results/anemoi_p2_n15_l1_a5_mPCICO_o3.txt

Model: PCICO. Use final LL: True.
====================================================================================================
ANEMOI GF(2^15), alpha = 5, QUAD = 3. With final LL. Model: PCICO
rmax = 10, tmax = 3600.
====================================================================================================
====================================================================================================
n_r: 1, n_v: 2, n_e: 2, mdeg: 5
degs = [5, 1]
Multivariate Polynomial Ring in S0100, Y0000 over Finite Field in z15 of size 2^15
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=1)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^15)
Rank: 2
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 2
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: 5, num pairs: 1
Basis total mons: 8, average length: 4.000
Number of pair polynomials: 1, at 7 column(s), 0.000
Average length for reductees: 3.00 [1], reductors: 3.13 [15]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 15 = 16 rows / 21 columns out of 21 (100.000%)
Density: 14.881% / 31.471% (3.125/r), total: 50 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 5 [1], av deg: 5.0
Degree counts: 5:1
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 2)
INTERREDUCE 2 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
2 + 0 = 2 rows / 7 columns
Density: 64.286% / 92.857% (4.5/r), total: 9 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [2]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 2
Number of pairs: 1
Max step: 1, time: 0.000
Max num entries matrix: 16 by 21
Max num rows matrix: 16 by 21
Approx mat cost: 99.1339, sym red cost: 50
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: 0.000
Time: 0.000
dregs = [ 5 ]
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Starting FGLM computation... (r=1)
Time: 0.000
unideg = 5
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Starting UNIV SOLVING computation... (r=1)
Time: 0.000
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=1)
nsols_mult = 1
====================================================================================================
n_r: 2, n_v: 3, n_e: 3, mdeg: 9
degs = [5, 9, 3]
Multivariate Polynomial Ring in S0200, S0100, Y0000 over Finite Field in z15 of size 2^15
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=2)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^15)
Rank: 3
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 2
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: 5, num pairs: 1
Basis total mons: 39, average length: 13.000
Number of pair polynomials: 1, at 11 column(s), 0.000
Average length for reductees: 7.00 [1], reductors: 6.67 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 25 columns out of 56 (44.643%)
Density: 26.857% / 32.301% (6.7143/r), total: 47 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 5 [1], av deg: 5.0
Degree counts: 5:1
Queue insertion time: 0.000
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: 4, queue length: 2, step degree: 6, num pairs: 1
Basis total mons: 54, average length: 13.500
Number of pair polynomials: 1, at 20 column(s), 0.000
Average length for reductees: 15.00 [1], reductors: 9.29 [7]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 7 = 8 rows / 31 columns out of 84 (36.905%)
Density: 32.258% / 37.964% (10/r), total: 80 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 6 [1], av deg: 6.0
Degree counts: 6:1
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: 5, queue length: 2, step degree: 7, num pairs: 1
Basis total mons: 75, average length: 15.000
Number of pair polynomials: 1, at 27 column(s), 0.000
Average length for reductees: 21.00 [1], reductors: 10.00 [8]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 8 = 9 rows / 35 columns out of 120 (29.167%)
Density: 32.063% / 37.751% (11.222/r), total: 101 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 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: 6, queue length: 3, step degree: 6, num pairs: 1
Basis total mons: 96, average length: 16.000
Number of pair polynomials: 1, at 28 column(s), 0.000
Average length for reductees: 21.00 [1], reductors: 12.43 [7]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 7 = 8 rows / 34 columns out of 84 (40.476%)
Density: 39.706% / 45.726% (13.5/r), total: 108 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 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, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 5
Basis length: 6, queue length: 2, step degree: 7, num pairs: 1
Basis total mons: 96, average length: 16.000
Number of pair polynomials: 1, at 34 column(s), 0.000
Average length for reductees: 21.00 [1], reductors: 20.00 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 43 columns out of 120 (35.833%)
Density: 46.844% / 52.076% (20.143/r), total: 141 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 7 [1], av deg: 7.0
Degree counts: 7:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 6
Basis length: 7, queue length: 2, step degree: 8, num pairs: 1
Basis total mons: 124, average length: 17.714
Number of pair polynomials: 1, at 40 column(s), 0.000
Average length for reductees: 28.00 [1], reductors: 14.20 [15]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 15 = 16 rows / 54 columns out of 165 (32.727%)
Density: 27.894% / 34.905% (15.062/r), total: 241 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 6 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 7, queue length: 1, step degree: 9, num pairs: 1
Basis total mons: 124, average length: 17.714
Number of pair polynomials: 1, at 28 column(s), 0.000
Average length for reductees: 27.00 [1], reductors: 11.08 [38]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 38 = 39 rows / 77 columns out of 220 (35.000%)
Density: 14.918% / 22.153% (11.487/r), total: 448 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 8
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 5 [1], av deg: 5.0
Degree counts: 5:1
Queue insertion time: 0.000
Step 7 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 8
Basis length: 8, queue length: 1, step degree: 9, num pairs: 1
Basis total mons: 129, average length: 16.125
Number of pair polynomials: 1, at 25 column(s), 0.000
Average length for reductees: 5.00 [1], reductors: 13.80 [25]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 25 = 26 rows / 90 columns out of 220 (40.909%)
Density: 14.957% / 22.488% (13.462/r), total: 350 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 8 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 9
Basis length: 9, queue length: 3, step degree: 10, num pairs: 2
Basis total mons: 184, average length: 20.444
Number of pair polynomials: 2, at 95 column(s), 0.000
Average length for reductees: 55.00 [2], reductors: 15.28 [43]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 43 = 45 rows / 108 columns out of 286 (37.762%)
Density: 15.782% / 22.789% (17.044/r), total: 767 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 9 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 10
Basis length: 9, queue length: 1, step degree: 11, num pairs: 1
Basis total mons: 184, average length: 20.444
Number of pair polynomials: 1, at 74 column(s), 0.000
Average length for reductees: 55.00 [1], reductors: 16.17 [47]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 47 = 48 rows / 112 columns out of 364 (30.769%)
Density: 15.16% / 22.34% (16.979/r), total: 815 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 8
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 10 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

