results/anemoi_p65537_n1_l1_a7_mPCICO_o1.txt

Model: PCICO. Use final LL: True.
====================================================================================================
ANEMOI GF(65537^1), alpha = 7, QUAD = 2. With final LL. Model: PCICO
rmax = 10, tmax = 3600.
====================================================================================================
====================================================================================================
n_r: 1, n_v: 2, n_e: 2, mdeg: 7
degs = [7, 2]
Multivariate Polynomial Ring in Y0000, S0100 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: 8, num pairs: 1
Basis total mons: 9, average length: 4.500
Number of pair polynomials: 1, at 8 column(s), 0.000
Average length for reductees: 5.00 [1], reductors: 4.70 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 20 columns out of 45 (44.444%)
Density: 23.636% / 40.368% (4.7273/r), total: 52 (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: 6 [1], av deg: 6.0
Degree counts: 6:1
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 3, queue length: 2, step degree: 7, num pairs: 2
Basis total mons: 19, average length: 6.333
Number of pair polynomials: 2, at 20 column(s), 0.000
Average length for reductees: 10.00 [2], reductors: 5.36 [11]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 11 = 13 rows / 21 columns out of 36 (58.333%)
Density: 28.938% / 45.124% (6.0769/r), total: 79 (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: 5 [1], av deg: 5.0
Degree counts: 5:1
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: 2, step degree: 6, num pairs: 2
Basis total mons: 29, average length: 7.250
Number of pair polynomials: 2, at 20 column(s), 0.000
Average length for reductees: 10.00 [2], reductors: 5.77 [13]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 13 = 15 rows / 23 columns out of 28 (82.143%)
Density: 27.536% / 44.069% (6.3333/r), total: 95 (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: 5 [1], av deg: 5.0
Degree counts: 5:1
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: 1, step degree: 6, num pairs: 1
Basis total mons: 39, average length: 7.800
Number of pair polynomials: 1, at 13 column(s), 0.000
Average length for reductees: 10.00 [1], reductors: 5.83 [18]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 18 = 19 rows / 27 columns out of 28 (96.429%)
Density: 22.417% / 38.702% (6.0526/r), total: 115 (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 4 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Reduce 5 final polynomial(s) by 5
0 redundant polynomial(s) removed; time: 0.000
Interreduce 3 (out of range [0 .. 4] = 5) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
3 + 0 = 3 rows / 12 columns
Density: 69.444% / 91.414% (8.3333/r), total: 25 (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: 5

Final basis length: 3
Number of pairs: 6
Max step: 1, time: 0.000
Max num entries matrix: 19 by 27
Max num rows matrix: 19 by 27
Approx mat cost: 740.829, sym red cost: 366
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 = [ 8, 7, 6, 6 ]
----------------------------------------------------------------------------------------------------
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: S0100
Get rep mat (dim: 9)
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 + 12 = 14 rows / 21 columns
Density: 29.932% / 45.741% (6.2857/r), total: 88 (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 = 9
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=1)
Time: 0.000
nsols = 0
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=1)
nsols_mult = 0
====================================================================================================
n_r: 2, n_v: 3, n_e: 3, mdeg: 7
degs = [7, 7, 3]
Multivariate Polynomial Ring in Y0000, S0200, S0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=2)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 3
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
Datum size: 4
No queue sort
Initial length: 3
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 2

*******
STEP 1
Basis length: 3, queue length: 2, step degree: 9, num pairs: 2
Basis total mons: 28, average length: 9.333
Number of pair polynomials: 2, at 37 column(s), 0.000
Average length for reductees: 11.00 [2], reductors: 9.80 [25]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 25 = 27 rows / 82 columns out of 220 (37.273%)
Density: 12.06% / 20.131% (9.8889/r), total: 267 (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: 7 [1], av deg: 7.5
Degree counts: 7:1 8:1
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 5, queue length: 5, step degree: 8, num pairs: 2
Basis total mons: 102, average length: 20.400
Number of pair polynomials: 2, at 75 column(s), 0.000
Average length for reductees: 40.00 [2], reductors: 12.08 [26]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 26 = 28 rows / 83 columns out of 165 (50.303%)
Density: 16.954% / 26.125% (14.071/r), total: 394 (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 2 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 6, queue length: 6, step degree: 9, num pairs: 4
Basis total mons: 150, average length: 25.000
Number of pair polynomials: 4, at 109 column(s), 0.000
Average length for reductees: 41.00 [4], reductors: 13.42 [43]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 43 = 47 rows / 116 columns out of 220 (52.727%)
Density: 13.591% / 21.152% (15.766/r), total: 741 (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 (50.0%), min deg: 8 [2], av deg: 8.0
Degree counts: 8:2
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: 8, queue length: 7, step degree: 9, num pairs: 3
Basis total mons: 251, average length: 31.375
Number of pair polynomials: 3, at 114 column(s), 0.000
Average length for reductees: 49.67 [3], reductors: 14.34 [56]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 56 = 59 rows / 131 columns out of 220 (59.545%)
Density: 12.317% / 19.389% (16.136/r), total: 952 (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 (33.3%), 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: 9, queue length: 7, step degree: 10, num pairs: 3
Basis total mons: 312, average length: 34.667
Number of pair polynomials: 3, at 133 column(s), 0.000
Average length for reductees: 61.00 [3], reductors: 14.67 [72]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 72 = 75 rows / 154 columns out of 286 (53.846%)
Density: 10.727% / 17.201% (16.52/r), total: 1239 (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 (66.7%), min deg: 8 [1], av deg: 8.5
Degree counts: 8:1 9:1
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: 11, queue length: 8, step degree: 9, num pairs: 3
Basis total mons: 472, average length: 42.909
Number of pair polynomials: 3, at 155 column(s), 0.000
Average length for reductees: 80.00 [3], reductors: 17.35 [74]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 74 = 77 rows / 164 columns out of 220 (74.545%)
Density: 12.068% / 18.789% (19.792/r), total: 1524 (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: 8 [3], av deg: 8.0
Degree counts: 8:3
Queue insertion time: 0.000
Step 6 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 14, queue length: 12, step degree: 9, num pairs: 6
Basis total mons: 723, average length: 51.643
Number of pair polynomials: 6, at 170 column(s), 0.000
Average length for reductees: 83.33 [6], reductors: 19.53 [108]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 108 = 114 rows / 199 columns out of 220 (90.455%)
Density: 11.5% / 17.84% (22.886/r), total: 2609 (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: 8 [4], av deg: 8.0
Degree counts: 8:4
Queue insertion time: 0.000
Step 7 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 8
Basis length: 18, queue length: 18, step degree: 9, num pairs: 10
Basis total mons: 1057, average length: 58.722
Number of pair polynomials: 10, at 175 column(s), 0.000
Average length for reductees: 83.40 [10], reductors: 23.07 [107]
Symbolic reduction time: 0.000, column sort time: 0.000
10 + 107 = 117 rows / 195 columns out of 220 (88.636%)
Density: 14.477% / 20.962% (28.231/r), total: 3303 (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 (40.0%), min deg: 8 [3], av deg: 8.2
Degree counts: 8:3 9:1
Queue insertion time: 0.000
New max step: 8, time: 0.001[r]
Step 8 time: 0.000[r], [0.001], mat/total: 0.000/0.004[r], mem: 32.1MB (=max)

*******
STEP 9
Basis length: 22, queue length: 15, step degree: 9, num pairs: 7
Basis total mons: 1394, average length: 63.364
Number of pair polynomials: 7, at 164 column(s), 0.000
Average length for reductees: 84.14 [7], reductors: 24.65 [91]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 91 = 98 rows / 175 columns out of 220 (79.545%)
Density: 16.513% / 23.107% (28.898/r), total: 2832 (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 (42.9%), min deg: 7 [1], av deg: 7.7
Degree counts: 7:1 8:2
Queue insertion time: 0.000
Step 9 time: 0.000, [0.000], mat/total: 0.000/0.004[r], mem: 32.1MB (=max)

*******
STEP 10
Basis length: 25, queue length: 14, step degree: 8, num pairs: 3
Basis total mons: 1640, average length: 65.600
Number of pair polynomials: 3, at 152 column(s), 0.000
Average length for reductees: 82.00 [3], reductors: 25.68 [81]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 81 = 84 rows / 162 columns out of 165 (98.182%)
Density: 17.093% / 24.067% (27.69/r), total: 2326 (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 10 time: 0.000, [0.001], mat/total: 0.000/0.005[r], mem: 32.1MB (=max)

*******
STEP 11
Basis length: 25, queue length: 11, step degree: 9, num pairs: 3
Basis total mons: 1640, average length: 65.600
Number of pair polynomials: 3, at 154 column(s), 0.000
Average length for reductees: 82.00 [3], reductors: 25.00 [84]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 84 = 87 rows / 165 columns out of 220 (75.000%)
Density: 16.343% / 23.316% (26.966/r), total: 2346 (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 11 time: 0.000, [0.000], mat/total: 0.000/0.005[r], mem: 32.1MB (=max)

*******
STEP 12
Basis length: 25, queue length: 8, step degree: 10, num pairs: 2
Basis total mons: 1640, average length: 65.600
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 13
Basis length: 25, queue length: 6, step degree: 11, num pairs: 3
Basis total mons: 1640, average length: 65.600
3 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 14
Basis length: 25, queue length: 3, step degree: 12, num pairs: 2
Basis total mons: 1640, average length: 65.600
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 15
Basis length: 25, queue length: 1, step degree: 13, num pairs: 1
Basis total mons: 1640, average length: 65.600
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 25 final polynomial(s) by 25
2 redundant polynomial(s) removed; time: 0.000
Interreduce 19 (out of range [0 .. 24] = 25) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
19 + 0 = 19 rows / 100 columns
Density: 61.105% / 69.411% (61.105/r), total: 1161 (0.0MB)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [19]
Total reduction time: 0.000
Reduction time: 0.000
Final number of polynomials: 23

Final basis length: 19
Number of pairs: 46
Max step: 8, time: 0.001
Max num entries matrix: 117 by 195
Max num rows matrix: 117 by 195
Approx mat cost: 134674, sym red cost: 19694
Total pair setup time: 0.000
Total symbolic reduction time: 0.010
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.000
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.006[r], real time: 0.007
Time: 0.010
dregs = [ 9, 8, 9, 9, 10, 9, 9, 9, 9, 8, 9, 10, 11, 12, 13 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=2)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 3
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 19
Try rep mat lex method; E: S0100
Get rep mat (dim: 81)
Rep mat time: 0.000
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 0.037[r]
Get kernel for min poly
Kernel mat time: 0.000
Nullity: 1
Get relations for all variables
REDUCE 3 polynomial(s) by 19 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
3 + 80 = 83 rows / 161 columns
Density: 17.346% / 24.441% (27.928/r), total: 2318 (0.0MB)
Row sort time: 0.000
0.000 = 0.000 [3]
Total reduction time: 0.000
Reduction time: 0.000
Relations time: 0.000
Time: 0.050
unideg = 81
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=2)
Time: 0.000
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=2)
nsols_mult = 1
====================================================================================================
n_r: 3, n_v: 4, n_e: 4, mdeg: 7
degs = [7, 7, 7, 4]
Multivariate Polynomial Ring in Y0000, S0300, S0200, S0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=3)
********************
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: 3

*******
STEP 1
Basis length: 4, queue length: 3, step degree: 10, num pairs: 3
Basis total mons: 83, average length: 20.750
Number of pair polynomials: 3, at 126 column(s), 0.000
Average length for reductees: 23.00 [3], reductors: 21.14 [58]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 58 = 61 rows / 286 columns out of 1001 (28.571%)
Density: 7.4229% / 10.905% (21.23/r), total: 1295 (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: 8 [1], av deg: 8.7
Degree counts: 8:1 9:2
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: 7, queue length: 10, step degree: 9, num pairs: 2
Basis total mons: 404, average length: 57.714
Number of pair polynomials: 2, at 180 column(s), 0.000
Average length for reductees: 103.00 [2], reductors: 21.59 [34]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 34 = 36 rows / 205 columns out of 715 (28.671%)
Density: 12.737% / 17.386% (26.111/r), total: 940 (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 2 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 8, queue length: 12, step degree: 10, num pairs: 5
Basis total mons: 538, average length: 67.250
Number of pair polynomials: 5, at 356 column(s), 0.000
Average length for reductees: 112.40 [5], reductors: 27.45 [98]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 98 = 103 rows / 398 columns out of 1001 (39.760%)
Density: 7.9329% / 11.264% (31.573/r), total: 3252 (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 (40.0%), min deg: 9 [1], av deg: 9.5
Degree counts: 9:1 10:1
Queue insertion time: 0.000
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 10, queue length: 16, step degree: 10, num pairs: 2
Basis total mons: 850, average length: 85.000
Number of pair polynomials: 2, at 212 column(s), 0.000
Average length for reductees: 122.00 [2], reductors: 22.90 [42]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 42 = 44 rows / 237 columns out of 1001 (23.676%)
Density: 11.565% / 15.957% (27.409/r), total: 1206 (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: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 4 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 11, queue length: 17, step degree: 11, num pairs: 4
Basis total mons: 1029, average length: 93.545
Number of pair polynomials: 4, at 432 column(s), 0.000
Average length for reductees: 184.50 [4], reductors: 26.07 [127]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 127 = 131 rows / 470 columns out of 1365 (34.432%)
Density: 6.5763% / 9.5451% (30.908/r), total: 4049 (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 (50.0%), min deg: 10 [2], av deg: 10.0
Degree counts: 10:2
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: 13, queue length: 21, step degree: 11, num pairs: 3
Basis total mons: 1499, average length: 115.308
Number of pair polynomials: 3, at 497 column(s), 0.000
Average length for reductees: 234.67 [3], reductors: 32.13 [163]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 163 = 166 rows / 549 columns out of 1365 (40.220%)
Density: 6.5201% / 9.397% (35.795/r), total: 5942 (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 (33.3%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 6 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 14, queue length: 21, step degree: 12, num pairs: 7
Basis total mons: 1811, average length: 129.357
Number of pair polynomials: 7, at 768 column(s), 0.000
Average length for reductees: 261.43 [7], reductors: 36.44 [296]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 296 = 303 rows / 852 columns out of 1820 (46.813%)
Density: 4.887% / 7.2771% (41.637/r), total: 12616 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000[r] + 0.000 = 0.000[r] [6]
After ech memory: 32.1MB (=max)
Num new polynomials: 6 (85.7%), min deg: 11 [3], av deg: 11.5
Degree counts: 11:3 12:3
Queue insertion time: 0.000
New max step: 7, time: 0.003[r]
Step 7 time: 0.003[r], [0.003], mat/total: 0.010/0.007[r], mem: 32.1MB (=max)

*******
STEP 8
Basis length: 20, queue length: 35, step degree: 12, num pairs: 9
Basis total mons: 4266, average length: 213.300
Number of pair polynomials: 9, at 965 column(s), 0.000
Average length for reductees: 410.44 [9], reductors: 43.62 [395]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 395 = 404 rows / 1022 columns out of 1820 (56.154%)
Density: 5.068% / 7.3491% (51.795/r), total: 20925 (0.1MB)
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 (66.7%), min deg: 11 [3], av deg: 11.5
Degree counts: 11:3 12:3
Queue insertion time: 0.000[r]
Step 8 time: 0.003[r], [0.003], mat/total: 0.010/0.010[r], mem: 32.1MB (=max)

*******
STEP 9
Basis length: 26, queue length: 51, step degree: 12, num pairs: 5
Basis total mons: 7102, average length: 273.154
Number of pair polynomials: 5, at 954 column(s), 0.000
Average length for reductees: 419.80 [5], reductors: 46.59 [421]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 421 = 426 rows / 1060 columns out of 1820 (58.242%)
Density: 4.8084% / 7.0399% (50.969/r), total: 21713 (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 (60.0%), min deg: 11 [1], av deg: 11.7
Degree counts: 11:1 12:2
Queue insertion time: 0.000
Step 9 time: 0.000, [0.003], mat/total: 0.010/0.013[r], mem: 32.1MB (=max)

*******
STEP 10
Basis length: 29, queue length: 58, step degree: 12, num pairs: 2
Basis total mons: 8651, average length: 298.310
Number of pair polynomials: 2, at 840 column(s), 0.000
Average length for reductees: 465.00 [2], reductors: 44.15 [396]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 396 = 398 rows / 1004 columns out of 1820 (55.165%)
Density: 4.6085% / 6.8283% (46.269/r), total: 18415 (0.1MB)
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: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.003], mat/total: 0.010/0.016[r], mem: 32.1MB (=max)

*******
STEP 11
Basis length: 30, queue length: 60, step degree: 13, num pairs: 35
Basis total mons: 9118, average length: 303.933
4 pairs eliminated
Number of pair polynomials: 31, at 1433 column(s), 0.000
Average length for reductees: 479.39 [31], reductors: 55.72 [790]
Symbolic reduction time: 0.001[r], column sort time: 0.000
31 + 790 = 821 rows / 1559 columns out of 2380 (65.504%)
Density: 4.6005% / 6.5583% (71.721/r), total: 58883 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [19]
After ech memory: 32.1MB (=max)
Num new polynomials: 19 (61.3%), min deg: 11 [2], av deg: 11.9
Degree counts: 11:2 12:17
Queue insertion time: 0.000
New max step: 11, time: 0.009[r]
Step 11 time: 0.009[r], [0.010], mat/total: 0.010/0.026[r], mem: 32.1MB (=max)

