basis total mons: 10404699, average length: 18917.635
110 pairs eliminated
Number of pair polynomials: 1306, at 106825 column(s), 3.570
At 100000: 67618 rows, 114845 columns, 4.519[r]
Average length for reductees: 26798.22 [1306], reductors: 927.40 [76913]
Symbolic reduction time: 5.207[r], column sort time: 0.060
1306 + 76913 = 78219 rows / 115545 columns out of 735471 (15.710%)
Density: 1.1765% / 1.4575% (1359.4/r), total: 106327553 (405.6MB)
Before ech memory: 618.4MB (=max)
Row sort time: 0.019
[5 threads]
103.019 + 0.546[r] = 103.570 [333]
After ech memory: 714.5MB, max: 879.2MB
Num new polynomials: 333 (25.5%), min deg: 15 [19], av deg: 15.9
Degree counts: 15:19 16:314
Queue insertion time: 0.200
New max step: 21, time: 112.660
Step 21 time: 112.660, [112.705], mat/total: 138.220/156.860, mem: 715.5MB, max: 879.2MB

*******
STEP 22
Basis length: 883, queue length: 3335, step degree: 16, num pairs: 117
Basis total mons: 21328929, average length: 24155.072
Number of pair polynomials: 117, at 99831 column(s), 0.278[r]
At 100000: 65181 rows, 112482 columns, 4.657[r]
Average length for reductees: 27675.36 [117], reductors: 1068.57 [75957]
Symbolic reduction time: 5.429, column sort time: 0.059[r]
117 + 75957 = 76074 rows / 114208 columns out of 735471 (15.529%)
Density: 0.97146% / 1.2469% (1109.5/r), total: 84403010 (322.0MB)
Before ech memory: 715.5MB, max: 879.2MB
Row sort time: 0.019
[5 threads]
11.629 + 0.008[r] = 11.640 [59]
After ech memory: 715.5MB, max: 879.2MB
Num new polynomials: 59 (50.4%), min deg: 15 [10], av deg: 15.8
Degree counts: 15:10 16:49
Queue insertion time: 0.047[r]
Step 22 time: 17.489, [17.497], mat/total: 149.880/174.349, mem: 716.6MB, max: 879.2MB

*******
STEP 23
Basis length: 942, queue length: 3675, step degree: 16, num pairs: 62
Basis total mons: 23232325, average length: 24662.765
Number of pair polynomials: 62, at 97221 column(s), 0.230
At 100000: 64680 rows, 110892 columns, 5.500
Average length for reductees: 28258.65 [62], reductors: 1091.61 [74118]
Symbolic reduction time: 6.358[r], column sort time: 0.065[r]
62 + 74118 = 74180 rows / 112246 columns out of 735471 (15.262%)
Density: 0.99275% / 1.2648% (1114.3/r), total: 82660057 (315.3MB)
Before ech memory: 716.6MB, max: 879.2MB
Row sort time: 0.020
[5 threads]
8.090 + 0.000 = 8.099 [32]
After ech memory: 716.6MB, max: 879.2MB
Num new polynomials: 32 (51.6%), min deg: 16 [32], av deg: 16.0
Degree counts: 16:32
Queue insertion time: 0.024[r]
Step 23 time: 14.810, [14.814], mat/total: 158.000/189.159, mem: 717.8MB, max: 879.2MB