Do extern interreduction (length 7)
INTERREDUCE 7 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
7 + 0 = 7 rows / 64 columns
Density: 33.929% / 47.333% (21.714/r), total: 152 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [7]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 7
Number of pairs: 11
Max step: 1, time: 0.000
Max num entries matrix: 48 by 112
Max num rows matrix: 48 by 112
Approx mat cost: 5209.28, sym red cost: 3098
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: 0.004
Time: 0.000
dregs = [ 5, 6, 7, 6, 7, 8, 9, 9, 10, 11 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=2)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(2^15)
Rank: 3
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 7
Try rep mat lex method; E: Y0000
Get rep mat (dim: 65)
Rep mat time: 0.000
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 0.050
Get kernel for min poly
Kernel mat time: 0.001[r]
Nullity: 1
Get relations for all variables
REDUCE 3 polynomial(s) by 7 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
3 + 61 = 64 rows / 126 columns
Density: 14.36% / 21.296% (18.094/r), total: 1158 (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: 0.060
unideg = 65
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=2)
Time: 0.000
nsols = 2
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Starting MULTIPLICITY computation... (r=2)
nsols_mult = 2
====================================================================================================
n_r: 3, n_v: 4, n_e: 4, mdeg: 21
degs = [5, 9, 21, 7]
Multivariate Polynomial Ring in S0300, S0200, S0100, Y0000 over Finite Field in z15 of size 2^15
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=3)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^15)
Rank: 4
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 2
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: 7, num pairs: 1
Basis total mons: 268, average length: 67.000
Number of pair polynomials: 1, at 25 column(s), 0.000
Average length for reductees: 21.00 [1], reductors: 5.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 25 columns out of 330 (7.576%)
Density: 52% / 52% (13/r), total: 26 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 7 [1], av deg: 7.0
Degree counts: 7:1
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: 3, step degree: 8, num pairs: 1
Basis total mons: 292, average length: 58.400
Number of pair polynomials: 1, at 28 column(s), 0.000
Average length for reductees: 24.00 [1], reductors: 5.00 [2]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 2 = 3 rows / 30 columns out of 495 (6.061%)
Density: 37.778% / 38.395% (11.333/r), total: 34 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 8 [1], av deg: 8.0
Degree counts: 8:1
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: 6, queue length: 3, step degree: 9, num pairs: 2
Basis total mons: 320, average length: 53.333
Number of pair polynomials: 2, at 65 column(s), 0.000
Average length for reductees: 27.50 [2], reductors: 7.92 [13]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 13 = 15 rows / 82 columns out of 715 (11.469%)
Density: 12.846% / 14.374% (10.533/r), total: 158 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 9 [2], av deg: 9.0
Degree counts: 9:2
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: 8, queue length: 4, step degree: 10, num pairs: 3
Basis total mons: 391, average length: 48.875
Number of pair polynomials: 3, at 96 column(s), 0.000
Average length for reductees: 33.00 [3], reductors: 18.15 [20]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 20 = 23 rows / 130 columns out of 1001 (12.987%)
Density: 15.452% / 16.883% (20.087/r), total: 462 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (100.0%), min deg: 6 [1], av deg: 8.0
Degree counts: 6:1 8:1 10:1
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: 11, queue length: 9, step degree: 9, num pairs: 1
Basis total mons: 508, average length: 46.182
Number of pair polynomials: 1, at 62 column(s), 0.000
Average length for reductees: 55.00 [1], reductors: 8.83 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 73 columns out of 715 (10.210%)
Density: 21.135% / 22.44% (15.429/r), total: 108 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 6
Basis length: 12, queue length: 10, step degree: 10, num pairs: 2
Basis total mons: 565, average length: 47.083
Number of pair polynomials: 2, at 115 column(s), 0.000
Average length for reductees: 56.00 [2], reductors: 21.27 [15]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 15 = 17 rows / 119 columns out of 1001 (11.888%)
Density: 21.305% / 23.127% (25.353/r), total: 431 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 6 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 13, queue length: 10, step degree: 11, num pairs: 3
Basis total mons: 642, average length: 49.385
Number of pair polynomials: 3, at 139 column(s), 0.000
Average length for reductees: 51.67 [3], reductors: 26.22 [36]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 36 = 39 rows / 177 columns out of 1365 (12.967%)
Density: 15.921% / 18.036% (28.179/r), total: 1099 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
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 7 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 8
Basis length: 14, queue length: 10, step degree: 10, num pairs: 3
Basis total mons: 676, average length: 48.286
Number of pair polynomials: 3, at 97 column(s), 0.000
Average length for reductees: 34.00 [3], reductors: 26.38 [24]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 24 = 27 rows / 148 columns out of 1001 (14.785%)
Density: 18.393% / 20.449% (27.222/r), total: 735 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (66.7%), min deg: 10 [2], av deg: 10.0
Degree counts: 10:2
Queue insertion time: 0.000
Step 8 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 9
Basis length: 16, queue length: 12, step degree: 11, num pairs: 4
Basis total mons: 764, average length: 47.750
Number of pair polynomials: 4, at 138 column(s), 0.000
Average length for reductees: 44.00 [4], reductors: 28.15 [48]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 48 = 52 rows / 200 columns out of 1365 (14.652%)
Density: 14.683% / 16.935% (29.365/r), total: 1527 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000[r] + 0.000 + 0.000 = 0.000[r] [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (25.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
New max step: 9, time: 0.001[r]
Step 9 time: 0.000[r], [0.001], mat/total: 0.010/0.003[r], mem: 32.1MB (=max)