*******
STEP 12
Basis length: 49, queue length: 89, step degree: 12, num pairs: 6
Basis total mons: 20304, average length: 414.367
Number of pair polynomials: 6, at 1174 column(s), 0.000
Average length for reductees: 599.17 [6], reductors: 59.94 [597]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 597 = 603 rows / 1328 columns out of 1820 (72.967%)
Density: 4.9176% / 7.0413% (65.305/r), total: 39379 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.002[r] + 0.000 = 0.002[r] [5]
After ech memory: 32.1MB (=max)
Num new polynomials: 5 (83.3%), min deg: 11 [2], av deg: 11.6
Degree counts: 11:2 12:3
Queue insertion time: 0.000
Step 12 time: 0.006[r], [0.007], mat/total: 0.020/0.033[r], mem: 32.1MB (=max)

*******
STEP 13
Basis length: 54, queue length: 102, step degree: 12, num pairs: 8
Basis total mons: 23390, average length: 433.148
Number of pair polynomials: 8, at 1167 column(s), 0.000
Average length for reductees: 546.00 [8], reductors: 71.60 [549]
Symbolic reduction time: 0.000, column sort time: 0.000
8 + 549 = 557 rows / 1281 columns out of 1820 (70.385%)
Density: 6.1211% / 8.3397% (78.411/r), total: 43675 (0.2MB)
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 (62.5%), min deg: 11 [3], av deg: 11.4
Degree counts: 11:3 12:2
Queue insertion time: 0.000
Step 13 time: 0.000, [0.009], mat/total: 0.020/0.040, mem: 32.1MB (=max)

*******
STEP 14
Basis length: 59, queue length: 112, step degree: 12, num pairs: 11
Basis total mons: 26555, average length: 450.085
Number of pair polynomials: 11, at 1266 column(s), 0.000
Average length for reductees: 618.91 [11], reductors: 78.70 [660]
Symbolic reduction time: 0.000, column sort time: 0.000
11 + 660 = 671 rows / 1421 columns out of 1820 (78.077%)
Density: 6.1616% / 8.357% (87.556/r), total: 58750 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [9]
After ech memory: 32.1MB (=max)
Num new polynomials: 9 (81.8%), min deg: 11 [4], av deg: 11.6
Degree counts: 11:4 12:5
Queue insertion time: 0.000
Step 14 time: 0.008[r], [0.008], mat/total: 0.020/0.050, mem: 32.1MB (=max)

*******
STEP 15
Basis length: 68, queue length: 133, step degree: 12, num pairs: 13
Basis total mons: 32818, average length: 482.618
Number of pair polynomials: 13, at 1303 column(s), 0.000
Average length for reductees: 668.62 [13], reductors: 84.50 [689]
Symbolic reduction time: 0.000, column sort time: 0.000
13 + 689 = 702 rows / 1451 columns out of 1820 (79.725%)
Density: 6.5689% / 8.7872% (95.315/r), total: 66911 (0.3MB)
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 (84.6%), min deg: 11 [1], av deg: 11.9
Degree counts: 11:1 12:10
Queue insertion time: 0.000
Step 15 time: 0.000, [0.010], mat/total: 0.020/0.050, mem: 32.1MB (=max)

*******
STEP 16
Basis length: 79, queue length: 157, step degree: 12, num pairs: 3
Basis total mons: 40834, average length: 516.886
Number of pair polynomials: 3, at 1304 column(s), 0.000
Average length for reductees: 706.00 [3], reductors: 90.85 [687]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 687 = 690 rows / 1452 columns out of 1820 (79.780%)
Density: 6.4412% / 8.7081% (93.526/r), total: 64533 (0.2MB)
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: 12 [3], av deg: 12.0
Degree counts: 12:3
Queue insertion time: 0.000
Step 16 time: 0.000, [0.010], mat/total: 0.020/0.060, mem: 32.1MB (=max)

*******
STEP 17
Basis length: 82, queue length: 166, step degree: 13, num pairs: 121
Basis total mons: 43086, average length: 525.439
18 pairs eliminated
Number of pair polynomials: 103, at 1834 column(s), 0.000
Average length for reductees: 659.11 [103], reductors: 98.67 [1130]
Symbolic reduction time: 0.003[r], column sort time: 0.000
103 + 1130 = 1233 rows / 1936 columns out of 2380 (81.345%)
Density: 7.515% / 9.8258% (145.49/r), total: 179389 (0.7MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.010 + 0.000 = 0.010 [39]
After ech memory: 32.1MB (=max)
Num new polynomials: 39 (37.9%), min deg: 11 [20], av deg: 11.5
Degree counts: 11:20 12:17 13:2
Queue insertion time: 0.000
New max step: 17, time: 0.020
Step 17 time: 0.020, [0.025], mat/total: 0.030/0.080, mem: 32.1MB (=max)

*******
STEP 18
Basis length: 121, queue length: 156, step degree: 12, num pairs: 75
Basis total mons: 71156, average length: 588.066
Number of pair polynomials: 75, at 1426 column(s), 0.002[r]
Average length for reductees: 706.27 [75], reductors: 130.64 [783]
Symbolic reduction time: 0.000, column sort time: 0.000
75 + 783 = 858 rows / 1546 columns out of 1820 (84.945%)
Density: 11.705% / 14.17% (180.95/r), total: 155259 (0.6MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.009[r] + 0.000 = 0.009[r] [22]
After ech memory: 32.1MB (=max)
Num new polynomials: 22 (29.3%), min deg: 11 [13], av deg: 11.4
Degree counts: 11:13 12:9
Queue insertion time: 0.000
Step 18 time: 0.019[r], [0.019], mat/total: 0.040/0.100, mem: 32.1MB (=max)

*******
STEP 19
Basis length: 143, queue length: 149, step degree: 12, num pairs: 49
Basis total mons: 86712, average length: 606.378
Number of pair polynomials: 49, at 1354 column(s), 0.000
Average length for reductees: 692.55 [49], reductors: 132.03 [736]
Symbolic reduction time: 0.004[r], column sort time: 0.000
49 + 736 = 785 rows / 1471 columns out of 1820 (80.824%)
Density: 11.354% / 13.878% (167.02/r), total: 131112 (0.5MB)
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 (8.2%), min deg: 11 [2], av deg: 11.5
Degree counts: 11:2 12:2
Queue insertion time: 0.000
Step 19 time: 0.010, [0.014], mat/total: 0.040/0.110, mem: 32.1MB (=max)

*******
STEP 20
Basis length: 147, queue length: 115, step degree: 12, num pairs: 7
Basis total mons: 89593, average length: 609.476
Number of pair polynomials: 7, at 1331 column(s), 0.000
Average length for reductees: 716.43 [7], reductors: 137.63 [721]
Symbolic reduction time: 0.003[r], column sort time: 0.000
7 + 721 = 728 rows / 1452 columns out of 1820 (79.780%)
Density: 9.8618% / 12.471% (143.19/r), total: 104245 (0.4MB)
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 (14.3%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 20 time: 0.007[r], [0.008], mat/total: 0.040/0.120, mem: 32.1MB (=max)

*******
STEP 21
Basis length: 148, queue length: 111, step degree: 12, num pairs: 3
Basis total mons: 90323, average length: 610.291
Number of pair polynomials: 3, at 1351 column(s), 0.000
Average length for reductees: 730.00 [3], reductors: 148.53 [781]
Symbolic reduction time: 0.005[r], column sort time: 0.000
3 + 781 = 784 rows / 1514 columns out of 1820 (83.187%)
Density: 9.9576% / 12.697% (150.76/r), total: 118194 (0.5MB)
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 (66.7%), min deg: 11 [1], av deg: 11.5
Degree counts: 11:1 12:1
Queue insertion time: 0.000
Step 21 time: 0.010, [0.014], mat/total: 0.040/0.130, mem: 32.1MB (=max)

*******
STEP 22
Basis length: 150, queue length: 115, step degree: 12, num pairs: 3
Basis total mons: 91784, average length: 611.893
Number of pair polynomials: 3, at 1353 column(s), 0.000
Average length for reductees: 730.00 [3], reductors: 150.64 [784]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 784 = 787 rows / 1518 columns out of 1820 (83.407%)
Density: 10.069% / 12.832% (152.84/r), total: 120289 (0.5MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000[r]
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (66.7%), min deg: 11 [1], av deg: 11.5
Degree counts: 11:1 12:1
Queue insertion time: 0.000
Step 22 time: 0.010, [0.014], mat/total: 0.050/0.140, mem: 32.1MB (=max)

*******
STEP 23
Basis length: 152, queue length: 119, step degree: 12, num pairs: 4
Basis total mons: 93248, average length: 613.474
Number of pair polynomials: 4, at 1358 column(s), 0.000
Average length for reductees: 731.00 [4], reductors: 153.31 [788]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 788 = 792 rows / 1522 columns out of 1820 (83.626%)
Density: 10.265% / 13.049% (156.23/r), total: 123734 (0.5MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.003[r] + 0.000 = 0.003[r] [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (75.0%), min deg: 11 [1], av deg: 11.7
Degree counts: 11:1 12:2
Queue insertion time: 0.000
Step 23 time: 0.010, [0.013], mat/total: 0.060/0.150, mem: 32.1MB (=max)

*******
STEP 24
Basis length: 155, queue length: 120, step degree: 12, num pairs: 4
Basis total mons: 95442, average length: 615.755
Number of pair polynomials: 4, at 1355 column(s), 0.000
Average length for reductees: 731.00 [4], reductors: 153.35 [788]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 788 = 792 rows / 1519 columns out of 1820 (83.462%)
Density: 10.288% / 13.064% (156.27/r), total: 123765 (0.5MB)
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 (50.0%), min deg: 11 [1], av deg: 11.5
Degree counts: 11:1 12:1
Queue insertion time: 0.000
Step 24 time: 0.000, [0.015], mat/total: 0.060/0.150, mem: 32.1MB (=max)

*******
STEP 25
Basis length: 157, queue length: 120, step degree: 12, num pairs: 3
Basis total mons: 96902, average length: 617.210
Number of pair polynomials: 3, at 1348 column(s), 0.000
Average length for reductees: 730.00 [3], reductors: 156.28 [792]
Symbolic reduction time: 0.003[r], column sort time: 0.000
3 + 792 = 795 rows / 1521 columns out of 1820 (83.571%)
Density: 10.417% / 13.208% (158.45/r), total: 125964 (0.5MB)
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 25 time: 0.010, [0.012], mat/total: 0.060/0.160, mem: 32.1MB (=max)

*******
STEP 26
Basis length: 157, queue length: 117, step degree: 13, num pairs: 64
Basis total mons: 96902, average length: 617.210
11 pairs eliminated
Number of pair polynomials: 53, at 1906 column(s), 0.000
Average length for reductees: 725.81 [53], reductors: 152.37 [1293]
Symbolic reduction time: 0.004[r], column sort time: 0.000
53 + 1293 = 1346 rows / 2022 columns out of 2380 (84.958%)
Density: 8.6522% / 11.769% (174.95/r), total: 235478 (0.9MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.009[r] + 0.000 = 0.009[r] [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 26 time: 0.019[r], [0.020], mat/total: 0.070/0.180, mem: 32.1MB (=max)

*******
STEP 27
Basis length: 157, queue length: 53, step degree: 14, num pairs: 28
Basis total mons: 96902, average length: 617.210
28 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 28
Basis length: 157, queue length: 25, step degree: 15, num pairs: 13
Basis total mons: 96902, average length: 617.210
13 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 29
Basis length: 157, queue length: 12, step degree: 16, num pairs: 10
Basis total mons: 96902, average length: 617.210
10 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 30
Basis length: 157, queue length: 2, step degree: 17, num pairs: 2
Basis total mons: 96902, average length: 617.210
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 157 final polynomial(s) by 157
9 redundant polynomial(s) removed; time: 0.000
Interreduce 107 (out of range [0 .. 156] = 157) polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
107 + 497 = 604 rows / 1333 columns
Density: 11.047% / 13.723% (147.25/r), total: 88939 (0.3MB)
Row sort time: 0.000
[5 threads]
0.002[r] + 0.000 = 0.002[r] [107]
Total reduction time: 0.008[r]
Reduction time: 0.011[r]
Final number of polynomials: 148

Final basis length: 107
Number of pairs: 418
Max step: 17, time: 0.020
Max num entries matrix: 1346 by 2022
Max num rows matrix: 1346 by 2022
Approx mat cost: 7.82151e+07, sym red cost: 1.92885e+06
Total pair setup time: 0.010
Total symbolic reduction time: 0.070
Total column sort time: 0.000
Total row sort time: 0.010
Total matrix time: 0.070
Total new polys time: 0.000
Total queue update time: 0.010
Total Faugere F4 time: 0.200, real time: 0.245
Time: 0.200
dregs = [ 10, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 12, 12, 12, 12, 12, 13, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 17 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=3)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 4
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 107
Try rep mat lex method; E: S0100
Get rep mat (dim: 729)
Rep mat time: 0.096[r]
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 1.418[r]
Get kernel for min poly
Kernel mat time: 0.319
Nullity: 1
Get relations for all variables
REDUCE 4 polynomial(s) by 107 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.026[r]
4 + 760 = 764 rows / 1489 columns
Density: 11.219% / 14.147% (167.06/r), total: 127631 (0.5MB)
Row sort time: 0.000
0.000 = 0.000 [4]
Total reduction time: 0.050
Reduction time: 0.060
Relations time: 0.387[r]
Time: 2.270
unideg = 729
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=3)
Time: 0.060
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=3)
nsols_mult = 1
====================================================================================================
n_r: 4, n_v: 5, n_e: 5, mdeg: 8
degs = [7, 7, 7, 8, 5]
Multivariate Polynomial Ring in Y0000, S0400, S0300, S0200, S0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=4)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(65537)
Rank: 5
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Modular FP
Datum size: 4
No queue sort
Initial length: 5
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 7

*******
STEP 1
Basis length: 5, queue length: 7, step degree: 9, num pairs: 1
Basis total mons: 246, average length: 49.200
Number of pair polynomials: 1, at 163 column(s), 0.000
Average length for reductees: 47.00 [1], reductors: 54.36 [25]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 25 = 26 rows / 302 columns out of 2002 (15.085%)
Density: 17.906% / 20.209% (54.077/r), total: 1406 (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: 8 [1], av deg: 8.0
Degree counts: 8:1
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: 6, queue length: 7, step degree: 11, num pairs: 3
Basis total mons: 358, average length: 59.667
Number of pair polynomials: 3, at 198 column(s), 0.000
Average length for reductees: 47.00 [3], reductors: 26.32 [94]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 94 = 97 rows / 597 columns out of 4368 (13.668%)
Density: 4.5157% / 6.006% (26.959/r), total: 2615 (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: 9 [1], av deg: 9.7
Degree counts: 9:1 10:2
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: 9, queue length: 17, step degree: 10, num pairs: 2
Basis total mons: 1066, average length: 118.444
Number of pair polynomials: 2, at 378 column(s), 0.000
Average length for reductees: 217.00 [2], reductors: 32.91 [46]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 46 = 48 rows / 439 columns out of 3003 (14.619%)
Density: 9.2445% / 11.361% (40.583/r), total: 1948 (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: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 10, queue length: 20, step degree: 11, num pairs: 5
Basis total mons: 1353, average length: 135.300
Number of pair polynomials: 5, at 802 column(s), 0.000
Average length for reductees: 245.00 [5], reductors: 45.58 [137]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 137 = 142 rows / 907 columns out of 4368 (20.765%)
Density: 5.8% / 7.4115% (52.606/r), total: 7470 (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 (40.0%), min deg: 10 [1], av deg: 10.5
Degree counts: 10:1 11:1
Queue insertion time: 0.000
Step 4 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 12, queue length: 26, step degree: 11, num pairs: 2
Basis total mons: 2059, average length: 171.583
Number of pair polynomials: 2, at 460 column(s), 0.000
Average length for reductees: 264.00 [2], reductors: 36.29 [55]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 55 = 57 rows / 521 columns out of 4368 (11.928%)
Density: 8.4992% / 10.509% (44.281/r), total: 2524 (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: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 6
Basis length: 13, queue length: 28, step degree: 12, num pairs: 5
Basis total mons: 2468, average length: 189.846
Number of pair polynomials: 5, at 1109 column(s), 0.000
Average length for reductees: 362.80 [5], reductors: 53.75 [224]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 224 = 229 rows / 1312 columns out of 6188 (21.202%)
Density: 4.6111% / 5.8838% (60.498/r), total: 13854 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.000[r] + 0.000 = 0.000[r] [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (40.0%), min deg: 11 [2], av deg: 11.0
Degree counts: 11:2
Queue insertion time: 0.000
New max step: 6, time: 0.007[r]
Step 6 time: 0.007[r], [0.008], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 15, queue length: 33, step degree: 12, num pairs: 3
Basis total mons: 3618, average length: 241.200
Number of pair polynomials: 3, at 1195 column(s), 0.000
Average length for reductees: 572.00 [3], reductors: 58.13 [240]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 240 = 243 rows / 1320 columns out of 6188 (21.332%)
Density: 4.8846% / 6.3277% (64.477/r), total: 15668 (0.1MB)
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 (33.3%), min deg: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 7 time: 0.000, [0.008], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 8
Basis length: 16, queue length: 34, step degree: 13, num pairs: 9
Basis total mons: 4413, average length: 275.812
Number of pair polynomials: 9, at 2004 column(s), 0.000
Average length for reductees: 462.78 [9], reductors: 57.57 [554]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 554 = 563 rows / 2293 columns out of 8568 (26.762%)
Density: 2.7931% / 3.8648% (64.046/r), total: 36058 (0.1MB)
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 (88.9%), min deg: 12 [5], av deg: 12.4
Degree counts: 12:5 13:3
Queue insertion time: 0.000
New max step: 8, time: 0.010
Step 8 time: 0.009, [0.012], mat/total: 0.020/0.020, mem: 32.1MB (=max)