*******
STEP 24
Basis length: 974, queue length: 3886, step degree: 17, num pairs: 2562
Basis total mons: 24311963, average length: 24960.948
194 pairs eliminated
Number of pair polynomials: 2368, at 139282 column(s), 7.390
At 100000: 73994 rows, 149724 columns, 7.829
Average length for reductees: 33171.25 [2368], reductors: 1443.94 [108452]
Symbolic reduction time: 11.219, column sort time: 0.079
2368 + 108452 = 110820 rows / 151781 columns out of 1081575 (14.033%)
Density: 1.398% / 1.7544% (2121.9/r), total: 235148235 (897.0MB)
Before ech memory: 1294.3MB (=max)
Row sort time: 0.032[r]
[5 threads]
386.019 + 2.200 = 388.230 [538]
After ech memory: 1486.5MB, max: 1694.9MB
Num new polynomials: 538 (22.7%), min deg: 16 [74], av deg: 16.9
Degree counts: 16:74 17:464
Queue insertion time: 0.549
New max step: 24, time: 407.520
Step 24 time: 407.519, [407.647], mat/total: 546.280/596.679, mem: 1487.8MB, max: 1694.9MB

*******
STEP 25
Basis length: 1512, queue length: 5317, step degree: 17, num pairs: 554
Basis total mons: 44826698, average length: 29647.287
Number of pair polynomials: 554, at 130103 column(s), 2.496[r]
At 100000: 71157 rows, 149692 columns, 9.460
Average length for reductees: 35351.39 [554], reductors: 1636.79 [109196]
Symbolic reduction time: 13.120, column sort time: 0.086[r]
554 + 109196 = 109750 rows / 151949 columns out of 1081575 (14.049%)
Density: 1.1892% / 1.5405% (1807/r), total: 198316117 (756.5MB)
Before ech memory: 1487.8MB, max: 1694.9MB
Row sort time: 0.036[r]
[5 threads]
105.750 + 0.670 = 106.420 [229]
After ech memory: 1487.8MB, max: 1695.8MB
Num new polynomials: 229 (41.3%), min deg: 16 [61], av deg: 16.7
Degree counts: 16:61 17:168
Queue insertion time: 0.299[r]
Step 25 time: 122.480, [122.513], mat/total: 652.750/719.159, mem: 1489.2MB, max: 1695.8MB

*******
STEP 26
Basis length: 1741, queue length: 6560, step degree: 17, num pairs: 451
Basis total mons: 53495465, average length: 30726.861
Number of pair polynomials: 451, at 129540 column(s), 1.810
At 100000: 71116 rows, 149192 columns, 8.990
Average length for reductees: 35914.47 [451], reductors: 1720.90 [108997]
Symbolic reduction time: 13.000, column sort time: 0.079
451 + 108997 = 109448 rows / 151484 columns out of 1081575 (14.006%)
Density: 1.229% / 1.5836% (1861.8/r), total: 203770486 (777.3MB)
Before ech memory: 1489.2MB, max: 1695.8MB
Row sort time: 0.036[r]
[5 threads]
97.980 + 0.819 = 98.799 [239]
After ech memory: 1553.3MB, max: 1728.5MB
Num new polynomials: 239 (53.0%), min deg: 16 [28], av deg: 16.9
Degree counts: 16:28 17:211
Queue insertion time: 0.340
Step 26 time: 114.090, [114.133], mat/total: 751.600/833.250, mem: 1554.9MB, max: 1728.5MB

*******
STEP 27
Basis length: 1980, queue length: 8024, step degree: 17, num pairs: 216
Basis total mons: 62670649, average length: 31651.843
Number of pair polynomials: 216, at 127142 column(s), 0.950
At 100000: 70786 rows, 149113 columns, 11.029
Average length for reductees: 36610.60 [216], reductors: 1806.75 [109263]
Symbolic reduction time: 16.299, column sort time: 0.087[r]
216 + 109263 = 109479 rows / 151503 columns out of 1081575 (14.008%)
Density: 1.2379% / 1.5971% (1875.4/r), total: 205318424 (783.2MB)
Before ech memory: 1554.9MB, max: 1728.5MB
Row sort time: 0.029
[5 threads]
49.250 + 0.220 = 49.480 [136]
After ech memory: 1586.9MB, max: 1793.9MB
Num new polynomials: 136 (63.0%), min deg: 16 [18], av deg: 16.9
Degree counts: 16:18 17:118
Queue insertion time: 0.230
Step 27 time: 67.090, [67.120], mat/total: 801.110/900.340, mem: 1586.9MB, max: 1793.9MB