*******
STEP 10
Basis length: 17, queue length: 10, step degree: 12, num pairs: 5
Basis total mons: 808, average length: 47.529
1 pair eliminated
Number of pair polynomials: 4, at 205 column(s), 0.000
Average length for reductees: 41.50 [4], reductors: 22.15 [107]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 107 = 111 rows / 324 columns out of 1820 (17.802%)
Density: 7.0515% / 8.9439% (22.847/r), total: 2536 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 5
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (25.0%), min deg: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.001], mat/total: 0.010/0.004[r], mem: 32.1MB (=max)

*******
STEP 11
Basis length: 18, queue length: 8, step degree: 13, num pairs: 3
Basis total mons: 943, average length: 52.389
1 pair eliminated
Number of pair polynomials: 2, at 240 column(s), 0.000
Average length for reductees: 135.00 [2], reductors: 20.54 [112]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 112 = 114 rows / 340 columns out of 2380 (14.286%)
Density: 6.6331% / 8.4004% (22.553/r), total: 2571 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 7
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 11 time: 0.000, [0.001], mat/total: 0.010/0.006[r], mem: 32.1MB (=max)

*******
STEP 12
Basis length: 18, queue length: 5, step degree: 14, num pairs: 3
Basis total mons: 943, average length: 52.389
2 pairs eliminated
Number of pair polynomials: 1, at 190 column(s), 0.000
Average length for reductees: 135.00 [1], reductors: 22.80 [138]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 138 = 139 rows / 393 columns out of 3060 (12.843%)
Density: 6.008% / 7.8011% (23.612/r), total: 3282 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 15
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 12 time: 0.000, [0.002], mat/total: 0.010/0.007[r], mem: 32.1MB (=max)

*******
STEP 13
Basis length: 18, queue length: 2, step degree: 15, num pairs: 1
Basis total mons: 943, average length: 52.389
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 14
Basis length: 18, queue length: 1, step degree: 21, num pairs: 1
Basis total mons: 943, average length: 52.389
Number of pair polynomials: 1, at 219 column(s), 0.000
Average length for reductees: 215.00 [1], reductors: 22.86 [578]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 578 = 579 rows / 952 columns out of 12650 (7.526%)
Density: 2.4359% / 3.9657% (23.19/r), total: 13427 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 322
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 5 [1], av deg: 5.0
Degree counts: 5:1
Queue insertion time: 0.000
Step 14 time: 0.000, [0.002], mat/total: 0.010/0.009[r], mem: 32.1MB (=max)

Do extern interreduction (length 17)
INTERREDUCE 15 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
15 + 0 = 15 rows / 180 columns
Density: 24.074% / 27.597% (43.333/r), total: 650 (0.0MB)
Row sort time: 0.000
0.000 + 0.000 = 0.000 [15]
Total reduction time: 0.000
Reduction time: 0.000
Final extern interreduction time: 0.000

Final basis length: 15
Number of pairs: 28
Max step: 9, time: 0.001
Max num entries matrix: 579 by 952
Max num rows matrix: 579 by 952
Approx mat cost: 59566.1, sym red cost: 26396
Total pair setup time: 0.000
Total symbolic reduction time: 0.000
Total column sort time: 0.000
Total row sort time: 0.000
Total matrix time: 0.010
Total new polys time: 0.000
Total queue update time: 0.000
Total Faugere F4 time: 0.009, real time: 0.011
Time: 0.010
dregs = [ 7, 8, 9, 10, 9, 10, 11, 10, 11, 12, 13, 14, 15, 21 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=3)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(2^15)
Rank: 4
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 15
Try rep mat lex method; E: Y0000
Get rep mat (dim: 845)
Rep mat time: 0.009[r]
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 2.379
Get kernel for min poly
Kernel mat time: 0.690
Nullity: 1
Get relations for all variables
REDUCE 4 polynomial(s) by 15 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
4 + 1068 = 1072 rows / 1913 columns
Density: 1.653% / 2.6455% (31.622/r), total: 33899 (0.1MB)
Row sort time: 0.000
0.000[r] = 0.001[r] [4]
Number of unused reductors: 45
Total reduction time: 0.006[r]
Reduction time: 0.006[r]
Relations time: 0.700
Time: 3.780
unideg = 845
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=3)
Time: 0.020
nsols = 3
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=3)
nsols_mult = 3
====================================================================================================
n_r: 4, n_v: 5, n_e: 5, mdeg: 45
degs = [5, 9, 21, 45, 15]
Multivariate Polynomial Ring in S0400, S0300, S0200, S0100, Y0000 over Finite Field in z15 of size 2^15
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=4)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^15)
Rank: 5
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 2
No queue sort
Initial length: 5
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 4