*******
STEP 9
Basis length: 24, queue length: 73, step degree: 13, num pairs: 9
Basis total mons: 11317, average length: 471.542
Number of pair polynomials: 9, at 2804 column(s), 0.000
Average length for reductees: 917.33 [9], reductors: 76.85 [717]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 717 = 726 rows / 2983 columns out of 8568 (34.816%)
Density: 2.9257% / 3.9674% (87.273/r), total: 63360 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.004[r] + 0.000 = 0.004[r] [4]
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (44.4%), min deg: 12 [1], av deg: 12.8
Degree counts: 12:1 13:3
Queue insertion time: 0.000
New max step: 9, time: 0.010
Step 9 time: 0.010, [0.017], mat/total: 0.030/0.030, mem: 32.1MB (=max)

*******
STEP 10
Basis length: 28, queue length: 84, step degree: 13, num pairs: 1
Basis total mons: 17655, average length: 630.536
Number of pair polynomials: 1, at 1408 column(s), 0.000
Average length for reductees: 1377.00 [1], reductors: 76.02 [465]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 465 = 466 rows / 2172 columns out of 8568 (25.350%)
Density: 3.6287% / 4.8483% (78.815/r), total: 36728 (0.1MB)
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: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.012], mat/total: 0.030/0.030, mem: 32.1MB (=max)

*******
STEP 11
Basis length: 29, queue length: 90, step degree: 13, num pairs: 2
Basis total mons: 19066, average length: 657.448
Number of pair polynomials: 2, at 2426 column(s), 0.000
Average length for reductees: 1411.00 [2], reductors: 84.43 [706]
Symbolic reduction time: 0.003[r], column sort time: 0.000[r]
2 + 706 = 708 rows / 2816 columns out of 8568 (32.866%)
Density: 3.1314% / 4.2173% (88.179/r), total: 62431 (0.2MB)
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: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
New max step: 11, time: 0.014[r]
Step 11 time: 0.014[r], [0.015], mat/total: 0.030/0.050, mem: 32.1MB (=max)

*******
STEP 12
Basis length: 30, queue length: 93, step degree: 14, num pairs: 28
Basis total mons: 20474, average length: 682.467
3 pairs eliminated
Number of pair polynomials: 25, at 4313 column(s), 0.000
Average length for reductees: 1212.56 [25], reductors: 92.44 [1675]
Symbolic reduction time: 0.007[r], column sort time: 0.000
25 + 1675 = 1700 rows / 4913 columns out of 11628 (42.251%)
Density: 2.2167% / 3.0481% (108.91/r), total: 185144 (0.7MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.010 + 0.000 = 0.010 [13]
After ech memory: 32.1MB (=max)
Num new polynomials: 13 (52.0%), min deg: 13 [10], av deg: 13.2
Degree counts: 13:10 14:3
Queue insertion time: 0.000
New max step: 12, time: 0.020
Step 12 time: 0.020, [0.030], mat/total: 0.040/0.070, mem: 32.1MB (=max)

*******
STEP 13
Basis length: 43, queue length: 137, step degree: 14, num pairs: 28
Basis total mons: 41653, average length: 968.674
Number of pair polynomials: 28, at 4633 column(s), 0.002[r]
Average length for reductees: 1397.25 [28], reductors: 108.13 [1797]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
28 + 1797 = 1825 rows / 5278 columns out of 11628 (45.390%)
Density: 2.4234% / 3.2471% (127.91/r), total: 233433 (0.9MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.010 + 0.000 = 0.010 [11]
After ech memory: 32.1MB (=max)
Num new polynomials: 11 (39.3%), min deg: 13 [2], av deg: 13.8
Degree counts: 13:2 14:9
Queue insertion time: 0.000
New max step: 13, time: 0.030
Step 13 time: 0.029, [0.034], mat/total: 0.050/0.100, mem: 32.1MB (=max)

*******
STEP 14
Basis length: 54, queue length: 161, step degree: 14, num pairs: 6
Basis total mons: 62391, average length: 1155.389
Number of pair polynomials: 6, at 2894 column(s), 0.000
Average length for reductees: 1295.00 [6], reductors: 103.88 [1050]
Symbolic reduction time: 0.005[r], column sort time: 0.000
6 + 1050 = 1056 rows / 3588 columns out of 11628 (30.857%)
Density: 3.0839% / 4.0747% (110.65/r), total: 116848 (0.4MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.008[r] + 0.000 = 0.009[r] [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 14 time: 0.019[r], [0.021], mat/total: 0.060/0.120, mem: 32.1MB (=max)

*******
STEP 15
Basis length: 54, queue length: 155, step degree: 15, num pairs: 60
Basis total mons: 62391, average length: 1155.389
6 pairs eliminated
Number of pair polynomials: 54, at 6942 column(s), 0.000
Average length for reductees: 1763.52 [54], reductors: 127.50 [3086]
Symbolic reduction time: 0.018[r], column sort time: 0.004[r]
54 + 3086 = 3140 rows / 7614 columns out of 15504 (49.110%)
Density: 2.0441% / 2.7759% (155.63/r), total: 488692 (1.9MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
[5 threads]
0.040 + 0.000 = 0.040 [30]
After ech memory: 32.1MB, max: 40.2MB
Num new polynomials: 30 (55.6%), min deg: 13 [1], av deg: 14.3
Degree counts: 13:1 14:20 15:9
Queue insertion time: 0.000
New max step: 15, time: 0.070
Step 15 time: 0.069, [0.078], mat/total: 0.100/0.189, mem: 32.1MB, max: 40.2MB

*******
STEP 16
Basis length: 84, queue length: 241, step degree: 14, num pairs: 3
Basis total mons: 135571, average length: 1613.940
Number of pair polynomials: 3, at 2154 column(s), 0.000
Average length for reductees: 973.00 [3], reductors: 101.88 [709]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 709 = 712 rows / 3893 columns out of 11628 (33.480%)
Density: 2.7113% / 3.8973% (105.55/r), total: 75152 (0.3MB)
Before ech memory: 32.1MB, max: 40.2MB
Row sort time: 0.000[r]
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB, max: 40.2MB
Num new polynomials: 2 (66.7%), min deg: 14 [2], av deg: 14.0
Degree counts: 14:2
Queue insertion time: 0.000
Step 16 time: 0.010, [0.017], mat/total: 0.110/0.200, mem: 32.1MB, max: 40.2MB

*******
STEP 17
Basis length: 86, queue length: 247, step degree: 15, num pairs: 76
Basis total mons: 139807, average length: 1625.663
Number of pair polynomials: 76, at 8126 column(s), 0.009[r]
Average length for reductees: 2268.17 [76], reductors: 159.24 [3901]
Symbolic reduction time: 0.030, column sort time: 0.004[r]
76 + 3901 = 3977 rows / 9028 columns out of 15504 (58.230%)
Density: 2.2102% / 2.9386% (199.54/r), total: 793576 (3.0MB)
Before ech memory: 32.1MB, max: 40.2MB
Row sort time: 0.000
[5 threads]
0.080 + 0.000 = 0.080 [33]
After ech memory: 32.1MB, max: 41.8MB
Num new polynomials: 33 (43.4%), min deg: 14 [20], av deg: 14.4
Degree counts: 14:20 15:13
Queue insertion time: 0.003[r]
New max step: 17, time: 0.138[r]
Step 17 time: 0.138[r], [0.139], mat/total: 0.190/0.339, mem: 32.1MB, max: 41.8MB

*******
STEP 18
Basis length: 119, queue length: 323, step degree: 15, num pairs: 71
Basis total mons: 247740, average length: 2081.849
Number of pair polynomials: 71, at 8721 column(s), 0.010
Average length for reductees: 3066.13 [71], reductors: 194.01 [4366]
Symbolic reduction time: 0.039[r], column sort time: 0.000
71 + 4366 = 4437 rows / 9751 columns out of 15504 (62.893%)
Density: 2.461% / 3.2041% (239.97/r), total: 1064741 (4.1MB)
Before ech memory: 32.1MB, max: 41.8MB
Row sort time: 0.000
[5 threads]
0.100 + 0.000 = 0.100 [33]
After ech memory: 32.1MB, max: 42.5MB
Num new polynomials: 33 (46.5%), min deg: 14 [15], av deg: 14.5
Degree counts: 14:15 15:18
Queue insertion time: 0.004[r]
New max step: 18, time: 0.160
Step 18 time: 0.160, [0.173], mat/total: 0.290/0.500, mem: 32.1MB, max: 42.5MB

*******
STEP 19
Basis length: 152, queue length: 414, step degree: 15, num pairs: 57
Basis total mons: 370880, average length: 2440.000
Number of pair polynomials: 57, at 8860 column(s), 0.010
Average length for reductees: 3591.35 [57], reductors: 222.94 [4400]
Symbolic reduction time: 0.040, column sort time: 0.004[r]
57 + 4400 = 4457 rows / 9942 columns out of 15504 (64.125%)
Density: 2.6757% / 3.4364% (266.02/r), total: 1185658 (4.5MB)
Before ech memory: 32.1MB, max: 42.5MB
Row sort time: 0.000
[5 threads]
0.116[r] + 0.000[r] = 0.116[r] [34]
After ech memory: 32.1MB, max: 42.7MB
Num new polynomials: 34 (59.6%), min deg: 14 [13], av deg: 14.6
Degree counts: 14:13 15:21
Queue insertion time: 0.000
New max step: 19, time: 0.190
Step 19 time: 0.189, [0.194], mat/total: 0.420/0.690, mem: 32.1MB, max: 42.7MB

*******
STEP 20
Basis length: 186, queue length: 527, step degree: 15, num pairs: 36
Basis total mons: 516254, average length: 2775.559
Number of pair polynomials: 36, at 9236 column(s), 0.010
Average length for reductees: 3829.25 [36], reductors: 259.46 [4826]
Symbolic reduction time: 0.065[r], column sort time: 0.006[r]
36 + 4826 = 4862 rows / 10536 columns out of 15504 (67.957%)
Density: 2.7134% / 3.4852% (285.89/r), total: 1389986 (5.3MB)
Before ech memory: 32.1MB, max: 42.7MB
Row sort time: 0.000
[5 threads]
0.099 + 0.000 = 0.099 [24]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 24 (66.7%), min deg: 14 [1], av deg: 15.0
Degree counts: 14:1 15:23
Queue insertion time: 0.006[r]
New max step: 20, time: 0.200
Step 20 time: 0.200, [0.202], mat/total: 0.520/0.890, mem: 64.1MB, max: 75.4MB

*******
STEP 21
Basis length: 210, queue length: 604, step degree: 15, num pairs: 5
Basis total mons: 627661, average length: 2988.862
Number of pair polynomials: 5, at 7376 column(s), 0.000
Average length for reductees: 3721.00 [5], reductors: 225.06 [3410]
Symbolic reduction time: 0.040, column sort time: 0.005[r]
5 + 3410 = 3415 rows / 8663 columns out of 15504 (55.876%)
Density: 2.657% / 3.4488% (230.18/r), total: 786053 (3.0MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000
[5 threads]
0.030 + 0.000 = 0.030 [4]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 4 (80.0%), min deg: 14 [3], av deg: 14.2
Degree counts: 14:3 15:1
Queue insertion time: 0.000
Step 21 time: 0.080, [0.094], mat/total: 0.550/0.970, mem: 64.1MB, max: 75.4MB

*******
STEP 22
Basis length: 214, queue length: 617, step degree: 15, num pairs: 13
Basis total mons: 645741, average length: 3017.481
Number of pair polynomials: 13, at 8871 column(s), 0.003[r]
Average length for reductees: 4368.54 [13], reductors: 277.04 [4434]
Symbolic reduction time: 0.060, column sort time: 0.000
13 + 4434 = 4447 rows / 10095 columns out of 15504 (65.112%)
Density: 2.8628% / 3.6562% (289/r), total: 1285174 (4.9MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000
[5 threads]
0.049 + 0.000 = 0.049 [11]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 11 (84.6%), min deg: 14 [2], av deg: 14.8
Degree counts: 14:2 15:9
Queue insertion time: 0.000
Step 22 time: 0.140, [0.141], mat/total: 0.610/1.110, mem: 64.1MB, max: 75.4MB

*******
STEP 23
Basis length: 225, queue length: 649, step degree: 15, num pairs: 7
Basis total mons: 698081, average length: 3102.582
Number of pair polynomials: 7, at 8700 column(s), 0.000
Average length for reductees: 4567.57 [7], reductors: 290.80 [4439]
Symbolic reduction time: 0.068[r], column sort time: 0.000
7 + 4439 = 4446 rows / 10106 columns out of 15504 (65.183%)
Density: 2.9441% / 3.745% (297.53/r), total: 1322820 (5.0MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000
[5 threads]
0.050 + 0.000 = 0.050 [7]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 7 (100.0%), min deg: 14 [1], av deg: 14.9
Degree counts: 14:1 15:6
Queue insertion time: 0.000
Step 23 time: 0.120, [0.137], mat/total: 0.660/1.230, mem: 64.1MB, max: 75.4MB

*******
STEP 24
Basis length: 232, queue length: 676, step degree: 15, num pairs: 3
Basis total mons: 733281, average length: 3160.694
Number of pair polynomials: 3, at 8205 column(s), 0.001[r]
Average length for reductees: 4470.00 [3], reductors: 284.79 [4192]
Symbolic reduction time: 0.059, column sort time: 0.000
3 + 4192 = 4195 rows / 9778 columns out of 15504 (63.068%)
Density: 2.9432% / 3.7381% (287.78/r), total: 1207249 (4.6MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000
[5 threads]
0.048[r] + 0.000 = 0.048[r] [3]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 3 (100.0%), min deg: 14 [1], av deg: 14.7
Degree counts: 14:1 15:2
Queue insertion time: 0.000
Step 24 time: 0.119, [0.124], mat/total: 0.710/1.349, mem: 64.1MB, max: 75.4MB

*******
STEP 25
Basis length: 235, queue length: 690, step degree: 15, num pairs: 5
Basis total mons: 747617, average length: 3181.349
Number of pair polynomials: 5, at 8644 column(s), 0.002[r]
Average length for reductees: 4443.00 [5], reductors: 295.78 [4363]
Symbolic reduction time: 0.066[r], column sort time: 0.000
5 + 4363 = 4368 rows / 10016 columns out of 15504 (64.603%)
Density: 3.0005% / 3.8014% (300.53/r), total: 1312706 (5.0MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000[r]
[5 threads]
0.040 + 0.000 = 0.040 [4]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 4 (80.0%), min deg: 14 [2], av deg: 14.5
Degree counts: 14:2 15:2
Queue insertion time: 0.000
Step 25 time: 0.130, [0.132], mat/total: 0.760/1.480, mem: 64.1MB, max: 75.4MB

*******
STEP 26
Basis length: 239, queue length: 704, step degree: 15, num pairs: 10
Basis total mons: 766627, average length: 3207.644
Number of pair polynomials: 10, at 8953 column(s), 0.000
Average length for reductees: 4520.00 [10], reductors: 303.83 [4554]
Symbolic reduction time: 0.069[r], column sort time: 0.006[r]
10 + 4554 = 4564 rows / 10315 columns out of 15504 (66.531%)
Density: 3.0351% / 3.8449% (313.07/r), total: 1428849 (5.5MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.000
[5 threads]
0.049 + 0.000 = 0.049 [6]
After ech memory: 64.1MB, max: 75.4MB
Num new polynomials: 6 (60.0%), min deg: 15 [6], av deg: 15.0
Degree counts: 15:6
Queue insertion time: 0.003[r]
Step 26 time: 0.139, [0.144], mat/total: 0.810/1.620, mem: 64.1MB, max: 75.4MB

*******
STEP 27
Basis length: 245, queue length: 720, step degree: 16, num pairs: 487
Basis total mons: 798005, average length: 3257.163
58 pairs eliminated
Number of pair polynomials: 429, at 14170 column(s), 0.095[r]
Average length for reductees: 4179.09 [429], reductors: 340.58 [8394]
Symbolic reduction time: 0.110, column sort time: 0.007[r]
429 + 8394 = 8823 rows / 14937 columns out of 20349 (73.404%)
Density: 3.5296% / 4.3948% (527.22/r), total: 4651671 (17.7MB)
Before ech memory: 64.1MB, max: 75.4MB
Row sort time: 0.003[r]
[5 threads]
1.180 + 0.009 = 1.190 [120]
After ech memory: 64.1MB, max: 80.1MB
Num new polynomials: 120 (28.0%), min deg: 14 [1], av deg: 15.2
Degree counts: 14:1 15:90 16:29
Queue insertion time: 0.020
New max step: 27, time: 1.440
Step 27 time: 1.440, [1.448], mat/total: 2.010/3.060, mem: 64.1MB, max: 80.1MB