*******
STEP 28
Basis length: 2116, queue length: 8865, step degree: 17, num pairs: 141
Basis total mons: 67984445, average length: 32128.755
Number of pair polynomials: 141, at 124404 column(s), 0.680[r]
At 100000: 70615 rows, 148751 columns, 10.320
Average length for reductees: 36802.66 [141], reductors: 1853.80 [109266]
Symbolic reduction time: 14.950, column sort time: 0.080
141 + 109266 = 109407 rows / 151367 columns out of 1081575 (13.995%)
Density: 1.2545% / 1.6159% (1898.8/r), total: 207746224 (792.5MB)
Before ech memory: 1586.9MB, max: 1793.9MB
Row sort time: 0.037[r]
[5 threads]
38.519 + 0.070 = 38.590 [108]
After ech memory: 1651.0MB, max: 1857.7MB
Num new polynomials: 108 (76.6%), min deg: 16 [9], av deg: 16.9
Degree counts: 16:9 17:99
Queue insertion time: 0.179[r]
Step 28 time: 54.549, [54.564], mat/total: 839.750/954.889, mem: 1652.7MB, max: 1857.7MB

*******
STEP 29
Basis length: 2224, queue length: 9575, step degree: 17, num pairs: 72
Basis total mons: 72164979, average length: 32448.282
Number of pair polynomials: 72, at 123831 column(s), 0.330
At 100000: 70436 rows, 148058 columns, 9.949
Average length for reductees: 36963.25 [72], reductors: 1882.04 [108875]
Symbolic reduction time: 14.840, column sort time: 0.089
72 + 108875 = 108947 rows / 150868 columns out of 1081575 (13.949%)
Density: 1.2628% / 1.6251% (1905.2/r), total: 207568671 (791.8MB)
Before ech memory: 1652.7MB, max: 1857.7MB
Row sort time: 0.037[r]
[5 threads]
20.499 + 0.009 = 20.509 [65]
After ech memory: 1684.7MB, max: 1890.8MB
Num new polynomials: 65 (90.3%), min deg: 16 [3], av deg: 17.0
Degree counts: 16:3 17:62
Queue insertion time: 0.125[r]
Step 29 time: 35.950, [35.967], mat/total: 860.300/990.840, mem: 1686.6MB, max: 1890.8MB

*******
STEP 30
Basis length: 2289, queue length: 10024, step degree: 17, num pairs: 23
Basis total mons: 74704668, average length: 32636.377
Number of pair polynomials: 23, at 124312 column(s), 0.125[r]
At 100000: 70655 rows, 149353 columns, 11.220
Average length for reductees: 37390.61 [23], reductors: 1905.04 [109803]
Symbolic reduction time: 16.450, column sort time: 0.080
23 + 109803 = 109826 rows / 151730 columns out of 1081575 (14.029%)
Density: 1.2604% / 1.6255% (1912.5/r), total: 210039475 (801.2MB)
Before ech memory: 1686.6MB, max: 1890.8MB
Row sort time: 0.029
[5 threads]
7.409 + 0.005[r] = 7.424[r] [23]
After ech memory: 1686.6MB, max: 1893.5MB
Num new polynomials: 23 (100.0%), min deg: 17 [23], av deg: 17.0
Degree counts: 17:23
Queue insertion time: 0.040
Step 30 time: 24.170, [24.180], mat/total: 867.760/1015.010, mem: 1686.6MB, max: 1893.5MB