*******
STEP 1
Basis length: 5, queue length: 4, step degree: 9, num pairs: 1
Basis total mons: 1826, average length: 365.200
Number of pair polynomials: 1, at 28 column(s), 0.000
Average length for reductees: 27.00 [1], reductors: 5.00 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 41 columns out of 2002 (2.048%)
Density: 17.073% / 20.071% (7/r), total: 77 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.004], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 2
Basis length: 6, queue length: 4, step degree: 10, num pairs: 1
Basis total mons: 1854, average length: 309.000
Number of pair polynomials: 1, at 32 column(s), 0.000
Average length for reductees: 28.00 [1], reductors: 10.75 [8]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 8 = 9 rows / 48 columns out of 3003 (1.598%)
Density: 26.389% / 30.059% (12.667/r), total: 114 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 2 time: 0.000, [0.004], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 3
Basis length: 7, queue length: 4, step degree: 11, num pairs: 1
Basis total mons: 1893, average length: 270.429
Number of pair polynomials: 1, at 46 column(s), 0.000
Average length for reductees: 39.00 [1], reductors: 18.70 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 55 columns out of 4368 (1.259%)
Density: 37.355% / 41.304% (20.545/r), total: 226 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 3 time: 0.000, [0.003], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 4
Basis length: 8, queue length: 5, step degree: 10, num pairs: 2
Basis total mons: 1927, average length: 240.875
Number of pair polynomials: 2, at 53 column(s), 0.000
Average length for reductees: 34.00 [2], reductors: 17.11 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 9 = 11 rows / 55 columns out of 3003 (1.832%)
Density: 36.694% / 41.188% (20.182/r), total: 222 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 10 [2], av deg: 10.0
Degree counts: 10:2
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: 10, queue length: 6, step degree: 11, num pairs: 2
Basis total mons: 2015, average length: 201.500
Number of pair polynomials: 2, at 62 column(s), 0.000
Average length for reductees: 44.00 [2], reductors: 26.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 14 = 16 rows / 65 columns out of 4368 (1.488%)
Density: 43.462% / 49.081% (28.25/r), total: 452 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 5 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 6
Basis length: 11, queue length: 5, step degree: 12, num pairs: 2
Basis total mons: 2059, average length: 187.182
1 pair eliminated
Number of pair polynomials: 1, at 65 column(s), 0.000
Average length for reductees: 44.00 [1], reductors: 26.44 [16]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 16 = 17 rows / 71 columns out of 6188 (1.147%)
Density: 38.691% / 45.136% (27.471/r), total: 467 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 6 time: 0.000, [0.000], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 7
Basis length: 11, queue length: 3, step degree: 15, num pairs: 1
Basis total mons: 2059, average length: 187.182
Number of pair polynomials: 1, at 62 column(s), 0.000
Average length for reductees: 58.00 [1], reductors: 19.33 [21]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 21 = 22 rows / 134 columns out of 15504 (0.864%)
Density: 15.739% / 17.042% (21.091/r), total: 464 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
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: 12, queue length: 5, step degree: 13, num pairs: 1
Basis total mons: 2139, average length: 178.250
Number of pair polynomials: 1, at 84 column(s), 0.000
Average length for reductees: 80.00 [1], reductors: 15.42 [36]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 36 = 37 rows / 290 columns out of 8568 (3.385%)
Density: 5.918% / 6.607% (17.162/r), total: 635 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 8 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 9
Basis length: 13, queue length: 6, step degree: 14, num pairs: 1
Basis total mons: 2325, average length: 178.846
Number of pair polynomials: 1, at 232 column(s), 0.000
Average length for reductees: 186.00 [1], reductors: 38.46 [26]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 26 = 27 rows / 350 columns out of 11628 (3.010%)
Density: 12.55% / 13.5% (43.926/r), total: 1186 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 9 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 10
Basis length: 14, queue length: 7, step degree: 15, num pairs: 1
Basis total mons: 2554, average length: 182.429
Number of pair polynomials: 1, at 305 column(s), 0.000
Average length for reductees: 229.00 [1], reductors: 35.10 [40]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 40 = 41 rows / 381 columns out of 15504 (2.457%)
Density: 10.454% / 11.465% (39.829/r), total: 1633 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 5
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.003], mat/total: 0.000/0.000, mem: 32.1MB (=max)

*******
STEP 11
Basis length: 15, queue length: 8, step degree: 14, num pairs: 2
Basis total mons: 2787, average length: 185.800
Number of pair polynomials: 2, at 369 column(s), 0.000
Average length for reductees: 233.00 [2], reductors: 31.64 [44]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 44 = 46 rows / 386 columns out of 11628 (3.320%)
Density: 10.464% / 11.41% (40.391/r), total: 1858 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000[r] [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (50.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
New max step: 11, time: 0.002[r]
Step 11 time: 0.002[r], [0.002], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 12
Basis length: 16, queue length: 8, step degree: 15, num pairs: 1
Basis total mons: 3084, average length: 192.750
Number of pair polynomials: 1, at 383 column(s), 0.000
Average length for reductees: 297.00 [1], reductors: 39.06 [71]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 71 = 72 rows / 490 columns out of 15504 (3.160%)
Density: 8.7018% / 9.6427% (42.639/r), total: 3070 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 14
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 12 time: 0.000, [0.004], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 13
Basis length: 16, queue length: 7, step degree: 17, num pairs: 2
Basis total mons: 3084, average length: 192.750
Number of pair polynomials: 2, at 172 column(s), 0.000
Average length for reductees: 80.00 [2], reductors: 48.78 [174]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 174 = 176 rows / 883 columns out of 26334 (3.353%)
Density: 5.5647% / 6.3438% (49.136/r), total: 8648 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 35
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 13 [1], av deg: 14.0
Degree counts: 13:1 15:1
Queue insertion time: 0.000
Step 13 time: 0.000, [0.006], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 14
Basis length: 18, queue length: 10, step degree: 15, num pairs: 1
Basis total mons: 3454, average length: 191.889
Number of pair polynomials: 1, at 258 column(s), 0.000
Average length for reductees: 218.00 [1], reductors: 13.57 [42]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 42 = 43 rows / 276 columns out of 15504 (1.780%)
Density: 6.6397% / 7.7792% (18.326/r), total: 788 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 14 time: 0.000, [0.003], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 15
Basis length: 18, queue length: 9, step degree: 16, num pairs: 1
Basis total mons: 3454, average length: 191.889
Number of pair polynomials: 1, at 222 column(s), 0.000
Average length for reductees: 152.00 [1], reductors: 25.16 [166]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 166 = 167 rows / 906 columns out of 20349 (4.452%)
Density: 2.8612% / 3.446% (25.922/r), total: 4329 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 58
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 15 time: 0.000, [0.004], mat/total: 0.010/0.010, mem: 32.1MB (=max)