*******
STEP 28
Basis length: 365, queue length: 743, step degree: 15, num pairs: 5
Basis total mons: 1436813, average length: 3936.474
Number of pair polynomials: 5, at 7482 column(s), 0.001[r]
Average length for reductees: 3845.00 [5], reductors: 228.17 [3429]
Symbolic reduction time: 0.029, column sort time: 0.003[r]
5 + 3429 = 3434 rows / 8779 columns out of 15504 (56.624%)
Density: 2.659% / 3.4515% (233.44/r), total: 801622 (3.1MB)
Before ech memory: 64.1MB, max: 80.1MB
Row sort time: 0.000
[5 threads]
0.019 + 0.000 = 0.019 [1]
After ech memory: 64.1MB, max: 80.1MB
Num new polynomials: 1 (20.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.002[r]
Step 28 time: 0.079, [0.081], mat/total: 2.030/3.139, mem: 64.1MB, max: 80.1MB

*******
STEP 29
Basis length: 366, queue length: 743, step degree: 15, num pairs: 4
Basis total mons: 1441589, average length: 3938.768
Number of pair polynomials: 4, at 8849 column(s), 0.000
Average length for reductees: 4776.00 [4], reductors: 350.64 [4823]
Symbolic reduction time: 0.090, column sort time: 0.000
4 + 4823 = 4827 rows / 10687 columns out of 15504 (68.931%)
Density: 3.3153% / 4.135% (354.31/r), total: 1710256 (6.5MB)
Before ech memory: 64.1MB, max: 80.1MB
Row sort time: 0.000
[5 threads]
0.059[r] + 0.000 = 0.059[r] [3]
After ech memory: 64.1MB, max: 80.1MB
Num new polynomials: 3 (75.0%), min deg: 14 [1], av deg: 14.7
Degree counts: 14:1 15:2
Queue insertion time: 0.000
Step 29 time: 0.160, [0.165], mat/total: 2.100/3.299, mem: 64.1MB, max: 80.1MB

*******
STEP 30
Basis length: 369, queue length: 753, step degree: 15, num pairs: 5
Basis total mons: 1456056, average length: 3945.951
Number of pair polynomials: 5, at 9365 column(s), 0.000
Average length for reductees: 4816.00 [5], reductors: 370.24 [4986]
Symbolic reduction time: 0.089, column sort time: 0.005[r]
5 + 4986 = 4991 rows / 10882 columns out of 15504 (70.188%)
Density: 3.4432% / 4.2703% (374.69/r), total: 1870086 (7.1MB)
Before ech memory: 64.1MB, max: 80.1MB
Row sort time: 0.000
[5 threads]
0.069[r] + 0.000 = 0.069[r] [5]
After ech memory: 64.1MB, max: 80.1MB
Num new polynomials: 5 (100.0%), min deg: 15 [5], av deg: 15.0
Degree counts: 15:5
Queue insertion time: 0.000
Step 30 time: 0.169, [0.177], mat/total: 2.170/3.469, mem: 64.1MB, max: 80.1MB

*******
STEP 31
Basis length: 374, queue length: 772, step degree: 16, num pairs: 401
Basis total mons: 1482818, average length: 3964.754
4 pairs eliminated
Number of pair polynomials: 397, at 14253 column(s), 0.104[r]
Average length for reductees: 5202.24 [397], reductors: 452.18 [9017]
Symbolic reduction time: 0.148[r], column sort time: 0.000
397 + 9017 = 9414 rows / 15634 columns out of 20349 (76.829%)
Density: 4.1736% / 5.138% (652.5/r), total: 6142602 (23.4MB)
Before ech memory: 64.1MB, max: 80.1MB
Row sort time: 0.003[r]
[5 threads]
1.550 + 0.009 = 1.560 [112]
After ech memory: 64.1MB, max: 80.8MB
Num new polynomials: 112 (28.2%), min deg: 14 [4], av deg: 15.2
Degree counts: 14:4 15:84 16:24
Queue insertion time: 0.029
New max step: 31, time: 1.860
Step 31 time: 1.860, [1.868], mat/total: 3.740/5.330, mem: 64.1MB, max: 80.8MB

*******
STEP 32
Basis length: 486, queue length: 853, step degree: 15, num pairs: 20
Basis total mons: 2115694, average length: 4353.280
Number of pair polynomials: 20, at 9498 column(s), 0.006[r]
Average length for reductees: 4797.85 [20], reductors: 411.46 [5199]
Symbolic reduction time: 0.099[r], column sort time: 0.000
20 + 5199 = 5219 rows / 11116 columns out of 15504 (71.698%)
Density: 3.8527% / 4.6917% (428.27/r), total: 2235139 (8.5MB)
Before ech memory: 64.1MB, max: 80.8MB
Row sort time: 0.000
[5 threads]
0.081[r] + 0.000 = 0.081[r] [4]
After ech memory: 64.1MB, max: 80.8MB
Num new polynomials: 4 (20.0%), min deg: 14 [1], av deg: 14.8
Degree counts: 14:1 15:3
Queue insertion time: 0.000
Step 32 time: 0.199, [0.204], mat/total: 3.830/5.529, mem: 64.1MB, max: 80.8MB

*******
STEP 33
Basis length: 490, queue length: 853, step degree: 15, num pairs: 5
Basis total mons: 2136114, average length: 4359.416
Number of pair polynomials: 5, at 9627 column(s), 0.000
Average length for reductees: 4991.00 [5], reductors: 417.52 [5294]
Symbolic reduction time: 0.116[r], column sort time: 0.000
5 + 5294 = 5299 rows / 11252 columns out of 15504 (72.575%)
Density: 3.749% / 4.5911% (421.84/r), total: 2235321 (8.5MB)
Before ech memory: 64.1MB, max: 80.8MB
Row sort time: 0.000
[5 threads]
0.078[r] + 0.000 = 0.080 [1]
After ech memory: 64.1MB, max: 80.8MB
Num new polynomials: 1 (20.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.002[r]
Step 33 time: 0.210, [0.213], mat/total: 3.910/5.740, mem: 64.1MB, max: 80.8MB

*******
STEP 34
Basis length: 491, queue length: 853, step degree: 16, num pairs: 369
Basis total mons: 2141944, average length: 4362.411
Number of pair polynomials: 369, at 14633 column(s), 0.116[r]
Average length for reductees: 5589.66 [369], reductors: 551.89 [9415]
Symbolic reduction time: 0.180, column sort time: 0.009[r]
369 + 9415 = 9784 rows / 16118 columns out of 20349 (79.208%)
Density: 4.6028% / 5.653% (741.89/r), total: 7258616 (27.7MB)
Before ech memory: 64.1MB, max: 80.8MB
Row sort time: 0.000
[5 threads]
1.789[r] + 0.008[r] = 1.799[r] [81]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 81 (22.0%), min deg: 15 [52], av deg: 15.4
Degree counts: 15:52 16:29
Queue insertion time: 0.030
New max step: 34, time: 2.140
Step 34 time: 2.140, [2.197], mat/total: 5.710/7.880, mem: 96.2MB, max: 113.4MB

*******
STEP 35
Basis length: 572, queue length: 808, step degree: 16, num pairs: 233
Basis total mons: 2628243, average length: 4594.830
Number of pair polynomials: 233, at 13584 column(s), 0.080
Average length for reductees: 5938.82 [233], reductors: 607.22 [9120]
Symbolic reduction time: 0.218[r], column sort time: 0.000
233 + 9120 = 9353 rows / 15778 columns out of 20349 (77.537%)
Density: 4.6903% / 5.7674% (740.04/r), total: 6921596 (26.4MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
1.270 + 0.000 = 1.270 [90]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 90 (38.6%), min deg: 15 [48], av deg: 15.5
Degree counts: 15:48 16:42
Queue insertion time: 0.034[r]
Step 35 time: 1.619, [1.630], mat/total: 6.980/9.500, mem: 96.2MB, max: 113.4MB

*******
STEP 36
Basis length: 662, queue length: 974, step degree: 16, num pairs: 204
Basis total mons: 3187530, average length: 4815.000
Number of pair polynomials: 204, at 14024 column(s), 0.070
Average length for reductees: 6113.55 [204], reductors: 655.27 [9440]
Symbolic reduction time: 0.250, column sort time: 0.008[r]
204 + 9440 = 9644 rows / 16068 columns out of 20349 (78.962%)
Density: 4.7967% / 5.9121% (770.73/r), total: 7432928 (28.4MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
1.367[r] + 0.006[r] = 1.374[r] [67]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 67 (32.8%), min deg: 15 [23], av deg: 15.7
Degree counts: 15:23 16:44
Queue insertion time: 0.029[r]
Step 36 time: 1.740, [1.741], mat/total: 8.360/11.240, mem: 96.2MB, max: 113.4MB

*******
STEP 37
Basis length: 729, queue length: 1069, step degree: 16, num pairs: 95
Basis total mons: 3610623, average length: 4952.844
Number of pair polynomials: 95, at 12730 column(s), 0.029
Average length for reductees: 6201.62 [95], reductors: 724.84 [9175]
Symbolic reduction time: 0.250, column sort time: 0.008[r]
95 + 9175 = 9270 rows / 15781 columns out of 20349 (77.552%)
Density: 4.9488% / 6.0928% (780.97/r), total: 7239551 (27.6MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
0.750 + 0.001[r] = 0.756[r] [25]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 25 (26.3%), min deg: 15 [13], av deg: 15.5
Degree counts: 15:13 16:12
Queue insertion time: 0.009
Step 37 time: 1.060, [1.070], mat/total: 9.120/12.300, mem: 96.2MB, max: 113.4MB

*******
STEP 38
Basis length: 754, queue length: 1084, step degree: 16, num pairs: 52
Basis total mons: 3771145, average length: 5001.519
Number of pair polynomials: 52, at 12633 column(s), 0.026[r]
Average length for reductees: 6385.40 [52], reductors: 744.99 [9377]
Symbolic reduction time: 0.310, column sort time: 0.007[r]
52 + 9377 = 9429 rows / 16002 columns out of 20349 (78.638%)
Density: 4.85% / 6.0128% (776.09/r), total: 7317772 (27.9MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
0.419 + 0.000 = 0.419 [33]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 33 (63.5%), min deg: 15 [6], av deg: 15.8
Degree counts: 15:6 16:27
Queue insertion time: 0.016[r]
Step 38 time: 0.790, [0.798], mat/total: 9.540/13.090, mem: 96.2MB, max: 113.4MB

*******
STEP 39
Basis length: 787, queue length: 1170, step degree: 16, num pairs: 29
Basis total mons: 3984403, average length: 5062.774
Number of pair polynomials: 29, at 12015 column(s), 0.009
Average length for reductees: 6447.93 [29], reductors: 762.04 [9191]
Symbolic reduction time: 0.300, column sort time: 0.008[r]
29 + 9191 = 9220 rows / 15785 columns out of 20349 (77.571%)
Density: 4.9409% / 6.1123% (779.93/r), total: 7190931 (27.4MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
0.424[r] + 0.000 = 0.427[r] [20]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 20 (69.0%), min deg: 15 [4], av deg: 15.8
Degree counts: 15:4 16:16
Queue insertion time: 0.009[r]
Step 39 time: 0.759, [0.771], mat/total: 9.970/13.849, mem: 96.2MB, max: 113.4MB

*******
STEP 40
Basis length: 807, queue length: 1234, step degree: 16, num pairs: 20
Basis total mons: 4113864, average length: 5097.725
Number of pair polynomials: 20, at 12553 column(s), 0.010
Average length for reductees: 6418.25 [20], reductors: 756.93 [9153]
Symbolic reduction time: 0.312[r], column sort time: 0.007[r]
20 + 9153 = 9173 rows / 15732 columns out of 20349 (77.311%)
Density: 4.8899% / 6.0558% (769.27/r), total: 7056558 (26.9MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.000
[5 threads]
0.232[r] + 0.000 = 0.233[r] [11]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 11 (55.0%), min deg: 15 [2], av deg: 15.8
Degree counts: 15:2 16:9
Queue insertion time: 0.000
Step 40 time: 0.579[r], [0.581], mat/total: 10.210/14.430, mem: 96.2MB, max: 113.4MB

*******
STEP 41
Basis length: 818, queue length: 1263, step degree: 16, num pairs: 10
Basis total mons: 4185227, average length: 5116.414
Number of pair polynomials: 10, at 12012 column(s), 0.006[r]
Average length for reductees: 6391.00 [10], reductors: 734.27 [8808]
Symbolic reduction time: 0.276[r], column sort time: 0.000
10 + 8808 = 8818 rows / 15368 columns out of 20349 (75.522%)
Density: 4.8197% / 5.9623% (740.69/r), total: 6531382 (24.9MB)
Before ech memory: 96.2MB, max: 113.4MB
Row sort time: 0.003[r]
[5 threads]
0.179 + 0.000 = 0.179 [5]
After ech memory: 96.2MB, max: 113.4MB
Num new polynomials: 5 (50.0%), min deg: 16 [5], av deg: 16.0
Degree counts: 16:5
Queue insertion time: 0.003[r]
Step 41 time: 0.486[r], [0.487], mat/total: 10.400/14.919, mem: 96.2MB, max: 113.4MB

*******
STEP 42
Basis length: 823, queue length: 1273, step degree: 17, num pairs: 912
Basis total mons: 4217710, average length: 5124.800
225 pairs eliminated
Number of pair polynomials: 690, at 18681 column(s), 0.250
Average length for reductees: 6289.11 [690], reductors: 782.65 [14327]
Symbolic reduction time: 0.429, column sort time: 0.010
690 + 14327 = 15017 rows / 20944 columns out of 26334 (79.532%)
Density: 4.9449% / 6.3301% (1035.7/r), total: 15552564 (59.3MB)
Before ech memory: 128.2MB (=max)
Row sort time: 0.005[r]
[5 threads]
6.380 + 0.000 = 6.380 [34]
After ech memory: 160.2MB, max: 182.6MB
Num new polynomials: 34 (4.9%), min deg: 15 [3], av deg: 16.1
Degree counts: 15:3 16:25 17:6
Queue insertion time: 0.017[r]
New max step: 42, time: 7.100
Step 42 time: 7.100, [7.110], mat/total: 16.790/22.020, mem: 160.2MB, max: 182.6MB

*******
STEP 43
Basis length: 857, queue length: 496, step degree: 16, num pairs: 14
Basis total mons: 4439512, average length: 5180.294
Number of pair polynomials: 14, at 11995 column(s), 0.006[r]
Average length for reductees: 6480.93 [14], reductors: 781.62 [9124]
Symbolic reduction time: 0.300, column sort time: 0.008[r]
14 + 9124 = 9138 rows / 15682 columns out of 20349 (77.065%)
Density: 5.0398% / 6.2101% (790.35/r), total: 7222203 (27.6MB)
Before ech memory: 160.2MB, max: 182.6MB
Row sort time: 0.000
[5 threads]
0.230 + 0.000 = 0.231[r] [0]
After ech memory: 160.2MB, max: 182.6MB
No new polynomials
Queue insertion time: 0.000
Step 43 time: 0.559, [0.564], mat/total: 17.030/22.579, mem: 160.2MB, max: 182.6MB

*******
STEP 44
Basis length: 857, queue length: 482, step degree: 17, num pairs: 107
Basis total mons: 4439512, average length: 5180.294
Number of pair polynomials: 107, at 15760 column(s), 0.049[r]
Average length for reductees: 6518.86 [107], reductors: 816.21 [14420]
Symbolic reduction time: 0.509, column sort time: 0.009[r]
107 + 14420 = 14527 rows / 21019 columns out of 26334 (79.817%)
Density: 4.0831% / 5.4905% (858.22/r), total: 12467321 (47.6MB)
Before ech memory: 160.2MB, max: 182.6MB
Row sort time: 0.000
[5 threads]
1.240 + 0.000 = 1.250 [26]
After ech memory: 160.2MB, max: 182.7MB
Num new polynomials: 26 (24.3%), min deg: 16 [20], av deg: 16.2
Degree counts: 16:20 17:6
Queue insertion time: 0.009
Step 44 time: 1.829, [1.847], mat/total: 18.280/24.409, mem: 160.2MB, max: 182.7MB

*******
STEP 45
Basis length: 883, queue length: 470, step degree: 17, num pairs: 91
Basis total mons: 4609681, average length: 5220.477
Number of pair polynomials: 91, at 15709 column(s), 0.040
Average length for reductees: 6541.30 [91], reductors: 824.28 [14144]
Symbolic reduction time: 0.498[r], column sort time: 0.009[r]
91 + 14144 = 14235 rows / 20716 columns out of 26334 (78.666%)
Density: 4.1554% / 5.5535% (860.83/r), total: 12253852 (46.7MB)
Before ech memory: 160.2MB, max: 182.7MB
Row sort time: 0.005[r]
[5 threads]
1.281[r] + 0.000 = 1.282[r] [10]
After ech memory: 160.2MB, max: 182.7MB
Num new polynomials: 10 (11.0%), min deg: 16 [8], av deg: 16.2
Degree counts: 16:8 17:2
Queue insertion time: 0.000
Step 45 time: 1.848[r], [1.850], mat/total: 19.580/26.259, mem: 160.2MB, max: 182.7MB