*******
STEP 31
Basis length: 2312, queue length: 10188, step degree: 18, num pairs: 7625
Basis total mons: 75634791, average length: 32714.010
681 pairs eliminated
Number of pair polynomials: 6944, at 174566 column(s), 28.879
At 100000: 86154 rows, 188642 columns, 14.319
Average length for reductees: 38584.97 [6944], reductors: 2382.41 [147573]
Symbolic reduction time: 25.750, column sort time: 0.110
6944 + 147573 = 154517 rows / 193099 columns out of 1562275 (12.360%)
Density: 2.0763% / 2.5931% (4009.4/r), total: 619513038 (2363.3MB)
Before ech memory: 3384.3MB, max: 3392.3MB
Row sort time: 0.051[r]
[5 threads]
2275.289 + 20.880 = 2296.180 [1212]
After ech memory: 3800.7MB, max: 4023.6MB
Num new polynomials: 1212 (17.5%), min deg: 16 [3], av deg: 17.4
Degree counts: 16:3 17:685 18:524
Queue insertion time: 2.680[r]
New max step: 31, time: 2353.680
Step 31 time: 2353.680, [2354.351], mat/total: 3164.000/3368.690, mem: 3802.8MB, max: 4023.6MB

*******
STEP 32
Basis length: 3524, queue length: 9687, step degree: 17, num pairs: 24
Basis total mons: 124385998, average length: 35296.821
Number of pair polynomials: 24, at 120280 column(s), 0.099
At 100000: 71044 rows, 148943 columns, 9.529
Average length for reductees: 37652.04 [24], reductors: 2134.98 [110230]
Symbolic reduction time: 14.019, column sort time: 0.085[r]
24 + 110230 = 110254 rows / 151446 columns out of 1081575 (14.002%)
Density: 1.4148% / 1.7928% (2142.7/r), total: 236242126 (901.2MB)
Before ech memory: 3802.8MB, max: 4023.6MB
Row sort time: 0.030
[5 threads]
7.750 + 0.000 = 7.759 [6]
After ech memory: 3802.8MB, max: 4023.6MB
Num new polynomials: 6 (25.0%), min deg: 17 [6], av deg: 17.0
Degree counts: 17:6
Queue insertion time: 0.019[r]
Step 32 time: 22.029, [22.047], mat/total: 3171.790/3390.719, mem: 3802.8MB, max: 4023.6MB

*******
STEP 33
Basis length: 3530, queue length: 9711, step degree: 18, num pairs: 5285
Basis total mons: 124616730, average length: 35302.190
Number of pair polynomials: 5285, at 171076 column(s), 16.599
At 100000: 83972 rows, 186673 columns, 13.950
Average length for reductees: 39248.81 [5285], reductors: 2743.32 [148119]
Symbolic reduction time: 25.380, column sort time: 0.110
5285 + 148119 = 153404 rows / 192191 columns out of 1562275 (12.302%)
Density: 2.0818% / 2.618% (4001/r), total: 613767911 (2341.3MB)
Before ech memory: 3802.8MB, max: 4023.6MB
Row sort time: 0.050
[5 threads]
1906.819 + 31.199 = 1938.029 [1308]
After ech memory: 4219.2MB, max: 4439.6MB
Num new polynomials: 1308 (24.7%), min deg: 16 [97], av deg: 17.2
Degree counts: 16:97 17:824 18:387
Queue insertion time: 3.918[r]
Step 33 time: 1984.110, [1984.661], mat/total: 5109.880/5374.829, mem: 4221.5MB, max: 4439.6MB

*******
STEP 34
Basis length: 4838, queue length: 12153, step degree: 17, num pairs: 775
Basis total mons: 175979712, average length: 36374.475
Number of pair polynomials: 775, at 131889 column(s), 2.560
At 100000: 73422 rows, 150243 columns, 10.769
Average length for reductees: 37929.56 [775], reductors: 2434.54 [111923]
Symbolic reduction time: 15.659, column sort time: 0.089[r]
775 + 111923 = 112698 rows / 152211 columns out of 1081575 (14.073%)
Density: 1.7598% / 2.1601% (2678.6/r), total: 301876679 (1151.6MB)
Before ech memory: 4221.5MB, max: 4439.6MB
Row sort time: 0.030
[5 threads]
226.250 + 12.329 = 238.589 [569]
After ech memory: 4221.5MB, max: 4439.6MB
Num new polynomials: 569 (73.4%), min deg: 16 [234], av deg: 16.6
Degree counts: 16:234 17:335
Queue insertion time: 1.860
Step 34 time: 258.810, [258.894], mat/total: 5348.510/5633.640, mem: 4221.5MB, max: 4439.6MB