*******
STEP 16
Basis length: 18, queue length: 8, step degree: 18, num pairs: 4
Basis total mons: 3454, average length: 191.889
Number of pair polynomials: 4, at 685 column(s), 0.000
Average length for reductees: 179.75 [4], reductors: 45.53 [473]
Symbolic reduction time: 0.001[r], column sort time: 0.000
4 + 473 = 477 rows / 1568 columns out of 33649 (4.660%)
Density: 2.9758% / 3.6451% (46.66/r), total: 22257 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 89
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
New max step: 16, time: 0.010[r]
Step 16 time: 0.009[r], [0.010], mat/total: 0.010/0.020, mem: 32.1MB (=max)

*******
STEP 17
Basis length: 18, queue length: 4, step degree: 19, num pairs: 2
Basis total mons: 3454, average length: 191.889
Number of pair polynomials: 2, at 656 column(s), 0.000
Average length for reductees: 224.50 [2], reductors: 47.13 [601]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 601 = 603 rows / 1827 columns out of 42504 (4.298%)
Density: 2.6119% / 3.2607% (47.72/r), total: 28775 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.006[r] [0]
Number of unused reductors: 153
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
New max step: 17, time: 0.010
Step 17 time: 0.009, [0.012], mat/total: 0.020/0.030, mem: 32.1MB (=max)

*******
STEP 18
Basis length: 18, queue length: 2, step degree: 21, num pairs: 1
Basis total mons: 3454, average length: 191.889
Number of pair polynomials: 1, at 219 column(s), 0.000
Average length for reductees: 215.00 [1], reductors: 15.61 [281]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 281 = 282 rows / 596 columns out of 65780 (0.906%)
Density: 2.7381% / 4.2458% (16.319/r), total: 4602 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 29
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 18 time: 0.000, [0.006], mat/total: 0.020/0.030, mem: 32.1MB (=max)

*******
STEP 19
Basis length: 19, queue length: 4, step degree: 16, num pairs: 2
Basis total mons: 3585, average length: 188.684
Number of pair polynomials: 2, at 325 column(s), 0.000
Average length for reductees: 131.00 [2], reductors: 43.53 [88]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 88 = 90 rows / 805 columns out of 20349 (3.956%)
Density: 5.6494% / 6.3397% (45.478/r), total: 4093 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 30
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (100.0%), min deg: 10 [1], av deg: 13.0
Degree counts: 10:1 16:1
Queue insertion time: 0.000
Step 19 time: 0.000, [0.006], mat/total: 0.020/0.030, mem: 32.1MB (=max)

*******
STEP 20
Basis length: 21, queue length: 8, step degree: 11, num pairs: 1
Basis total mons: 3863, average length: 183.952
Number of pair polynomials: 1, at 119 column(s), 0.000
Average length for reductees: 75.00 [1], reductors: 80.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 119 columns out of 4368 (2.724%)
Density: 65.126% / 65.126% (77.5/r), total: 155 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000[r] [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 20 time: 0.003[r], [0.004], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 21
Basis length: 22, queue length: 10, step degree: 10, num pairs: 1
Basis total mons: 3962, average length: 180.091
Number of pair polynomials: 1, at 103 column(s), 0.000
Average length for reductees: 99.00 [1], reductors: 5.00 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 129 columns out of 3003 (4.296%)
Density: 10.5% / 11.198% (13.545/r), total: 149 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 21 time: 0.000, [0.003], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 22
Basis length: 23, queue length: 12, step degree: 11, num pairs: 1
Basis total mons: 4080, average length: 177.391
Number of pair polynomials: 1, at 186 column(s), 0.000
Average length for reductees: 118.00 [1], reductors: 25.89 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 9 = 10 rows / 236 columns out of 4368 (5.403%)
Density: 14.873% / 15.642% (35.1/r), total: 351 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 22 time: 0.000, [0.004], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 23
Basis length: 24, queue length: 14, step degree: 12, num pairs: 4
Basis total mons: 4266, average length: 177.750
Number of pair polynomials: 4, at 373 column(s), 0.000
Average length for reductees: 119.50 [4], reductors: 27.48 [65]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 65 = 69 rows / 629 columns out of 6188 (10.165%)
Density: 5.2165% / 5.7816% (32.812/r), total: 2264 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (100.0%), min deg: 10 [2], av deg: 11.0
Degree counts: 10:2 12:2
Queue insertion time: 0.000
Step 23 time: 0.000, [0.003], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 24
Basis length: 28, queue length: 29, step degree: 11, num pairs: 1
Basis total mons: 5244, average length: 187.286
Number of pair polynomials: 1, at 394 column(s), 0.000
Average length for reductees: 237.00 [1], reductors: 59.73 [22]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 22 = 23 rows / 490 columns out of 4368 (11.218%)
Density: 13.762% / 14.439% (67.435/r), total: 1551 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 24 time: 0.000, [0.001], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 25
Basis length: 29, queue length: 33, step degree: 12, num pairs: 2
Basis total mons: 5575, average length: 192.241
Number of pair polynomials: 2, at 534 column(s), 0.000
Average length for reductees: 284.00 [2], reductors: 44.12 [77]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 77 = 79 rows / 665 columns out of 6188 (10.747%)
Density: 7.5473% / 8.1881% (50.19/r), total: 3965 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 2
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 25 time: 0.000, [0.003], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 26
Basis length: 29, queue length: 31, step degree: 13, num pairs: 6
Basis total mons: 5575, average length: 192.241
1 pair eliminated
Number of pair polynomials: 5, at 698 column(s), 0.000
Average length for reductees: 229.60 [5], reductors: 56.46 [72]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 72 = 77 rows / 790 columns out of 8568 (9.220%)
Density: 8.5698% / 9.3593% (67.701/r), total: 5213 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 3
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (40.0%), min deg: 13 [2], av deg: 13.0
Degree counts: 13:2
Queue insertion time: 0.000
Step 26 time: 0.000, [0.002], mat/total: 0.030/0.040, mem: 32.1MB (=max)