*******
STEP 46
Basis length: 893, queue length: 416, step degree: 17, num pairs: 35
Basis total mons: 4675081, average length: 5235.253
Number of pair polynomials: 35, at 13779 column(s), 0.016[r]
Average length for reductees: 6535.66 [35], reductors: 821.16 [14104]
Symbolic reduction time: 0.480, column sort time: 0.009[r]
35 + 14104 = 14139 rows / 20668 columns out of 26334 (78.484%)
Density: 4.0415% / 5.4444% (835.3/r), total: 11810336 (45.1MB)
Before ech memory: 160.2MB, max: 182.7MB
Row sort time: 0.004[r]
[5 threads]
0.618[r] + 0.000 = 0.619[r] [3]
After ech memory: 160.2MB, max: 182.7MB
Num new polynomials: 3 (8.6%), min deg: 16 [3], av deg: 16.0
Degree counts: 16:3
Queue insertion time: 0.000
Step 46 time: 1.140, [1.141], mat/total: 20.210/27.399, mem: 160.2MB, max: 182.7MB

*******
STEP 47
Basis length: 896, queue length: 393, step degree: 17, num pairs: 12
Basis total mons: 4694745, average length: 5239.671
Number of pair polynomials: 12, at 12926 column(s), 0.006[r]
Average length for reductees: 6554.67 [12], reductors: 824.59 [14228]
Symbolic reduction time: 0.520, column sort time: 0.009
12 + 14228 = 14240 rows / 20789 columns out of 26334 (78.944%)
Density: 3.9897% / 5.4003% (829.42/r), total: 11810952 (45.1MB)
Before ech memory: 160.2MB, max: 182.7MB
Row sort time: 0.005[r]
[5 threads]
0.379 + 0.000 = 0.379 [0]
After ech memory: 160.2MB, max: 182.7MB
No new polynomials
Queue insertion time: 0.000
Step 47 time: 0.929, [0.941], mat/total: 20.600/28.329, mem: 160.2MB, max: 182.7MB

*******
STEP 48
Basis length: 896, queue length: 381, step degree: 18, num pairs: 194
Basis total mons: 4694745, average length: 5239.671
188 pairs eliminated
Number of pair polynomials: 6, at 15381 column(s), 0.000
Average length for reductees: 6372.00 [6], reductors: 808.03 [16732]
Symbolic reduction time: 0.601[r], column sort time: 0.010
6 + 16732 = 16738 rows / 23293 columns out of 33649 (69.223%)
Density: 3.4775% / 4.9442% (810.02/r), total: 13558113 (51.7MB)
Before ech memory: 160.2MB, max: 182.7MB
Row sort time: 0.006[r]
[5 threads]
0.419 + 0.000 = 0.419 [0]
After ech memory: 160.2MB, max: 185.1MB
No new polynomials
Queue insertion time: 0.000
Step 48 time: 1.049[r], [1.051], mat/total: 21.030/29.379, mem: 160.2MB, max: 185.1MB

*******
STEP 49
Basis length: 896, queue length: 187, step degree: 19, num pairs: 96
Basis total mons: 4694745, average length: 5239.671
96 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 50
Basis length: 896, queue length: 91, step degree: 20, num pairs: 62
Basis total mons: 4694745, average length: 5239.671
62 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 51
Basis length: 896, queue length: 29, step degree: 21, num pairs: 25
Basis total mons: 4694745, average length: 5239.671
25 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 52
Basis length: 896, queue length: 4, step degree: 22, num pairs: 4
Basis total mons: 4694745, average length: 5239.671
4 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 896 final polynomial(s) by 896
51 redundant polynomial(s) removed; time: 0.000
Interreduce 754 (out of range [0 .. 895] = 896) polynomial(s)
Symbolic reduction time: 0.298[r]
Column sort time: 0.000
754 + 8168 = 8922 rows / 15483 columns
Density: 5.0471% / 6.2023% (781.44/r), total: 6971990 (26.6MB)
Row sort time: 0.003[r]
[5 threads]
0.467[r] + 0.000 = 0.470 [754]
Total reduction time: 0.839
Reduction time: 1.100
Final number of polynomials: 845

Final basis length: 754
Number of pairs: 3270
Max step: 42, time: 7.100
Max num entries matrix: 16738 by 23293
Max num rows matrix: 16738 by 23293
Approx mat cost: 3.77967e+10, sym red cost: 1.81364e+08
Total pair setup time: 1.050
Total symbolic reduction time: 6.750
Total column sort time: 0.230
Total row sort time: 0.110
Total matrix time: 21.030
Total new polys time: 0.030
Total queue update time: 0.260
Total Faugere F4 time: 30.609, real time: 30.947
Time: 30.610
dregs = [ 9, 11, 10, 11, 11, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 15, 15, 15, 16, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 16, 17, 17, 17, 17, 18, 19, 20, 21, 22 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=4)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(65537)
Rank: 5
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 754
Try rep mat lex method; E: S0100
Get rep mat (dim: 6561)
Rep mat time: 142.389
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 766.070
Get kernel for min poly
Kernel mat time: 38.009
Nullity: 1
Get relations for all variables
REDUCE 5 polynomial(s) by 754 polynomial(s)
Symbolic reduction time: 2.399
Column sort time: 0.009
5 + 12975 = 12980 rows / 19536 columns
Density: 8.2656% / 10.287% (1614.8/r), total: 20959587 (80.0MB)
Row sort time: 0.003[r]
0.648[r] = 0.648[r] [5]
Number of unused reductors: 74
Total reduction time: 3.069
Reduction time: 3.069
Relations time: 41.959
Time: 988.500
unideg = 6561
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=4)
Time: 0.230
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=4)
nsols_mult = 1
====================================================================================================
n_r: 5, n_v: 6, n_e: 6, mdeg: 10
degs = [7, 7, 7, 8, 10, 6]
Multivariate Polynomial Ring in Y0000, S0500, S0400, S0300, S0200, S0100 over Finite Field of size 65537
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=5)
********************
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: 8

*******
STEP 1
Basis length: 6, queue length: 8, step degree: 10, num pairs: 2
Basis total mons: 733, average length: 122.167
Number of pair polynomials: 2, at 604 column(s), 0.000
Average length for reductees: 267.00 [2], reductors: 102.86 [28]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 28 = 30 rows / 768 columns out of 8008 (9.590%)
Density: 14.818% / 16.092% (113.8/r), total: 3414 (0.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 2 (100.0%), min deg: 9 [2], av deg: 9.0
Degree counts: 9:2
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.005], mat/total: 0.000/0.000, mem: 192.2MB, max: 1565.5MB

*******
STEP 2
Basis length: 8, queue length: 9, step degree: 10, num pairs: 1
Basis total mons: 1235, average length: 154.375
Number of pair polynomials: 1, at 390 column(s), 0.000
Average length for reductees: 259.00 [1], reductors: 120.56 [18]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 18 = 19 rows / 534 columns out of 8008 (6.668%)
Density: 23.94% / 24.904% (127.84/r), total: 2429 (0.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 1 (100.0%), min deg: 8 [1], av deg: 8.0
Degree counts: 8:1
Queue insertion time: 0.000
Step 2 time: 0.000, [0.005], mat/total: 0.000/0.000, mem: 192.2MB, max: 1565.5MB

*******
STEP 3
Basis length: 9, queue length: 10, step degree: 12, num pairs: 3
Basis total mons: 1408, average length: 156.444
Number of pair polynomials: 3, at 342 column(s), 0.000
Average length for reductees: 95.00 [3], reductors: 29.94 [166]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 166 = 169 rows / 1219 columns out of 18564 (6.566%)
Density: 2.5508% / 3.1925% (31.095/r), total: 5255 (0.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [3]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 3 (100.0%), min deg: 10 [1], av deg: 10.7
Degree counts: 10:1 11:2
Queue insertion time: 0.000
Step 3 time: 0.000, [0.006], mat/total: 0.000/0.000, mem: 192.2MB, max: 1565.5MB

*******
STEP 4
Basis length: 12, queue length: 23, step degree: 11, num pairs: 2
Basis total mons: 2860, average length: 238.333
Number of pair polynomials: 2, at 774 column(s), 0.000
Average length for reductees: 445.00 [2], reductors: 43.91 [70]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 70 = 72 rows / 907 columns out of 12376 (7.329%)
Density: 6.0701% / 7.0057% (55.056/r), total: 3964 (0.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 1 (50.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
New max step: 4, time: 0.005[r]
Step 4 time: 0.005[r], [0.005], mat/total: 0.000/0.009, mem: 192.2MB, max: 1565.5MB

*******
STEP 5
Basis length: 13, queue length: 27, step degree: 12, num pairs: 5
Basis total mons: 3453, average length: 265.615
Number of pair polynomials: 5, at 1669 column(s), 0.000
Average length for reductees: 504.20 [5], reductors: 61.92 [206]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 206 = 211 rows / 1903 columns out of 18564 (10.251%)
Density: 3.8044% / 4.5345% (72.398/r), total: 15276 (0.1MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [2]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 2 (40.0%), min deg: 11 [1], av deg: 11.5
Degree counts: 11:1 12:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.008], mat/total: 0.000/0.009, mem: 192.2MB, max: 1565.5MB

*******
STEP 6
Basis length: 15, queue length: 35, step degree: 12, num pairs: 2
Basis total mons: 4933, average length: 328.867
Number of pair polynomials: 2, at 956 column(s), 0.000
Average length for reductees: 548.00 [2], reductors: 50.17 [81]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 81 = 83 rows / 1089 columns out of 18564 (5.866%)
Density: 5.7088% / 6.5919% (62.169/r), total: 5160 (0.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 1 (50.0%), min deg: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 6 time: 0.000, [0.006], mat/total: 0.000/0.009, mem: 192.2MB, max: 1565.5MB

*******
STEP 7
Basis length: 16, queue length: 38, step degree: 13, num pairs: 9
Basis total mons: 5796, average length: 362.250
Number of pair polynomials: 9, at 2875 column(s), 0.000
Average length for reductees: 493.22 [9], reductors: 80.87 [572]
Symbolic reduction time: 0.003[r], column sort time: 0.000
9 + 572 = 581 rows / 3758 columns out of 27132 (13.851%)
Density: 2.322% / 2.7913% (87.26/r), total: 50698 (0.2MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [5]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 5 (55.6%), min deg: 12 [5], av deg: 12.0
Degree counts: 12:5
Queue insertion time: 0.000
New max step: 7, time: 0.010
Step 7 time: 0.009, [0.013], mat/total: 0.000/0.019, mem: 192.2MB, max: 1565.5MB

*******
STEP 8
Basis length: 21, queue length: 71, step degree: 13, num pairs: 3
Basis total mons: 9432, average length: 449.143
Number of pair polynomials: 3, at 2586 column(s), 0.000
Average length for reductees: 1233.00 [3], reductors: 79.89 [362]
Symbolic reduction time: 0.000, column sort time: 0.000[r]
3 + 362 = 365 rows / 2853 columns out of 27132 (10.515%)
Density: 3.1325% / 3.7597% (89.37/r), total: 32620 (0.1MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [1]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 1 (33.3%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 8 time: 0.009[r], [0.011], mat/total: 0.000/0.029, mem: 192.2MB, max: 1565.5MB

*******
STEP 9
Basis length: 22, queue length: 73, step degree: 14, num pairs: 16
Basis total mons: 11162, average length: 507.364
1 pair eliminated
Number of pair polynomials: 15, at 5133 column(s), 0.000
Average length for reductees: 769.20 [15], reductors: 88.41 [1044]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
15 + 1044 = 1059 rows / 5884 columns out of 38760 (15.181%)
Density: 1.6665% / 2.1136% (98.058/r), total: 103843 (0.4MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.000 + 0.000 = 0.000 [8]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 8 (53.3%), min deg: 13 [3], av deg: 13.6
Degree counts: 13:3 14:5
Queue insertion time: 0.001[r]
New max step: 9, time: 0.020
Step 9 time: 0.019, [0.021], mat/total: 0.000/0.049, mem: 192.2MB, max: 1565.5MB

*******
STEP 10
Basis length: 30, queue length: 100, step degree: 14, num pairs: 9
Basis total mons: 27955, average length: 931.833
Number of pair polynomials: 9, at 6466 column(s), 0.000
Average length for reductees: 2208.89 [9], reductors: 106.07 [1267]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
9 + 1267 = 1276 rows / 7359 columns out of 38760 (18.986%)
Density: 1.6429% / 2.0916% (120.9/r), total: 154272 (0.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.009[r] + 0.000 = 0.009[r] [6]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 6 (66.7%), min deg: 13 [1], av deg: 13.8
Degree counts: 13:1 14:5
Queue insertion time: 0.000
Step 10 time: 0.019, [0.026], mat/total: 0.010/0.069, mem: 192.2MB, max: 1565.5MB

*******
STEP 11
Basis length: 36, queue length: 130, step degree: 14, num pairs: 2
Basis total mons: 45830, average length: 1273.056
Number of pair polynomials: 2, at 2731 column(s), 0.000
Average length for reductees: 1328.00 [2], reductors: 90.32 [645]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 645 = 647 rows / 3984 columns out of 38760 (10.279%)
Density: 2.3631% / 2.9377% (94.147/r), total: 60913 (0.2MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.003[r] + 0.000 = 0.003[r] [0]
After ech memory: 192.2MB, max: 1565.5MB
No new polynomials
Queue insertion time: 0.000
Step 11 time: 0.009, [0.014], mat/total: 0.020/0.079, mem: 192.2MB, max: 1565.5MB

*******
STEP 12
Basis length: 36, queue length: 128, step degree: 15, num pairs: 31
Basis total mons: 45830, average length: 1273.056
3 pairs eliminated
Number of pair polynomials: 28, at 10136 column(s), 0.000
Average length for reductees: 2623.25 [28], reductors: 127.99 [2650]
Symbolic reduction time: 0.016[r], column sort time: 0.000
28 + 2650 = 2678 rows / 11305 columns out of 54264 (20.833%)
Density: 1.3629% / 1.7432% (154.08/r), total: 412616 (1.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.029 + 0.000 = 0.029 [16]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 16 (57.1%), min deg: 14 [14], av deg: 14.1
Degree counts: 14:14 15:2
Queue insertion time: 0.000
New max step: 12, time: 0.050
Step 12 time: 0.049, [0.064], mat/total: 0.050/0.129, mem: 192.2MB, max: 1565.5MB

*******
STEP 13
Basis length: 52, queue length: 202, step degree: 15, num pairs: 37
Basis total mons: 98656, average length: 1897.231
Number of pair polynomials: 37, at 11996 column(s), 0.006[r]
Average length for reductees: 3059.22 [37], reductors: 149.53 [3599]
Symbolic reduction time: 0.019, column sort time: 0.006[r]
37 + 3599 = 3636 rows / 13992 columns out of 54264 (25.785%)
Density: 1.2803% / 1.6173% (179.14/r), total: 651337 (2.5MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.055[r] + 0.000 = 0.056[r] [14]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 14 (37.8%), min deg: 14 [6], av deg: 14.6
Degree counts: 14:6 15:8
Queue insertion time: 0.000
New max step: 13, time: 0.100
Step 13 time: 0.100, [0.102], mat/total: 0.110/0.230, mem: 192.2MB, max: 1565.5MB

*******
STEP 14
Basis length: 66, queue length: 251, step degree: 15, num pairs: 18
Basis total mons: 158350, average length: 2399.242
Number of pair polynomials: 18, at 10759 column(s), 0.000
Average length for reductees: 3296.11 [18], reductors: 160.70 [2908]
Symbolic reduction time: 0.023[r], column sort time: 0.000
18 + 2908 = 2926 rows / 12483 columns out of 54264 (23.004%)
Density: 1.4419% / 1.8061% (179.99/r), total: 526640 (2.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.036[r] + 0.000 = 0.036[r] [5]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 5 (27.8%), min deg: 14 [1], av deg: 14.8
Degree counts: 14:1 15:4
Queue insertion time: 0.000
Step 14 time: 0.069, [0.075], mat/total: 0.150/0.299, mem: 192.2MB, max: 1565.5MB

*******
STEP 15
Basis length: 71, queue length: 273, step degree: 15, num pairs: 3
Basis total mons: 177225, average length: 2496.127
Number of pair polynomials: 3, at 5962 column(s), 0.000
Average length for reductees: 3368.00 [3], reductors: 123.98 [1148]
Symbolic reduction time: 0.008[r], column sort time: 0.000
3 + 1148 = 1151 rows / 6747 columns out of 54264 (12.434%)
Density: 1.9629% / 2.4344% (132.44/r), total: 152433 (0.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.007[r] + 0.000 = 0.008[r] [0]
After ech memory: 192.2MB, max: 1565.5MB
No new polynomials
Queue insertion time: 0.000
Step 15 time: 0.019, [0.027], mat/total: 0.160/0.319, mem: 192.2MB, max: 1565.5MB

*******
STEP 16
Basis length: 71, queue length: 270, step degree: 16, num pairs: 73
Basis total mons: 177225, average length: 2496.127
5 pairs eliminated
Number of pair polynomials: 68, at 19016 column(s), 0.009
Average length for reductees: 3873.68 [68], reductors: 177.91 [6823]
Symbolic reduction time: 0.059[r], column sort time: 0.009
68 + 6823 = 6891 rows / 21966 columns out of 74613 (29.440%)
Density: 0.97598% / 1.2596% (214.38/r), total: 1477324 (5.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.002[r]
[5 threads]
0.180 + 0.000 = 0.180 [37]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 37 (54.4%), min deg: 14 [1], av deg: 15.4
Degree counts: 14:1 15:20 16:16
Queue insertion time: 0.005[r]
New max step: 16, time: 0.280
Step 16 time: 0.279, [0.281], mat/total: 0.350/0.599, mem: 192.2MB, max: 1565.5MB