*******
STEP 35
Basis length: 5407, queue length: 15714, step degree: 17, num pairs: 1855
Basis total mons: 197587557, average length: 36542.918
Number of pair polynomials: 1855, at 132967 column(s), 5.689
At 100000: 75376 rows, 149447 columns, 10.828[r]
Average length for reductees: 37510.25 [1855], reductors: 2608.95 [111988]
Symbolic reduction time: 15.590, column sort time: 0.085[r]
1855 + 111988 = 113843 rows / 151690 columns out of 1081575 (14.025%)
Density: 2.0948% / 2.514% (3177.6/r), total: 361753168 (1380.0MB)
Before ech memory: 4221.5MB, max: 4439.6MB
Row sort time: 0.037[r]
[5 threads]
557.200 + 67.219 = 624.429 [1235]
After ech memory: 4221.5MB, max: 4439.6MB
Num new polynomials: 1235 (66.6%), min deg: 16 [737], av deg: 16.4
Degree counts: 16:737 17:498
Queue insertion time: 4.278[r]
Step 35 time: 650.119, [650.305], mat/total: 5972.980/6283.760, mem: 4224.0MB, max: 4439.6MB

*******
STEP 36
Basis length: 6642, queue length: 23075, step degree: 17, num pairs: 5809
Basis total mons: 243218719, average length: 36618.296
Number of pair polynomials: 5809, at 132794 column(s), 15.909
At 100000: 81890 rows, 148631 columns, 11.840
Average length for reductees: 36689.65 [5809], reductors: 3005.36 [112359]
Symbolic reduction time: 16.630, column sort time: 0.079
5809 + 112359 = 118168 rows / 150739 columns out of 1081575 (13.937%)
Density: 3.0923% / 3.5828% (4661.2/r), total: 550809883 (2101.2MB)
Before ech memory: 4384.2MB, max: 4439.6MB
Row sort time: 0.037[r]
[5 threads]
1860.520 + 137.739 = 1998.269 [1851]
After ech memory: 4896.7MB, max: 5098.7MB
Num new polynomials: 1851 (31.9%), min deg: 16 [1418], av deg: 16.2
Degree counts: 16:1418 17:433
Queue insertion time: 7.175[r]
Step 36 time: 2038.119, [2038.692], mat/total: 7971.290/8321.880, mem: 4896.7MB, max: 5098.7MB

*******
STEP 37
Basis length: 8493, queue length: 31061, step degree: 17, num pairs: 11192
Basis total mons: 308642624, average length: 36340.825
Number of pair polynomials: 11192, at 131883 column(s), 26.699
At 100000: 90016 rows, 145847 columns, 12.570
Average length for reductees: 35229.15 [11192], reductors: 3560.07 [112901]
Symbolic reduction time: 17.290, column sort time: 0.079
11192 + 112901 = 124093 rows / 149278 columns out of 1081575 (13.802%)
Density: 4.2982% / 4.9502% (6416.3/r), total: 796220020 (3037.3MB)
Before ech memory: 5892.4MB (=max)
Row sort time: 0.039[r]
[5 threads]
3724.770 + 187.760 = 3912.540 [2224]
After ech memory: 6501.0MB, max: 6699.4MB
Num new polynomials: 2224 (19.9%), min deg: 16 [1906], av deg: 16.1
Degree counts: 16:1906 17:318
Queue insertion time: 10.039[r]
New max step: 37, time: 3966.710
Step 37 time: 3966.709, [3967.825], mat/total: 11883.880/12288.590, mem: 6501.0MB, max: 6699.4MB