*******
STEP 27
Basis length: 31, queue length: 31, step degree: 14, num pairs: 4
Basis total mons: 6229, average length: 200.935
Number of pair polynomials: 4, at 869 column(s), 0.000
Average length for reductees: 327.00 [4], reductors: 62.67 [108]
Symbolic reduction time: 0.000, column sort time: 0.000[r]
4 + 108 = 112 rows / 963 columns out of 11628 (8.282%)
Density: 7.4878% / 8.3061% (72.107/r), total: 8076 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 3
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (50.0%), min deg: 12 [2], av deg: 12.0
Degree counts: 12:2
Queue insertion time: 0.000
Step 27 time: 0.003[r], [0.004], mat/total: 0.030/0.050, mem: 32.1MB (=max)

*******
STEP 28
Basis length: 33, queue length: 34, step degree: 13, num pairs: 5
Basis total mons: 6921, average length: 209.727
Number of pair polynomials: 5, at 1027 column(s), 0.000
Average length for reductees: 320.40 [5], reductors: 64.14 [135]
Symbolic reduction time: 0.000[r], column sort time: 0.000
5 + 135 = 140 rows / 1267 columns out of 8568 (14.788%)
Density: 5.7848% / 6.5424% (73.293/r), total: 10261 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 17
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (40.0%), min deg: 13 [2], av deg: 13.0
Degree counts: 13:2
Queue insertion time: 0.000
Step 28 time: 0.004[r], [0.004], mat/total: 0.030/0.060, mem: 32.1MB (=max)

*******
STEP 29
Basis length: 35, queue length: 36, step degree: 14, num pairs: 5
Basis total mons: 7861, average length: 224.600
Number of pair polynomials: 5, at 1433 column(s), 0.000
Average length for reductees: 470.80 [5], reductors: 79.32 [244]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 244 = 249 rows / 1733 columns out of 11628 (14.904%)
Density: 5.0304% / 5.7672% (87.177/r), total: 21707 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 18
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (40.0%), min deg: 14 [2], av deg: 14.0
Degree counts: 14:2
Queue insertion time: 0.000
Step 29 time: 0.000, [0.010], mat/total: 0.030/0.060, mem: 32.1MB (=max)

*******
STEP 30
Basis length: 37, queue length: 38, step degree: 15, num pairs: 7
Basis total mons: 9431, average length: 254.892
1 pair eliminated
Number of pair polynomials: 6, at 1921 column(s), 0.000
Average length for reductees: 579.17 [6], reductors: 88.40 [630]
Symbolic reduction time: 0.002[r], column sort time: 0.000
6 + 630 = 636 rows / 2876 columns out of 15504 (18.550%)
Density: 3.2346% / 3.8562% (93.028/r), total: 59166 (0.2MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [4]
Number of unused reductors: 107
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (66.7%), min deg: 13 [3], av deg: 13.5
Degree counts: 13:3 15:1
Queue insertion time: 0.000
New max step: 30, time: 0.020
Step 30 time: 0.019, [0.022], mat/total: 0.040/0.080, mem: 32.1MB (=max)

*******
STEP 31
Basis length: 41, queue length: 53, step degree: 14, num pairs: 1
Basis total mons: 11007, average length: 268.463
Number of pair polynomials: 1, at 345 column(s), 0.000
Average length for reductees: 227.00 [1], reductors: 145.77 [13]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 13 = 14 rows / 553 columns out of 11628 (4.756%)
Density: 27.409% / 29.019% (151.57/r), total: 2122 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 31 time: 0.000, [0.003], mat/total: 0.040/0.080, mem: 32.1MB (=max)

*******
STEP 32
Basis length: 41, queue length: 52, step degree: 16, num pairs: 14
Basis total mons: 11007, average length: 268.463
1 pair eliminated
Number of pair polynomials: 13, at 2525 column(s), 0.000
Average length for reductees: 299.00 [13], reductors: 87.76 [1295]
Symbolic reduction time: 0.004[r], column sort time: 0.000
13 + 1295 = 1308 rows / 4234 columns out of 20349 (20.807%)
Density: 2.1223% / 2.6673% (89.86/r), total: 117537 (0.4MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.029[r] + 0.000 + 0.000 = 0.029 [4]
Number of unused reductors: 176
After ech memory: 32.1MB (=max)
Num new polynomials: 4 (30.8%), min deg: 12 [1], av deg: 14.0
Degree counts: 12:1 14:2 16:1
Queue insertion time: 0.000
New max step: 32, time: 0.040
Step 32 time: 0.040, [0.043], mat/total: 0.070/0.120, mem: 32.1MB (=max)

*******
STEP 33
Basis length: 45, queue length: 54, step degree: 13, num pairs: 2
Basis total mons: 12658, average length: 281.289
Number of pair polynomials: 2, at 481 column(s), 0.000
Average length for reductees: 184.00 [2], reductors: 65.53 [157]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 157 = 159 rows / 1160 columns out of 8568 (13.539%)
Density: 5.7775% / 6.4238% (67.019/r), total: 10656 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.001[r] + 0.000 + 0.000 = 0.001[r] [1]
Number of unused reductors: 36
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
Step 33 time: 0.006[r], [0.008], mat/total: 0.080/0.129, mem: 32.1MB (=max)