*******
STEP 17
Basis length: 108, queue length: 423, step degree: 15, num pairs: 3
Basis total mons: 395297, average length: 3660.157
Number of pair polynomials: 3, at 4766 column(s), 0.000
Average length for reductees: 2229.00 [3], reductors: 142.64 [1066]
Symbolic reduction time: 0.009[r], column sort time: 0.000
3 + 1066 = 1069 rows / 7362 columns out of 54264 (13.567%)
Density: 2.017% / 2.5487% (148.49/r), total: 158739 (0.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.009[r] + 0.000 = 0.009[r] [2]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 2 (66.7%), min deg: 15 [2], av deg: 15.0
Degree counts: 15:2
Queue insertion time: 0.000
Step 17 time: 0.019, [0.028], mat/total: 0.360/0.619, mem: 192.2MB, max: 1565.5MB

*******
STEP 18
Basis length: 110, queue length: 431, step degree: 16, num pairs: 76
Basis total mons: 400759, average length: 3643.264
Number of pair polynomials: 76, at 21277 column(s), 0.019
Average length for reductees: 5125.03 [76], reductors: 219.65 [7627]
Symbolic reduction time: 0.086[r], column sort time: 0.009
76 + 7627 = 7703 rows / 24786 columns out of 74613 (33.219%)
Density: 1.0814% / 1.3604% (268.05/r), total: 2064760 (7.9MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.002[r]
[5 threads]
0.349 + 0.000 = 0.349 [31]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 31 (40.8%), min deg: 15 [15], av deg: 15.5
Degree counts: 15:15 16:16
Queue insertion time: 0.005[r]
New max step: 18, time: 0.490
Step 18 time: 0.490, [0.497], mat/total: 0.720/1.109, mem: 192.2MB, max: 1565.5MB

*******
STEP 19
Basis length: 141, queue length: 546, step degree: 16, num pairs: 49
Basis total mons: 634969, average length: 4503.326
Number of pair polynomials: 49, at 25514 column(s), 0.019
Average length for reductees: 8012.94 [49], reductors: 268.92 [9078]
Symbolic reduction time: 0.158[r], column sort time: 0.013[r]
49 + 9078 = 9127 rows / 28704 columns out of 74613 (38.471%)
Density: 1.0817% / 1.3591% (310.5/r), total: 2833891 (10.8MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.250 + 0.002[r] = 0.257[r] [24]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 24 (49.0%), min deg: 15 [4], av deg: 15.8
Degree counts: 15:4 16:20
Queue insertion time: 0.000
Step 19 time: 0.460, [0.471], mat/total: 0.980/1.569, mem: 192.2MB, max: 1565.5MB

*******
STEP 20
Basis length: 165, queue length: 657, step degree: 16, num pairs: 13
Basis total mons: 872153, average length: 5285.776
Number of pair polynomials: 13, at 23111 column(s), 0.008[r]
Average length for reductees: 8483.15 [13], reductors: 267.11 [7596]
Symbolic reduction time: 0.119, column sort time: 0.009
13 + 7596 = 7609 rows / 26125 columns out of 74613 (35.014%)
Density: 1.0762% / 1.363% (281.15/r), total: 2139261 (8.2MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.134[r] + 0.000 = 0.136[r] [8]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 8 (61.5%), min deg: 16 [8], av deg: 16.0
Degree counts: 16:8
Queue insertion time: 0.000
Step 20 time: 0.289[r], [0.291], mat/total: 1.120/1.859, mem: 192.2MB, max: 1565.5MB

*******
STEP 21
Basis length: 173, queue length: 695, step degree: 17, num pairs: 284
Basis total mons: 961776, average length: 5559.399
33 pairs eliminated
Number of pair polynomials: 251, at 42063 column(s), 0.209[r]
Average length for reductees: 8143.14 [251], reductors: 334.97 [18398]
Symbolic reduction time: 0.509[r], column sort time: 0.027[r]
251 + 18398 = 18649 rows / 46678 columns out of 100947 (46.240%)
Density: 0.94277% / 1.1808% (440.07/r), total: 8206783 (31.3MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.006[r]
[5 threads]
1.970 + 0.007[r] = 1.980 [101]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 101 (40.2%), min deg: 15 [3], av deg: 16.4
Degree counts: 15:3 16:54 17:44
Queue insertion time: 0.026[r]
New max step: 21, time: 2.770
Step 21 time: 2.769, [2.775], mat/total: 3.110/4.629, mem: 192.2MB, max: 1565.5MB

*******
STEP 22
Basis length: 274, queue length: 961, step degree: 16, num pairs: 11
Basis total mons: 2355640, average length: 8597.226
Number of pair polynomials: 11, at 23824 column(s), 0.009
Average length for reductees: 10078.45 [11], reductors: 287.89 [7875]
Symbolic reduction time: 0.128[r], column sort time: 0.009
11 + 7875 = 7886 rows / 27239 columns out of 74613 (36.507%)
Density: 1.107% / 1.3968% (301.55/r), total: 2378005 (9.1MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.156[r] + 0.000 = 0.157[r] [2]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 2 (18.2%), min deg: 16 [2], av deg: 16.0
Degree counts: 16:2
Queue insertion time: 0.000
Step 22 time: 0.309, [0.324], mat/total: 3.270/4.939, mem: 192.2MB, max: 1565.5MB

*******
STEP 23
Basis length: 276, queue length: 963, step degree: 17, num pairs: 224
Basis total mons: 2379918, average length: 8622.891
Number of pair polynomials: 224, at 45465 column(s), 0.259
Average length for reductees: 12322.80 [224], reductors: 453.56 [20286]
Symbolic reduction time: 0.654[r], column sort time: 0.029
224 + 20286 = 20510 rows / 50644 columns out of 100947 (50.169%)
Density: 1.1515% / 1.398% (583.19/r), total: 11961151 (45.6MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.007[r]
[5 threads]
2.750 + 0.013[r] = 2.769 [80]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 80 (35.7%), min deg: 16 [23], av deg: 16.7
Degree counts: 16:23 17:57
Queue insertion time: 0.019
New max step: 23, time: 3.750
Step 23 time: 3.750, [3.763], mat/total: 6.050/8.689, mem: 192.2MB, max: 1565.5MB

*******
STEP 24
Basis length: 356, queue length: 1186, step degree: 17, num pairs: 99
Basis total mons: 3746800, average length: 10524.719
Number of pair polynomials: 99, at 45176 column(s), 0.129[r]
Average length for reductees: 14220.26 [99], reductors: 521.57 [20383]
Symbolic reduction time: 0.772[r], column sort time: 0.029
99 + 20383 = 20482 rows / 51616 columns out of 100947 (51.132%)
Density: 1.1388% / 1.3893% (587.79/r), total: 12039038 (45.9MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.006[r]
[5 threads]
1.727[r] + 0.005[r] = 1.734[r] [53]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 53 (53.5%), min deg: 16 [7], av deg: 16.9
Degree counts: 16:7 17:46
Queue insertion time: 0.019
Step 24 time: 2.703[r], [2.705], mat/total: 7.800/11.399, mem: 192.2MB, max: 1565.5MB

*******
STEP 25
Basis length: 409, queue length: 1425, step degree: 17, num pairs: 24
Basis total mons: 4686088, average length: 11457.428
Number of pair polynomials: 24, at 43117 column(s), 0.037[r]
Average length for reductees: 17063.75 [24], reductors: 538.13 [19726]
Symbolic reduction time: 0.850, column sort time: 0.029[r]
24 + 19726 = 19750 rows / 51832 columns out of 100947 (51.346%)
Density: 1.077% / 1.3248% (558.21/r), total: 11024633 (42.1MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.006[r]
[5 threads]
0.589 + 0.000 = 0.589 [16]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 16 (66.7%), min deg: 16 [1], av deg: 16.9
Degree counts: 16:1 17:15
Queue insertion time: 0.009[r]
Step 25 time: 1.529, [1.537], mat/total: 8.400/12.929, mem: 192.2MB, max: 1565.5MB

*******
STEP 26
Basis length: 425, queue length: 1504, step degree: 17, num pairs: 3
Basis total mons: 5015978, average length: 11802.301
Number of pair polynomials: 3, at 34627 column(s), 0.006[r]
Average length for reductees: 20635.67 [3], reductors: 560.58 [16236]
Symbolic reduction time: 0.840, column sort time: 0.028[r]
3 + 16236 = 16239 rows / 47099 columns out of 100947 (46.657%)
Density: 1.1981% / 1.4626% (564.29/r), total: 9163470 (35.0MB)
Before ech memory: 192.2MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.541[r] + 0.000 = 0.542[r] [3]
After ech memory: 192.2MB, max: 1565.5MB
Num new polynomials: 3 (100.0%), min deg: 17 [3], av deg: 17.0
Degree counts: 17:3
Queue insertion time: 0.000
Step 26 time: 1.430, [1.439], mat/total: 8.950/14.359, mem: 192.2MB, max: 1565.5MB

*******
STEP 27
Basis length: 428, queue length: 1519, step degree: 18, num pairs: 803
Basis total mons: 5089972, average length: 11892.458
69 pairs eliminated
Number of pair polynomials: 734, at 72733 column(s), 1.299
Average length for reductees: 16789.82 [734], reductors: 644.48 [37507]
Symbolic reduction time: 1.799, column sort time: 0.045[r]
734 + 37507 = 38241 rows / 78201 columns out of 134596 (58.101%)
Density: 1.2204% / 1.467% (954.38/r), total: 36496283 (139.2MB)
Before ech memory: 288.3MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
20.349 + 0.125[r] = 20.490 [257]
After ech memory: 320.4MB, max: 1565.5MB
Num new polynomials: 257 (35.0%), min deg: 16 [4], av deg: 17.3
Degree counts: 16:4 17:163 18:90
Queue insertion time: 0.118[r]
New max step: 27, time: 23.770
Step 27 time: 23.769, [23.788], mat/total: 29.450/38.129, mem: 320.4MB, max: 1565.5MB

*******
STEP 28
Basis length: 685, queue length: 2097, step degree: 17, num pairs: 12
Basis total mons: 11374313, average length: 16604.836
Number of pair polynomials: 12, at 41247 column(s), 0.009
Average length for reductees: 15182.08 [12], reductors: 587.88 [18146]
Symbolic reduction time: 0.789, column sort time: 0.026[r]
12 + 18146 = 18158 rows / 49617 columns out of 100947 (49.152%)
Density: 1.2043% / 1.4643% (597.53/r), total: 10849943 (41.4MB)
Before ech memory: 320.4MB, max: 1565.5MB
Row sort time: 0.000
[5 threads]
0.516[r] + 0.000 = 0.518[r] [8]
After ech memory: 320.4MB, max: 1565.5MB
Num new polynomials: 8 (66.7%), min deg: 17 [8], av deg: 17.0
Degree counts: 17:8
Queue insertion time: 0.006[r]
Step 28 time: 1.377[r], [1.378], mat/total: 29.980/39.509, mem: 320.4MB, max: 1565.5MB

*******
STEP 29
Basis length: 693, queue length: 2131, step degree: 18, num pairs: 749
Basis total mons: 11560152, average length: 16681.316
Number of pair polynomials: 749, at 78750 column(s), 2.220
Average length for reductees: 23063.41 [749], reductors: 886.06 [42488]
Symbolic reduction time: 2.949[r], column sort time: 0.049[r]
749 + 42488 = 43237 rows / 86257 columns out of 134596 (64.086%)
Density: 1.4726% / 1.7418% (1270.2/r), total: 54921531 (209.5MB)
Before ech memory: 416.5MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
31.039 + 0.129 = 31.179 [254]
After ech memory: 480.5MB, max: 1565.5MB
Num new polynomials: 254 (33.9%), min deg: 16 [1], av deg: 17.5
Degree counts: 16:1 17:113 18:140
Queue insertion time: 0.194[r]
New max step: 29, time: 36.620
Step 29 time: 36.619, [36.638], mat/total: 61.170/76.129, mem: 491.3MB, max: 1565.5MB

*******
STEP 30
Basis length: 947, queue length: 2848, step degree: 17, num pairs: 6
Basis total mons: 18809708, average length: 19862.416
Number of pair polynomials: 6, at 39899 column(s), 0.009
Average length for reductees: 17807.00 [6], reductors: 589.87 [16968]
Symbolic reduction time: 0.819, column sort time: 0.027[r]
6 + 16968 = 16974 rows / 49441 columns out of 100947 (48.977%)
Density: 1.2054% / 1.4728% (595.96/r), total: 10115812 (38.6MB)
Before ech memory: 491.3MB, max: 1565.5MB
Row sort time: 0.005[r]
[5 threads]
0.459[r] + 0.000 = 0.459 [3]
After ech memory: 491.3MB, max: 1565.5MB
Num new polynomials: 3 (50.0%), min deg: 17 [3], av deg: 17.0
Degree counts: 17:3
Queue insertion time: 0.000
Step 30 time: 1.329, [1.344], mat/total: 61.640/77.459, mem: 491.3MB, max: 1565.5MB

*******
STEP 31
Basis length: 950, queue length: 2861, step degree: 18, num pairs: 513
Basis total mons: 18872280, average length: 19865.558
Number of pair polynomials: 513, at 79052 column(s), 1.760
Average length for reductees: 26666.04 [513], reductors: 1099.43 [43445]
Symbolic reduction time: 3.919[r], column sort time: 0.049
513 + 43445 = 43958 rows / 88141 columns out of 134596 (65.486%)
Density: 1.5859% / 1.8691% (1397.8/r), total: 61444601 (234.4MB)
Before ech memory: 523.3MB, max: 1565.5MB
Row sort time: 0.015[r]
[5 threads]
25.919 + 0.069 = 25.989 [160]
After ech memory: 555.3MB, max: 1565.5MB
Num new polynomials: 160 (31.2%), min deg: 17 [27], av deg: 17.8
Degree counts: 17:27 18:133
Queue insertion time: 0.148[r]
Step 31 time: 31.900, [31.912], mat/total: 87.650/109.359, mem: 556.4MB, max: 1565.5MB

*******
STEP 32
Basis length: 1110, queue length: 3293, step degree: 18, num pairs: 127
Basis total mons: 23992596, average length: 21614.951
Number of pair polynomials: 127, at 74085 column(s), 0.516[r]
Average length for reductees: 29770.19 [127], reductors: 1170.58 [42560]
Symbolic reduction time: 4.799, column sort time: 0.049[r]
127 + 42560 = 42687 rows / 87474 columns out of 134596 (64.990%)
Density: 1.4355% / 1.7226% (1255.7/r), total: 53600487 (204.5MB)
Before ech memory: 556.4MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
8.645[r] + 0.009 = 8.658[r] [70]
After ech memory: 556.4MB, max: 1565.5MB
Num new polynomials: 70 (55.1%), min deg: 17 [10], av deg: 17.9
Degree counts: 17:10 18:60
Queue insertion time: 0.070
Step 32 time: 14.120, [14.131], mat/total: 96.320/123.480, mem: 557.6MB, max: 1565.5MB

*******
STEP 33
Basis length: 1180, queue length: 3557, step degree: 18, num pairs: 47
Basis total mons: 26348679, average length: 22329.389
Number of pair polynomials: 47, at 71157 column(s), 0.199
Average length for reductees: 30493.06 [47], reductors: 1196.88 [42086]
Symbolic reduction time: 4.776[r], column sort time: 0.039
47 + 42086 = 42133 rows / 86716 columns out of 134596 (64.427%)
Density: 1.4179% / 1.7047% (1229.6/r), total: 51804910 (197.6MB)
Before ech memory: 557.6MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
3.829 + 0.000 = 3.839 [32]
After ech memory: 557.6MB, max: 1565.5MB
Num new polynomials: 32 (68.1%), min deg: 17 [3], av deg: 17.9
Degree counts: 17:3 18:29
Queue insertion time: 0.038[r]
Step 33 time: 8.929, [8.936], mat/total: 100.170/132.409, mem: 558.9MB, max: 1565.5MB

*******
STEP 34
Basis length: 1212, queue length: 3697, step degree: 18, num pairs: 12
Basis total mons: 27447217, average length: 22646.219
Number of pair polynomials: 12, at 65465 column(s), 0.060
Average length for reductees: 32627.00 [12], reductors: 1204.44 [40961]
Symbolic reduction time: 5.099, column sort time: 0.049[r]
12 + 40961 = 40973 rows / 85375 columns out of 134596 (63.431%)
Density: 1.4215% / 1.7074% (1213.6/r), total: 49726531 (189.7MB)
Before ech memory: 558.9MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
2.055[r] + 0.000 = 2.059 [9]
After ech memory: 558.9MB, max: 1565.5MB
Num new polynomials: 9 (75.0%), min deg: 18 [9], av deg: 18.0
Degree counts: 18:9
Queue insertion time: 0.009
Step 34 time: 7.299, [7.315], mat/total: 102.240/139.709, mem: 560.3MB, max: 1565.5MB

*******
STEP 35
Basis length: 1221, queue length: 3737, step degree: 19, num pairs: 2215
Basis total mons: 27760039, average length: 22735.495
258 pairs eliminated
Number of pair polynomials: 1957, at 117512 column(s), 7.706[r]
At 100000: 59981 rows, 123252 columns, 7.470
Average length for reductees: 30589.19 [1957], reductors: 1442.33 [71986]
Symbolic reduction time: 9.070, column sort time: 0.069
1957 + 71986 = 73943 rows / 124399 columns out of 177100 (70.242%)
Density: 1.7795% / 2.1343% (2213.7/r), total: 163690571 (624.4MB)
Before ech memory: 1040.8MB, max: 1565.5MB
Row sort time: 0.027[r]
[5 threads]
168.549 + 0.546[r] = 169.109 [434]
After ech memory: 1201.0MB, max: 1565.5MB
Num new polynomials: 434 (22.2%), min deg: 17 [4], av deg: 18.2
Degree counts: 17:4 18:324 19:106
Queue insertion time: 0.530
New max step: 35, time: 186.520
Step 35 time: 186.520, [186.542], mat/total: 271.380/326.230, mem: 1202.5MB, max: 1565.5MB