*******
STEP 38
Basis length: 10717, queue length: 36065, step degree: 17, num pairs: 15056
Basis total mons: 382627801, average length: 35702.883
Number of pair polynomials: 15056, at 125179 column(s), 30.600
At 100000: 96345 rows, 144775 columns, 15.479
Average length for reductees: 33216.37 [15056], reductors: 4181.94 [113973]
Symbolic reduction time: 20.809, column sort time: 0.079
15056 + 113973 = 129029 rows / 147934 columns out of 1081575 (13.678%)
Density: 5.1171% / 6.0211% (7569.9/r), total: 976733901 (3725.9MB)
Before ech memory: 7269.8MB (=max)
Row sort time: 0.040
[5 threads]
4896.100 + 213.759 = 5109.869 [2318]
After ech memory: 7846.3MB, max: 8040.7MB
Num new polynomials: 2318 (15.4%), min deg: 15 [1587], av deg: 15.4
Degree counts: 15:1587 16:615 17:116
Queue insertion time: 10.806[r]
New max step: 38, time: 5172.240
Step 38 time: 5172.239, [5173.688], mat/total: 16993.800/17460.829, mem: 7846.3MB, max: 8040.7MB

*******
STEP 39
Basis length: 13035, queue length: 38663, step degree: 16, num pairs: 12687
Basis total mons: 454973632, average length: 34903.999
Number of pair polynomials: 12687, at 112925 column(s), 22.159
At 100000: 90369 rows, 117465 columns, 9.920
Average length for reductees: 31197.88 [12687], reductors: 3642.26 [86531]
Symbolic reduction time: 10.930, column sort time: 0.060
12687 + 86531 = 99218 rows / 117887 columns out of 735471 (16.029%)
Density: 6.0785% / 6.775% (7165.8/r), total: 710975795 (2712.2MB)
Before ech memory: 7846.3MB, max: 8040.7MB
Row sort time: 0.029
[5 threads]
3294.680 + 86.729 = 3381.420 [1853]
After ech memory: 7846.3MB, max: 8040.7MB
Num new polynomials: 1853 (14.6%), min deg: 15 [1741], av deg: 15.1
Degree counts: 15:1741 16:112
Queue insertion time: 4.639
Step 39 time: 3419.250, [3420.177], mat/total: 20375.260/20880.079, mem: 7849.4MB, max: 8040.7MB

*******
STEP 40
Basis length: 14888, queue length: 40692, step degree: 16, num pairs: 13926
Basis total mons: 509561169, average length: 34226.301
Number of pair polynomials: 13926, at 101783 column(s), 12.790
At 100000: 90779 rows, 107731 columns, 5.493[r]
Average length for reductees: 29458.54 [13926], reductors: 3770.94 [78349]
Symbolic reduction time: 5.509, column sort time: 0.039[r]
13926 + 78349 = 92275 rows / 107850 columns out of 735471 (14.664%)
Density: 7.091% / 7.7927% (7647.7/r), total: 705689060 (2692.0MB)
Before ech memory: 7849.4MB, max: 8040.7MB
Row sort time: 0.017[r]
[5 threads]
1886.229 + 20.178[r] = 1906.409 [934]
After ech memory: 7849.4MB, max: 8040.7MB
Num new polynomials: 934 (6.7%), min deg: 15 [895], av deg: 15.0
Degree counts: 15:895 16:39
Queue insertion time: 2.463[r]
Step 40 time: 1927.250, [1927.654], mat/total: 22281.690/22807.329, mem: 7849.4MB, max: 8040.7MB