*******
STEP 34
Basis length: 46, queue length: 57, step degree: 14, num pairs: 5
Basis total mons: 12825, average length: 278.804
Number of pair polynomials: 5, at 966 column(s), 0.000
Average length for reductees: 186.20 [5], reductors: 58.51 [235]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 235 = 240 rows / 1552 columns out of 11628 (13.347%)
Density: 3.9412% / 4.5171% (61.167/r), total: 14680 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.001[r] + 0.000 + 0.000 = 0.003[r] [3]
Number of unused reductors: 47
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (60.0%), min deg: 12 [2], av deg: 12.7
Degree counts: 12:2 14:1
Queue insertion time: 0.000
Step 34 time: 0.008[r], [0.009], mat/total: 0.090/0.140, mem: 32.1MB (=max)

*******
STEP 35
Basis length: 49, queue length: 77, step degree: 13, num pairs: 2
Basis total mons: 13458, average length: 274.653
Number of pair polynomials: 2, at 519 column(s), 0.000
Average length for reductees: 220.00 [2], reductors: 71.47 [141]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 141 = 143 rows / 1233 columns out of 8568 (14.391%)
Density: 5.9648% / 6.5061% (73.545/r), total: 10517 (0.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 27
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 35 time: 0.000, [0.007], mat/total: 0.090/0.140, mem: 32.1MB (=max)

*******
STEP 36
Basis length: 49, queue length: 75, step degree: 15, num pairs: 9
Basis total mons: 13458, average length: 274.653
3 pairs eliminated
Number of pair polynomials: 6, at 1376 column(s), 0.000
Average length for reductees: 215.50 [6], reductors: 66.12 [570]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 570 = 576 rows / 2715 columns out of 15504 (17.512%)
Density: 2.4926% / 2.973% (67.674/r), total: 38980 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000[r]
0.009[r] + 0.000 + 0.000 = 0.009 [2]
Number of unused reductors: 95
After ech memory: 32.1MB (=max)
Num new polynomials: 2 (33.3%), min deg: 15 [2], av deg: 15.0
Degree counts: 15:2
Queue insertion time: 0.000
Step 36 time: 0.018[r], [0.019], mat/total: 0.110/0.160, mem: 32.1MB (=max)

*******
STEP 37
Basis length: 51, queue length: 75, step degree: 16, num pairs: 9
Basis total mons: 14570, average length: 285.686
Number of pair polynomials: 9, at 2531 column(s), 0.000
Average length for reductees: 372.89 [9], reductors: 85.61 [973]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 973 = 982 rows / 4198 columns out of 20349 (20.630%)
Density: 2.102% / 2.5807% (88.241/r), total: 86653 (0.3MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.019[r] + 0.000 + 0.000 = 0.020 [3]
Number of unused reductors: 216
After ech memory: 32.1MB (=max)
Num new polynomials: 3 (33.3%), min deg: 14 [1], av deg: 15.3
Degree counts: 14:1 16:2
Queue insertion time: 0.000
Step 37 time: 0.020, [0.032], mat/total: 0.130/0.180, mem: 32.1MB (=max)

*******
STEP 38
Basis length: 54, queue length: 80, step degree: 15, num pairs: 3
Basis total mons: 16397, average length: 303.648
Number of pair polynomials: 3, at 1433 column(s), 0.000
Average length for reductees: 422.00 [3], reductors: 90.60 [194]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 194 = 197 rows / 1911 columns out of 15504 (12.326%)
Density: 5.0052% / 5.6621% (95.65/r), total: 18843 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.004[r] [1]
Number of unused reductors: 30
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (33.3%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 38 time: 0.009, [0.011], mat/total: 0.140/0.190, mem: 32.1MB (=max)

*******
STEP 39
Basis length: 55, queue length: 82, step degree: 16, num pairs: 5
Basis total mons: 16885, average length: 307.000
Number of pair polynomials: 5, at 1713 column(s), 0.000
Average length for reductees: 474.80 [5], reductors: 79.63 [417]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 417 = 422 rows / 2354 columns out of 20349 (11.568%)
Density: 3.5815% / 4.1574% (84.308/r), total: 35578 (0.1MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.007[r] + 0.000 + 0.000 = 0.009[r] [1]
Number of unused reductors: 53
After ech memory: 32.1MB (=max)
Num new polynomials: 1 (20.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 39 time: 0.009, [0.016], mat/total: 0.150/0.200, mem: 32.1MB (=max)

*******
STEP 40
Basis length: 56, queue length: 82, step degree: 17, num pairs: 26
Basis total mons: 17575, average length: 313.839
7 pairs eliminated
Number of pair polynomials: 19, at 3602 column(s), 0.000
Average length for reductees: 499.47 [19], reductors: 79.13 [1685]
Symbolic reduction time: 0.000, column sort time: 0.001[r]
19 + 1685 = 1704 rows / 4949 columns out of 26334 (18.793%)
Density: 1.6936% / 2.1359% (83.819/r), total: 142827 (0.5MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.039[r] + 0.000 + 0.000 = 0.039[r] [0]
Number of unused reductors: 139
After ech memory: 32.1MB (=max)
No new polynomials
Queue insertion time: 0.000
New max step: 40, time: 0.050
Step 40 time: 0.049, [0.054], mat/total: 0.190/0.250, mem: 32.1MB (=max)

*******
STEP 41
Basis length: 56, queue length: 56, step degree: 18, num pairs: 20
Basis total mons: 17575, average length: 313.839
6 pairs eliminated
Number of pair polynomials: 14, at 3807 column(s), 0.000
Average length for reductees: 377.14 [14], reductors: 93.50 [2756]
Symbolic reduction time: 0.010, column sort time: 0.000
14 + 2756 = 2770 rows / 7293 columns out of 33649 (21.674%)
Density: 1.3017% / 1.7236% (94.932/r), total: 262962 (1.0MB)
Before ech memory: 32.1MB (=max)
Row sort time: 0.000
0.059 + 0.000 + 0.000 = 0.068[r] [1]
Number of unused reductors: 541
After ech memory: 64.1MB (=max)
Num new polynomials: 1 (7.1%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000
New max step: 41, time: 0.080
Step 41 time: 0.080, [0.089], mat/total: 0.260/0.330, mem: 64.1MB (=max)