*******
STEP 36
Basis length: 1655, queue length: 3874, step degree: 18, num pairs: 21
Basis total mons: 44419537, average length: 26839.599
Number of pair polynomials: 21, at 66986 column(s), 0.099
Average length for reductees: 31640.62 [21], reductors: 1217.08 [38234]
Symbolic reduction time: 4.398[r], column sort time: 0.046[r]
21 + 38234 = 38255 rows / 81708 columns out of 134596 (60.706%)
Density: 1.51% / 1.7941% (1233.8/r), total: 47198289 (180.0MB)
Before ech memory: 1202.5MB, max: 1565.5MB
Row sort time: 0.009
[5 threads]
1.849 + 0.000 = 1.859 [7]
After ech memory: 1202.5MB, max: 1565.5MB
Num new polynomials: 7 (33.3%), min deg: 18 [7], av deg: 18.0
Degree counts: 18:7
Queue insertion time: 0.015[r]
Step 36 time: 6.439, [6.444], mat/total: 273.250/332.669, mem: 1204.2MB, max: 1565.5MB

*******
STEP 37
Basis length: 1662, queue length: 3895, step degree: 19, num pairs: 1582
Basis total mons: 44667949, average length: 26876.022
Number of pair polynomials: 1582, at 122285 column(s), 7.836[r]
At 100000: 60450 rows, 129662 columns, 9.970
Average length for reductees: 37713.26 [1582], reductors: 1847.12 [77492]
Symbolic reduction time: 12.699, column sort time: 0.077[r]
1582 + 77492 = 79074 rows / 131144 columns out of 177100 (74.051%)
Density: 1.9556% / 2.3388% (2564.7/r), total: 202799617 (773.6MB)
Before ech memory: 1364.4MB, max: 1565.5MB
Row sort time: 0.027[r]
[5 threads]
220.960 + 0.539 = 221.509 [387]
After ech memory: 1524.6MB, max: 1689.9MB
Num new polynomials: 387 (24.5%), min deg: 17 [1], av deg: 18.6
Degree counts: 17:1 18:161 19:225
Queue insertion time: 0.619
New max step: 37, time: 242.790
Step 37 time: 242.789, [243.019], mat/total: 494.800/575.459, mem: 1524.6MB, max: 1689.9MB

*******
STEP 38
Basis length: 2049, queue length: 4327, step degree: 18, num pairs: 6
Basis total mons: 61307008, average length: 29920.453
Number of pair polynomials: 6, at 63357 column(s), 0.030
Average length for reductees: 31863.00 [6], reductors: 1192.98 [37068]
Symbolic reduction time: 4.107[r], column sort time: 0.045[r]
6 + 37068 = 37074 rows / 80233 columns out of 134596 (59.610%)
Density: 1.4931% / 1.7741% (1197.9/r), total: 44412490 (169.4MB)
Before ech memory: 1524.6MB, max: 1689.9MB
Row sort time: 0.009
[5 threads]
1.756[r] + 0.000 = 1.759 [1]
After ech memory: 1524.6MB, max: 1689.9MB
Num new polynomials: 1 (16.7%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.006[r]
Step 38 time: 5.970, [5.976], mat/total: 496.570/581.429, mem: 1526.5MB, max: 1689.9MB

*******
STEP 39
Basis length: 2050, queue length: 4327, step degree: 19, num pairs: 837
Basis total mons: 61344985, average length: 29924.383
Number of pair polynomials: 837, at 113917 column(s), 4.050
At 100000: 58297 rows, 128067 columns, 11.019[r]
Average length for reductees: 40820.39 [837], reductors: 2060.43 [76428]
Symbolic reduction time: 13.740, column sort time: 0.063[r]
837 + 76428 = 77265 rows / 130096 columns out of 177100 (73.459%)
Density: 1.9065% / 2.2997% (2480.3/r), total: 191641101 (731.1MB)
Before ech memory: 1526.5MB, max: 1689.9MB
Row sort time: 0.023[r]
[5 threads]
128.339 + 0.369[r] = 128.710 [279]
After ech memory: 1590.5MB, max: 1754.8MB
Num new polynomials: 279 (33.3%), min deg: 18 [90], av deg: 18.7
Degree counts: 18:90 19:189
Queue insertion time: 0.523[r]
Step 39 time: 147.130, [147.149], mat/total: 625.310/728.559, mem: 1592.6MB, max: 1754.8MB

*******
STEP 40
Basis length: 2329, queue length: 4976, step degree: 19, num pairs: 458
Basis total mons: 73924361, average length: 31740.816
Number of pair polynomials: 458, at 110877 column(s), 2.819
At 100000: 57394 rows, 128771 columns, 12.434[r]
Average length for reductees: 42851.90 [458], reductors: 2222.62 [76861]
Symbolic reduction time: 15.470, column sort time: 0.075[r]
458 + 76861 = 77319 rows / 130862 columns out of 177100 (73.892%)
Density: 1.8824% / 2.2829% (2463.3/r), total: 190458593 (726.5MB)
Before ech memory: 1592.6MB, max: 1754.8MB
Row sort time: 0.026[r]
[5 threads]
83.840 + 0.240 = 84.080 [174]
After ech memory: 1656.7MB, max: 1854.2MB
Num new polynomials: 174 (38.0%), min deg: 18 [35], av deg: 18.8
Degree counts: 18:35 19:139
Queue insertion time: 0.359
Step 40 time: 102.849, [102.871], mat/total: 709.430/831.409, mem: 1656.7MB, max: 1854.2MB

*******
STEP 41
Basis length: 2503, queue length: 5518, step degree: 19, num pairs: 180
Basis total mons: 82113212, average length: 32805.918
Number of pair polynomials: 180, at 104675 column(s), 1.122[r]
At 100000: 56416 rows, 127831 columns, 12.359
Average length for reductees: 44870.06 [180], reductors: 2310.29 [76758]
Symbolic reduction time: 15.440, column sort time: 0.075[r]
180 + 76758 = 76938 rows / 130797 columns out of 177100 (73.855%)
Density: 1.8424% / 2.2464% (2409.9/r), total: 185409968 (707.3MB)
Before ech memory: 1656.7MB, max: 1854.2MB
Row sort time: 0.026[r]
[5 threads]
38.198[r] + 0.109 = 38.309 [100]
After ech memory: 1688.7MB, max: 1886.2MB
Num new polynomials: 100 (55.6%), min deg: 18 [13], av deg: 18.9
Degree counts: 18:13 19:87
Queue insertion time: 0.223[r]
Step 41 time: 55.220, [55.232], mat/total: 747.770/886.629, mem: 1691.0MB, max: 1886.2MB

*******
STEP 42
Basis length: 2603, queue length: 5923, step degree: 19, num pairs: 69
Basis total mons: 86917106, average length: 33391.128
Number of pair polynomials: 69, at 100044 column(s), 0.450
At 100000: 55638 rows, 128351 columns, 12.680
Average length for reductees: 45701.00 [69], reductors: 2356.85 [77514]
Symbolic reduction time: 15.970, column sort time: 0.065[r]
69 + 77514 = 77583 rows / 131894 columns out of 177100 (74.474%)
Density: 1.8162% / 2.2259% (2395.4/r), total: 185842140 (708.9MB)
Before ech memory: 1691.0MB, max: 1886.2MB
Row sort time: 0.023[r]
[5 threads]
14.395[r] + 0.009[r] = 14.410 [46]
After ech memory: 1691.0MB, max: 1890.0MB
Num new polynomials: 46 (66.7%), min deg: 18 [4], av deg: 18.9
Degree counts: 18:4 19:42
Queue insertion time: 0.099
Step 42 time: 31.039, [31.051], mat/total: 762.220/917.669, mem: 1693.6MB, max: 1890.0MB

*******
STEP 43
Basis length: 2649, queue length: 6107, step degree: 19, num pairs: 20
Basis total mons: 89181942, average length: 33666.267
Number of pair polynomials: 20, at 100130 column(s), 0.145[r]
At 100000: 55843 rows, 128334 columns, 13.299
Average length for reductees: 47616.30 [20], reductors: 2363.86 [77172]
Symbolic reduction time: 16.650, column sort time: 0.075[r]
20 + 77172 = 77192 rows / 131501 columns out of 177100 (74.252%)
Density: 1.8065% / 2.2159% (2375.6/r), total: 183376420 (699.5MB)
Before ech memory: 1693.6MB, max: 1890.0MB
Row sort time: 0.026[r]
[5 threads]
6.500 + 0.005[r] = 6.509 [17]
After ech memory: 1693.6MB, max: 1892.1MB
Num new polynomials: 17 (85.0%), min deg: 19 [17], av deg: 19.0
Degree counts: 19:17
Queue insertion time: 0.039
Step 43 time: 23.470, [23.487], mat/total: 768.760/941.139, mem: 1693.6MB, max: 1892.1MB

*******
STEP 44
Basis length: 2666, queue length: 6185, step degree: 20, num pairs: 4047
Basis total mons: 90040861, average length: 33773.766
516 pairs eliminated
Number of pair polynomials: 3531, at 166579 column(s), 19.230
At 100000: 72030 rows, 175314 columns, 14.763[r]
Average length for reductees: 44890.07 [3531], reductors: 2608.63 [120835]
Symbolic reduction time: 25.269, column sort time: 0.100
3531 + 120835 = 124366 rows / 178979 columns out of 230230 (77.739%)
Density: 2.1282% / 2.6546% (3809.1/r), total: 473720509 (1807.1MB)
Before ech memory: 2910.8MB (=max)
Row sort time: 0.039
[5 threads]
924.140 + 1.647[r] = 925.810 [572]
After ech memory: 3167.0MB, max: 3420.3MB
Num new polynomials: 572 (16.2%), min deg: 18 [6], av deg: 19.2
Degree counts: 18:6 19:423 20:143
Queue insertion time: 1.460
New max step: 44, time: 971.930
Step 44 time: 971.930, [971.971], mat/total: 1694.620/1913.069, mem: 3169.8MB, max: 3420.3MB

*******
STEP 45
Basis length: 3238, queue length: 5056, step degree: 19, num pairs: 36
Basis total mons: 119224573, average length: 36820.436
Number of pair polynomials: 36, at 97570 column(s), 0.300
At 100000: 55973 rows, 130440 columns, 16.338[r]
Average length for reductees: 48666.44 [36], reductors: 2611.10 [79218]
Symbolic reduction time: 20.739, column sort time: 0.077[r]
36 + 79218 = 79254 rows / 134102 columns out of 177100 (75.721%)
Density: 1.9627% / 2.3837% (2632/r), total: 208598064 (795.7MB)
Before ech memory: 3169.8MB, max: 3420.3MB
Row sort time: 0.028[r]
[5 threads]
13.630 + 0.000 = 13.639 [6]
After ech memory: 3169.8MB, max: 3420.3MB
Num new polynomials: 6 (16.7%), min deg: 19 [6], av deg: 19.0
Degree counts: 19:6
Queue insertion time: 0.009
Step 45 time: 34.809, [34.829], mat/total: 1708.300/1947.879, mem: 3169.8MB, max: 3420.3MB

*******
STEP 46
Basis length: 3244, queue length: 5054, step degree: 20, num pairs: 2144
Basis total mons: 119536040, average length: 36848.348
Number of pair polynomials: 2144, at 162330 column(s), 15.593[r]
At 100000: 70100 rows, 177986 columns, 19.738[r]
Average length for reductees: 50594.29 [2144], reductors: 3029.65 [124130]
Symbolic reduction time: 34.000, column sort time: 0.099
2144 + 124130 = 126274 rows / 182507 columns out of 230230 (79.272%)
Density: 2.1025% / 2.6452% (3837.2/r), total: 484544253 (1848.4MB)
Before ech memory: 3233.8MB, max: 3420.3MB
Row sort time: 0.046[r]
[5 threads]
744.929 + 0.750 = 745.690 [371]
After ech memory: 3426.0MB, max: 3651.3MB
Num new polynomials: 371 (17.3%), min deg: 19 [167], av deg: 19.5
Degree counts: 19:167 20:204
Queue insertion time: 0.929
Step 46 time: 796.400, [796.442], mat/total: 2454.050/2744.279, mem: 3429.1MB, max: 3651.3MB

*******
STEP 47
Basis length: 3615, queue length: 4851, step degree: 20, num pairs: 883
Basis total mons: 139455569, average length: 38576.921
Number of pair polynomials: 883, at 150207 column(s), 6.013[r]
At 100000: 67478 rows, 176836 columns, 19.119
Average length for reductees: 52658.35 [883], reductors: 3208.48 [124476]
Symbolic reduction time: 33.110, column sort time: 0.089
883 + 124476 = 125359 rows / 182804 columns out of 230230 (79.401%)
Density: 1.9457% / 2.4945% (3556.8/r), total: 445876359 (1700.9MB)
Before ech memory: 3429.1MB, max: 3651.3MB
Row sort time: 0.039[r]
[5 threads]
350.230 + 0.380 = 350.619 [217]
After ech memory: 3429.1MB, max: 3686.7MB
Num new polynomials: 217 (24.6%), min deg: 19 [48], av deg: 19.8
Degree counts: 19:48 20:169
Queue insertion time: 0.699
Step 47 time: 390.599, [390.609], mat/total: 2804.720/3134.880, mem: 3429.1MB, max: 3686.7MB

*******
STEP 48
Basis length: 3832, queue length: 5142, step degree: 20, num pairs: 256
Basis total mons: 151417337, average length: 39513.919
Number of pair polynomials: 256, at 138832 column(s), 2.300
At 100000: 65574 rows, 173445 columns, 23.699
Average length for reductees: 53909.61 [256], reductors: 3256.46 [121399]
Symbolic reduction time: 40.050, column sort time: 0.105[r]
256 + 121399 = 121655 rows / 179641 columns out of 230230 (78.027%)
Density: 1.8721% / 2.4168% (3363.1/r), total: 409132415 (1560.7MB)
Before ech memory: 3429.1MB, max: 3686.7MB
Row sort time: 0.043[r]
[5 threads]
118.909 + 0.070 = 118.989 [93]
After ech memory: 3429.1MB, max: 3686.7MB
Num new polynomials: 93 (36.3%), min deg: 19 [16], av deg: 19.8
Degree counts: 19:16 20:77
Queue insertion time: 0.312[r]
Step 48 time: 161.840, [161.853], mat/total: 2923.770/3296.720, mem: 3432.5MB, max: 3686.7MB

*******
STEP 49
Basis length: 3925, queue length: 5420, step degree: 20, num pairs: 83
Basis total mons: 156605901, average length: 39899.593
Number of pair polynomials: 83, at 133932 column(s), 0.750
At 100000: 65208 rows, 174211 columns, 23.939
Average length for reductees: 54649.25 [83], reductors: 3292.19 [122420]
Symbolic reduction time: 40.970, column sort time: 0.099
83 + 122420 = 122503 rows / 180663 columns out of 230230 (78.471%)
Density: 1.8415% / 2.3899% (3327/r), total: 407565570 (1554.7MB)
Before ech memory: 3432.5MB, max: 3686.7MB
Row sort time: 0.046[r]
[5 threads]
38.769 + 0.010 = 38.789 [41]
After ech memory: 3432.5MB, max: 3687.7MB
Num new polynomials: 41 (49.4%), min deg: 19 [5], av deg: 19.9
Degree counts: 19:5 20:36
Queue insertion time: 0.139[r]
Step 49 time: 80.819, [80.844], mat/total: 2962.620/3377.539, mem: 3432.5MB, max: 3687.7MB

*******
STEP 50
Basis length: 3966, queue length: 5560, step degree: 20, num pairs: 27
Basis total mons: 158913626, average length: 40068.993
Number of pair polynomials: 27, at 118297 column(s), 0.239
At 100000: 63564 rows, 169866 columns, 22.730
Average length for reductees: 55326.22 [27], reductors: 3261.45 [120142]
Symbolic reduction time: 38.420, column sort time: 0.103[r]
27 + 120142 = 120169 rows / 178409 columns out of 230230 (77.492%)
Density: 1.8346% / 2.3785% (3273.1/r), total: 393330616 (1500.4MB)
Before ech memory: 3432.5MB, max: 3687.7MB
Row sort time: 0.044[r]
[5 threads]
14.129[r] + 0.000 = 14.139 [18]
After ech memory: 3432.5MB, max: 3687.7MB
Num new polynomials: 18 (66.7%), min deg: 20 [18], av deg: 20.0
Degree counts: 20:18
Queue insertion time: 0.059
Step 50 time: 53.029, [53.540], mat/total: 2976.820/3430.569, mem: 3436.2MB, max: 3687.7MB