*******
STEP 41
Basis length: 15822, queue length: 34179, step degree: 16, num pairs: 7160
Basis total mons: 536239561, average length: 33892.021
Number of pair polynomials: 7160, at 93838 column(s), 7.250
Average length for reductees: 28563.56 [7160], reductors: 3542.67 [72746]
Symbolic reduction time: 5.150, column sort time: 0.036[r]
7160 + 72746 = 79906 rows / 101313 columns out of 735471 (13.775%)
Density: 5.7097% / 6.3117% (5784.7/r), total: 462229959 (1763.3MB)
Before ech memory: 7849.4MB, max: 8040.7MB
Row sort time: 0.014[r]
[5 threads]
822.400 + 0.000 = 822.400 [6]
After ech memory: 7849.4MB, max: 8040.7MB
Num new polynomials: 6 (0.1%), min deg: 15 [2], av deg: 15.7
Degree counts: 15:2 16:4
Queue insertion time: 0.019
Step 41 time: 834.889, [835.064], mat/total: 23104.120/23642.219, mem: 7849.4MB, max: 8040.7MB

*******
STEP 42
Basis length: 15828, queue length: 27067, step degree: 16, num pairs: 16
Basis total mons: 536410928, average length: 33890.001
Number of pair polynomials: 16, at 88915 column(s), 0.030
Average length for reductees: 28561.50 [16], reductors: 3242.56 [69834]
Symbolic reduction time: 6.379, column sort time: 0.035[r]
16 + 69834 = 69850 rows / 98395 columns out of 735471 (13.379%)
Density: 3.3013% / 3.8394% (3248.4/r), total: 226897821 (865.5MB)
Before ech memory: 7849.4MB, max: 8040.7MB
Row sort time: 0.013[r]
[5 threads]
3.438[r] + 0.000 = 3.439 [0]
After ech memory: 7849.4MB, max: 8040.7MB
No new polynomials
Queue insertion time: 0.000
Step 42 time: 9.909, [9.917], mat/total: 23107.580/23652.129, mem: 7849.4MB, max: 8040.7MB

*******
STEP 43
Basis length: 15828, queue length: 27051, step degree: 17, num pairs: 5482
Basis total mons: 536410928, average length: 33890.001
1034 pairs eliminated
Number of pair polynomials: 4448, at 114845 column(s), 4.740
At 100000: 84450 rows, 137240 columns, 11.770
Average length for reductees: 30840.71 [4448], reductors: 5282.52 [110985]
Symbolic reduction time: 15.240, column sort time: 0.049[r]
4448 + 110985 = 115433 rows / 139546 columns out of 1081575 (12.902%)
Density: 4.4912% / 5.6225% (6267.4/r), total: 723459634 (2759.8MB)
Before ech memory: 7849.4MB, max: 8040.7MB
Row sort time: 0.023[r]
[5 threads]
859.599 + 0.000 = 859.610 [0]
After ech memory: 7849.4MB, max: 8040.7MB
No new polynomials
Queue insertion time: 0.000
Step 43 time: 879.680, [879.868], mat/total: 23967.230/24531.809, mem: 7849.4MB, max: 8040.7MB

*******
STEP 44
Basis length: 15828, queue length: 21569, step degree: 18, num pairs: 13842
Basis total mons: 536410928, average length: 33890.001
13332 pairs eliminated
Number of pair polynomials: 510, at 118748 column(s), 1.089[r]
At 100000: 84172 rows, 183367 columns, 14.600
Average length for reductees: 39966.21 [510], reductors: 5684.59 [160817]
Symbolic reduction time: 24.250, column sort time: 0.069
510 + 160817 = 161327 rows / 189378 columns out of 1562275 (12.122%)
Density: 3.0589% / 4.5032% (5793/r), total: 934561609 (3565.1MB)
Before ech memory: 8714.3MB, max: 8722.3MB
Row sort time: 0.036[r]
[5 threads]
206.150 + 0.000 = 206.159 [0]
After ech memory: 8746.3MB, max: 8979.1MB
No new polynomials
Queue insertion time: 0.000
Step 44 time: 231.630, [231.683], mat/total: 24173.440/24763.439, mem: 8746.3MB, max: 8979.1MB