*******
STEP 51
Basis length: 3984, queue length: 5637, step degree: 21, num pairs: 3646
Basis total mons: 159934118, average length: 40144.106
814 pairs eliminated
Number of pair polynomials: 2833, at 205595 column(s), 21.730
At 100000: 77651 rows, 225101 columns, 27.060
At 200000: 151378 rows, 232350 columns, 53.340
Average length for reductees: 54180.26 [2833], reductors: 3410.61 [175835]
Symbolic reduction time: 60.090, column sort time: 0.142[r]
2833 + 175835 = 178668 rows / 235458 columns out of 296010 (79.544%)
Density: 1.7904% / 2.43% (4215.6/r), total: 753198065 (2873.2MB)
Before ech memory: 4813.5MB, max: 4821.6MB
Row sort time: 0.059
[5 threads]
1532.470 + 1.299 = 1533.789 [439]
After ech memory: 5045.9MB, max: 5338.1MB
Num new polynomials: 439 (15.5%), min deg: 19 [5], av deg: 20.3
Degree counts: 19:5 20:306 21:128
Queue insertion time: 1.579
New max step: 51, time: 1617.430
Step 51 time: 1617.430, [1617.984], mat/total: 4510.680/5048.000, mem: 5037.8MB, max: 5338.1MB

*******
STEP 52
Basis length: 4423, queue length: 4185, step degree: 20, num pairs: 29
Basis total mons: 185001311, average length: 41827.111
Number of pair polynomials: 29, at 121498 column(s), 0.259[r]
At 100000: 63822 rows, 170959 columns, 22.921[r]
Average length for reductees: 55501.83 [29], reductors: 3327.30 [120164]
Symbolic reduction time: 38.559[r], column sort time: 0.100
29 + 120164 = 120193 rows / 178477 columns out of 230230 (77.521%)
Density: 1.8713% / 2.4164% (3339.9/r), total: 401431651 (1531.3MB)
Before ech memory: 5037.8MB, max: 5338.1MB
Row sort time: 0.039
[5 threads]
25.760 + 0.000 = 25.769 [5]
After ech memory: 5037.8MB, max: 5338.1MB
Num new polynomials: 5 (17.2%), min deg: 20 [5], av deg: 20.0
Degree counts: 20:5
Queue insertion time: 0.027[r]
Step 52 time: 64.789[r], [64.790], mat/total: 4536.500/5112.789, mem: 5041.8MB, max: 5338.1MB

*******
STEP 53
Basis length: 4428, queue length: 4185, step degree: 21, num pairs: 1667
Basis total mons: 185285702, average length: 41844.106
2 pairs eliminated
Number of pair polynomials: 1665, at 198834 column(s), 14.070
At 100000: 76145 rows, 229089 columns, 29.644[r]
At 200000: 150578 rows, 236183 columns, 58.429
Average length for reductees: 56886.03 [1665], reductors: 3647.64 [179700]
Symbolic reduction time: 66.489, column sort time: 0.142[r]
1665 + 179700 = 181365 rows / 239055 columns out of 296010 (80.759%)
Density: 1.7303% / 2.3767% (4136.4/r), total: 750196428 (2861.8MB)
Before ech memory: 5041.8MB, max: 5338.1MB
Row sort time: 0.068[r]
[5 threads]
1095.469 + 0.619 = 1096.109 [271]
After ech memory: 5178.2MB, max: 5506.1MB
Num new polynomials: 271 (16.3%), min deg: 20 [157], av deg: 20.4
Degree counts: 20:157 21:114
Queue insertion time: 1.055[r]
Step 53 time: 1177.980, [1178.000], mat/total: 5632.690/6290.770, mem: 5169.9MB, max: 5506.1MB

*******
STEP 54
Basis length: 4699, queue length: 3944, step degree: 21, num pairs: 842
Basis total mons: 200979612, average length: 42770.720
Number of pair polynomials: 842, at 178827 column(s), 7.659
At 100000: 74322 rows, 227233 columns, 28.986[r]
At 200000: 148749 rows, 234878 columns, 57.205[r]
Average length for reductees: 57700.25 [842], reductors: 3726.55 [178598]
Symbolic reduction time: 65.198[r], column sort time: 0.119
842 + 178598 = 179440 rows / 237751 columns out of 296010 (80.319%)
Density: 1.6739% / 2.3215% (3979.8/r), total: 714137770 (2724.2MB)
Before ech memory: 5169.9MB, max: 5506.1MB
Row sort time: 0.061[r]
[5 threads]
580.769 + 0.299[r] = 581.090 [141]
After ech memory: 5178.2MB, max: 5506.1MB
Num new polynomials: 141 (16.7%), min deg: 20 [60], av deg: 20.6
Degree counts: 20:60 21:81
Queue insertion time: 0.569
Step 54 time: 654.729, [654.753], mat/total: 6213.850/6945.500, mem: 5169.9MB, max: 5506.1MB

*******
STEP 55
Basis length: 4840, queue length: 3837, step degree: 21, num pairs: 306
Basis total mons: 209194278, average length: 43221.958
Number of pair polynomials: 306, at 154589 column(s), 2.898[r]
At 100000: 72492 rows, 222746 columns, 31.199
At 200000: 146755 rows, 231993 columns, 60.768[r]
Average length for reductees: 58138.26 [306], reductors: 3769.84 [175960]
Symbolic reduction time: 68.049[r], column sort time: 0.140
306 + 175960 = 176266 rows / 235039 columns out of 296010 (79.402%)
Density: 1.6441% / 2.2906% (3864.2/r), total: 681132110 (2598.3MB)
Before ech memory: 5169.9MB, max: 5506.1MB
Row sort time: 0.067[r]
[5 threads]
225.639 + 0.096[r] = 225.750 [75]
After ech memory: 5178.0MB, max: 5506.1MB
Num new polynomials: 75 (24.5%), min deg: 20 [5], av deg: 20.9
Degree counts: 20:5 21:70
Queue insertion time: 0.316[r]
Step 55 time: 297.250, [297.284], mat/total: 6439.670/7242.750, mem: 5174.4MB, max: 5506.1MB

*******
STEP 56
Basis length: 4915, queue length: 3954, step degree: 21, num pairs: 27
Basis total mons: 213591330, average length: 43457.036
Number of pair polynomials: 27, at 129815 column(s), 0.299
At 100000: 71262 rows, 221245 columns, 32.940
At 200000: 145745 rows, 231406 columns, 63.640
Average length for reductees: 58486.04 [27], reductors: 3769.53 [176608]
Symbolic reduction time: 71.570, column sort time: 0.139
27 + 176608 = 176635 rows / 235675 columns out of 296010 (79.617%)
Density: 1.603% / 2.251% (3777.9/r), total: 667308773 (2545.6MB)
Before ech memory: 5174.4MB, max: 5506.1MB
Row sort time: 0.066[r]
[5 threads]
23.879 + 0.005[r] = 23.907[r] [16]
After ech memory: 5182.5MB, max: 5506.4MB
Num new polynomials: 16 (59.3%), min deg: 21 [16], av deg: 21.0
Degree counts: 21:16
Queue insertion time: 0.069
Step 56 time: 96.090, [96.128], mat/total: 6463.660/7338.840, mem: 5174.4MB, max: 5506.4MB

*******
STEP 57
Basis length: 4931, queue length: 4019, step degree: 22, num pairs: 2688
Basis total mons: 214532162, average length: 43506.827
929 pairs eliminated
Number of pair polynomials: 1759, at 237915 column(s), 14.909
At 100000: 80921 rows, 279157 columns, 32.888[r]
At 200000: 160065 rows, 289740 columns, 64.620
Average length for reductees: 57960.09 [1759], reductors: 3752.93 [238534]
Symbolic reduction time: 90.352[r], column sort time: 0.180
1759 + 238534 = 240293 rows / 297722 columns out of 376740 (79.026%)
Density: 1.3938% / 2.095% (4149.7/r), total: 997152419 (3803.8MB)
Before ech memory: 6423.7MB, max: 6431.7MB
Row sort time: 0.090
[5 threads]
1488.659 + 0.170 = 1488.860 [110]
After ech memory: 6498.7MB, max: 6891.4MB
Num new polynomials: 110 (6.3%), min deg: 20 [2], av deg: 21.2
Degree counts: 20:2 21:84 22:24
Queue insertion time: 0.417[r]
Step 57 time: 1594.870, [1594.899], mat/total: 7952.630/8933.710, mem: 6487.7MB, max: 6891.4MB

*******
STEP 58
Basis length: 5041, queue length: 1874, step degree: 21, num pairs: 12
Basis total mons: 221008196, average length: 43842.134
Number of pair polynomials: 12, at 117971 column(s), 0.129
At 100000: 71014 rows, 219834 columns, 33.959
At 200000: 145408 rows, 230228 columns, 65.680
Average length for reductees: 58716.50 [12], reductors: 3794.70 [175621]
Symbolic reduction time: 73.450, column sort time: 0.139
12 + 175621 = 175633 rows / 234636 columns out of 296010 (79.266%)
Density: 1.6189% / 2.2659% (3798.5/r), total: 667134376 (2544.9MB)
Before ech memory: 6487.7MB, max: 6891.4MB
Row sort time: 0.065[r]
[5 threads]
24.010 + 0.003[r] = 24.036[r] [2]
After ech memory: 6495.8MB, max: 6891.4MB
Num new polynomials: 2 (16.7%), min deg: 21 [2], av deg: 21.0
Degree counts: 21:2
Queue insertion time: 0.019[r]
Step 58 time: 97.869, [97.934], mat/total: 7976.750/9031.579, mem: 6492.7MB, max: 6891.4MB

*******
STEP 59
Basis length: 5043, queue length: 1872, step degree: 22, num pairs: 472
Basis total mons: 221125909, average length: 43848.088
Number of pair polynomials: 472, at 199597 column(s), 4.850
At 100000: 78323 rows, 276672 columns, 36.750
At 200000: 157354 rows, 286858 columns, 70.700
Average length for reductees: 58856.65 [472], reductors: 3784.69 [235436]
Symbolic reduction time: 97.489, column sort time: 0.179[r]
472 + 235436 = 235908 rows / 294512 columns out of 376740 (78.174%)
Density: 1.3225% / 2.0214% (3894.9/r), total: 918833450 (3505.1MB)
Before ech memory: 6492.7MB, max: 6891.4MB
Row sort time: 0.090
[5 threads]
488.209 + 0.020 = 488.260 [27]
After ech memory: 6503.5MB, max: 6892.4MB
Num new polynomials: 27 (5.7%), min deg: 21 [20], av deg: 21.3
Degree counts: 21:20 22:7
Queue insertion time: 0.120
Step 59 time: 591.040, [591.325], mat/total: 8465.110/9622.620, mem: 6492.7MB, max: 6892.4MB

*******
STEP 60
Basis length: 5070, queue length: 1543, step degree: 22, num pairs: 102
Basis total mons: 222718093, average length: 43928.618
Number of pair polynomials: 102, at 160649 column(s), 1.149
At 100000: 76968 rows, 272538 columns, 37.957[r]
At 200000: 155819 rows, 283959 columns, 72.414[r]
Average length for reductees: 58964.35 [102], reductors: 3819.17 [234201]
Symbolic reduction time: 98.966[r], column sort time: 0.170
102 + 234201 = 234303 rows / 293254 columns out of 376740 (77.840%)
Density: 1.3105% / 2.0124% (3843.2/r), total: 900468021 (3435.0MB)
Before ech memory: 6492.7MB, max: 6892.4MB
Row sort time: 0.079
[5 threads]
125.329 + 0.004[r] = 125.368[r] [4]
After ech memory: 6503.4MB, max: 6892.4MB
Num new polynomials: 4 (3.9%), min deg: 21 [1], av deg: 21.8
Degree counts: 21:1 22:3
Queue insertion time: 0.020
Step 60 time: 225.809, [225.822], mat/total: 8590.570/9848.430, mem: 6492.7MB, max: 6892.4MB

*******
STEP 61
Basis length: 5074, queue length: 1462, step degree: 22, num pairs: 4
Basis total mons: 222954159, average length: 43940.512
Number of pair polynomials: 4, at 112482 column(s), 0.049
At 100000: 74794 rows, 262081 columns, 37.811[r]
At 200000: 153265 rows, 276879 columns, 72.720
Average length for reductees: 58994.75 [4], reductors: 3727.92 [232234]
Symbolic reduction time: 98.246[r], column sort time: 0.177[r]
4 + 232234 = 232238 rows / 291283 columns out of 376740 (77.317%)
Density: 1.2802% / 1.9781% (3728.9/r), total: 865985593 (3303.5MB)
Before ech memory: 6492.7MB, max: 6892.4MB
Row sort time: 0.088[r]
[5 threads]
32.623[r] + 0.000 = 32.649 [0]
After ech memory: 6503.3MB, max: 6892.4MB
No new polynomials
Queue insertion time: 0.000
Step 61 time: 131.260, [131.265], mat/total: 8623.320/9979.690, mem: 6492.7MB, max: 6892.4MB

*******
STEP 62
Basis length: 5074, queue length: 1458, step degree: 23, num pairs: 858
Basis total mons: 222954159, average length: 43940.512
737 pairs eliminated
Number of pair polynomials: 121, at 206589 column(s), 1.389
At 100000: 80322 rows, 318753 columns, 39.877[r]
At 200000: 162511 rows, 336477 columns, 75.878[r]
At 300000: 245264 rows, 346437 columns, 111.540
Average length for reductees: 58722.51 [121], reductors: 3665.69 [296158]
Symbolic reduction time: 122.690, column sort time: 0.218[r]
121 + 296158 = 296279 rows / 355207 columns out of 475020 (74.777%)
Density: 1.0383% / 1.7574% (3688.2/r), total: 1092730158 (4168.4MB)
Before ech memory: 7069.2MB, max: 7077.2MB
Row sort time: 0.119[r]
[5 threads]
189.236[r] + 0.005[r] = 189.278[r] [0]
After ech memory: 7114.8MB, max: 7570.9MB
No new polynomials
Queue insertion time: 0.000
Step 62 time: 313.750, [313.764], mat/total: 8812.740/10293.450, mem: 7101.2MB, max: 7570.9MB

*******
STEP 63
Basis length: 5074, queue length: 600, step degree: 24, num pairs: 395
Basis total mons: 222954159, average length: 43940.512
393 pairs eliminated
Number of pair polynomials: 2, at 118362 column(s), 0.029
At 100000: 81238 rows, 341521 columns, 38.579
At 200000: 164670 rows, 362671 columns, 74.130
At 300000: 248943 rows, 371680 columns, 107.280
Average length for reductees: 58858.50 [2], reductors: 3665.11 [325247]
Symbolic reduction time: 128.630, column sort time: 0.199
2 + 325247 = 325249 rows / 384296 columns out of 593775 (64.721%)
Density: 0.95381% / 1.6723% (3665.4/r), total: 1192182446 (4547.8MB)
Before ech memory: 7549.7MB, max: 7570.9MB
Row sort time: 0.113[r]
[5 threads]
41.059 + 0.005[r] = 41.110 [0]
After ech memory: 7596.6MB, max: 8084.9MB
No new polynomials
Queue insertion time: 0.003[r]
Step 63 time: 170.149, [170.163], mat/total: 8853.980/10463.600, mem: 7581.7MB, max: 8084.9MB

*******
STEP 64
Basis length: 5074, queue length: 205, step degree: 25, num pairs: 164
Basis total mons: 222954159, average length: 43940.512
164 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 65
Basis length: 5074, queue length: 41, step degree: 26, num pairs: 31
Basis total mons: 222954159, average length: 43940.512
31 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 66
Basis length: 5074, queue length: 10, step degree: 27, num pairs: 8
Basis total mons: 222954159, average length: 43940.512
8 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 67
Basis length: 5074, queue length: 2, step degree: 28, num pairs: 2
Basis total mons: 222954159, average length: 43940.512
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Reduce 5074 final polynomial(s) by 5074
432 redundant polynomial(s) removed; time: 0.010
Interreduce 4452 (out of range [0 .. 5073] = 5074) polynomial(s)
At 104451: 45402 rows, 178139 columns, 53.559
Symbolic reduction time: 83.559
Column sort time: 0.117[r]
4452 + 139318 = 143770 rows / 202819 columns
Density: 1.8233% / 2.4149% (3698/r), total: 531654736 (2028.1MB)
Row sort time: 0.039[r]
[5 threads]
109.517[r] + 0.404[r] = 109.930[r] [4452]
Total reduction time: 202.479
Reduction time: 247.286[r]
Final number of polynomials: 4642

Final basis length: 4452
Number of pairs: 23423
Max step: 51, time: 1617.430
Max num entries matrix: 325249 by 384296
Max num rows matrix: 325249 by 384296
Approx mat cost: 1.76722e+13, sym red cost: 1.57457e+10
Total pair setup time: 144.960
Total symbolic reduction time: 1449.200
Total column sort time: 3.990
Total row sort time: 1.760
Total matrix time: 8853.980
Total new polys time: 1.530
Total queue update time: 9.460
Total Faugere F4 time: 10729.430, real time: 10731.792
Time: 10729.430
dregs = [ 10, 10, 12, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 15, 16, 16, 16, 17, 16, 17, 17, 17, 17, 18, 17, 18, 17, 18, 18, 18, 18, 19, 18, 19, 18, 19, 19, 19, 19, 19, 20, 19, 20, 20, 20, 20, 20, 21, 20, 21, 21, 21, 21, 22, 21, 22, 22, 22, 23, 24, 25, 26, 27, 28 ]
4.61user 0.90system 3:16:03elapsed 0%CPU (0avgtext+0avgdata 229744maxresident)k
0inputs+392outputs (0major+98644minor)pagefaults 0swaps