*******
STEP 45
Basis length: 15828, queue length: 7727, step degree: 19, num pairs: 2691
Basis total mons: 536410928, average length: 33890.001
2691 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 46
Basis length: 15828, queue length: 5036, step degree: 20, num pairs: 974
Basis total mons: 536410928, average length: 33890.001
974 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 47
Basis length: 15828, queue length: 4062, step degree: 21, num pairs: 768
Basis total mons: 536410928, average length: 33890.001
768 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 48
Basis length: 15828, queue length: 3294, step degree: 22, num pairs: 673
Basis total mons: 536410928, average length: 33890.001
673 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 49
Basis length: 15828, queue length: 2621, step degree: 23, num pairs: 615
Basis total mons: 536410928, average length: 33890.001
615 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 50
Basis length: 15828, queue length: 2006, step degree: 24, num pairs: 515
Basis total mons: 536410928, average length: 33890.001
515 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 51
Basis length: 15828, queue length: 1491, step degree: 25, num pairs: 403
Basis total mons: 536410928, average length: 33890.001
403 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 52
Basis length: 15828, queue length: 1088, step degree: 26, num pairs: 351
Basis total mons: 536410928, average length: 33890.001
351 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 53
Basis length: 15828, queue length: 737, step degree: 27, num pairs: 296
Basis total mons: 536410928, average length: 33890.001
296 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 54
Basis length: 15828, queue length: 441, step degree: 28, num pairs: 201
Basis total mons: 536410928, average length: 33890.001
201 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 55
Basis length: 15828, queue length: 240, step degree: 29, num pairs: 108
Basis total mons: 536410928, average length: 33890.001
108 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 56
Basis length: 15828, queue length: 132, step degree: 30, num pairs: 68
Basis total mons: 536410928, average length: 33890.001
68 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 57
Basis length: 15828, queue length: 64, step degree: 31, num pairs: 44
Basis total mons: 536410928, average length: 33890.001
44 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 58
Basis length: 15828, queue length: 20, step degree: 32, num pairs: 14
Basis total mons: 536410928, average length: 33890.001
14 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 59
Basis length: 15828, queue length: 6, step degree: 33, num pairs: 4
Basis total mons: 536410928, average length: 33890.001
4 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 60
Basis length: 15828, queue length: 2, step degree: 34, num pairs: 2
Basis total mons: 536410928, average length: 33890.001
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 15828 final polynomial(s) by 15828
183 redundant polynomial(s) removed; time: 0.039[r]
Interreduce 6005 (out of range [0 .. 15827] = 15828) polynomial(s)
Symbolic reduction time: 0.689
Column sort time: 0.025[r]
6005 + 35107 = 41112 rows / 69673 columns
Density: 6.6038% / 7.063% (4601/r), total: 189158320 (721.6MB)
Row sort time: 0.000
[5 threads]
471.299 + 0.159 = 471.469 [6005]
Total reduction time: 473.600
Reduction time: 480.470
Final number of polynomials: 15645

Final basis length: 6005
Number of pairs: 92379
Max step: 38, time: 5172.240
Max num entries matrix: 161327 by 189378
Max num rows matrix: 161327 by 189378
Approx mat cost: 6.64806e+13, sym red cost: 1.03043e+10
Total pair setup time: 194.500
Total symbolic reduction time: 342.970
Total column sort time: 2.210
Total row sort time: 0.940
Total matrix time: 24173.440
Total new polys time: 2.840
Total queue update time: 47.300
Total Faugere F4 time: 25248.279, real time: 25255.181
Time: 25248.280
dregs = [ 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 17, 18, 17, 17, 17, 17, 17, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 ]
3.83user 0.53system 7:01:45elapsed 0%CPU (0avgtext+0avgdata 229616maxresident)k
0inputs+712outputs (0major+91630minor)pagefaults 0swaps