*******
STEP 42
Basis length: 57, queue length: 40, step degree: 19, num pairs: 19
Basis total mons: 18590, average length: 326.140
10 pairs eliminated
Number of pair polynomials: 9, at 4429 column(s), 0.000
Average length for reductees: 635.22 [9], reductors: 92.34 [3325]
Symbolic reduction time: 0.010, column sort time: 0.000
9 + 3325 = 3334 rows / 8134 columns out of 42504 (19.137%)
Density: 1.1533% / 1.5697% (93.807/r), total: 312751 (1.2MB)
Before ech memory: 64.1MB (=max)
Row sort time: 0.000[r]
0.080 + 0.000 + 0.000 = 0.080 [0]
Number of unused reductors: 340
After ech memory: 64.1MB (=max)
No new polynomials
Queue insertion time: 0.000
New max step: 42, time: 0.107[r]
Step 42 time: 0.108[r], [0.108], mat/total: 0.360/0.440, mem: 64.1MB (=max)

*******
STEP 43
Basis length: 57, queue length: 21, step degree: 20, num pairs: 8
Basis total mons: 18590, average length: 326.140
5 pairs eliminated
Number of pair polynomials: 3, at 3021 column(s), 0.000
Average length for reductees: 696.33 [3], reductors: 86.73 [2930]
Symbolic reduction time: 0.009, column sort time: 0.003[r]
3 + 2930 = 2933 rows / 7494 columns out of 53130 (14.105%)
Density: 1.1657% / 1.5758% (87.357/r), total: 256217 (1.0MB)
Before ech memory: 64.1MB (=max)
Row sort time: 0.000
0.060 + 0.000 + 0.000 = 0.060 [0]
Number of unused reductors: 571
After ech memory: 64.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 43 time: 0.080, [0.084], mat/total: 0.420/0.520, mem: 64.1MB (=max)

*******
STEP 44
Basis length: 57, queue length: 13, step degree: 21, num pairs: 5
Basis total mons: 18590, average length: 326.140
4 pairs eliminated
Number of pair polynomials: 1, at 1166 column(s), 0.000
Average length for reductees: 265.00 [1], reductors: 81.04 [3139]
Symbolic reduction time: 0.009, column sort time: 0.002[r]
1 + 3139 = 3140 rows / 7645 columns out of 65780 (11.622%)
Density: 1.0608% / 1.4666% (81.1/r), total: 254653 (1.0MB)
Before ech memory: 64.1MB (=max)
Row sort time: 0.000
0.060 + 0.000 + 0.000 = 0.060 [0]
Number of unused reductors: 635
After ech memory: 64.1MB (=max)
No new polynomials
Queue insertion time: 0.000
Step 44 time: 0.080, [0.084], mat/total: 0.480/0.600, mem: 64.1MB (=max)

*******
STEP 45
Basis length: 57, queue length: 8, step degree: 22, num pairs: 3
Basis total mons: 18590, average length: 326.140
3 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 46
Basis length: 57, queue length: 5, step degree: 23, num pairs: 2
Basis total mons: 18590, average length: 326.140
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 47
Basis length: 57, queue length: 3, step degree: 24, num pairs: 1
Basis total mons: 18590, average length: 326.140
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 48
Basis length: 57, queue length: 2, step degree: 25, num pairs: 1
Basis total mons: 18590, average length: 326.140
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 49
Basis length: 57, queue length: 1, step degree: 45, num pairs: 1
Basis total mons: 18590, average length: 326.140
Number of pair polynomials: 1, at 1525 column(s), 0.000
Average length for reductees: 1521.00 [1], reductors: 72.70 [14557]
Symbolic reduction time: 0.044[r], column sort time: 0.000
1 + 14557 = 14558 rows / 20206 columns out of 2118760 (0.954%)
Density: 0.36028% / 0.71953% (72.798/r), total: 1059797 (4.0MB)
Before ech memory: 64.1MB (=max)
Row sort time: 0.000
0.065[r] + 0.000 + 0.000 = 0.070 [1]
Number of unused reductors: 9176
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 1 (100.0%), min deg: 7 [1], av deg: 7.0
Degree counts: 7:1
Queue insertion time: 0.000
New max step: 49, time: 0.130
Step 49 time: 0.129, [0.138], mat/total: 0.550/0.730, mem: 64.1MB, max: 99.9MB

*******
STEP 50
Basis length: 58, queue length: 5, step degree: 8, num pairs: 1
Basis total mons: 18616, average length: 320.966
Number of pair polynomials: 1, at 30 column(s), 0.000
Average length for reductees: 26.00 [1], reductors: 5.00 [2]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 2 = 3 rows / 32 columns out of 1287 (2.486%)
Density: 37.5% / 38.244% (12/r), total: 36 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 1 (100.0%), min deg: 8 [1], av deg: 8.0
Degree counts: 8:1
Queue insertion time: 0.000
Step 50 time: 0.000, [0.004], mat/total: 0.550/0.730, mem: 64.1MB, max: 99.9MB

*******
STEP 51
Basis length: 59, queue length: 9, step degree: 9, num pairs: 2
Basis total mons: 18646, average length: 316.034
Number of pair polynomials: 2, at 139 column(s), 0.000
Average length for reductees: 28.00 [2], reductors: 30.43 [7]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 7 = 9 rows / 148 columns out of 2002 (7.393%)
Density: 20.195% / 21.192% (29.889/r), total: 269 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 2 (100.0%), min deg: 7 [1], av deg: 8.0
Degree counts: 7:1 9:1
Queue insertion time: 0.000
Step 51 time: 0.000, [0.005], mat/total: 0.550/0.730, mem: 64.1MB, max: 99.9MB

*******
STEP 52
Basis length: 61, queue length: 30, step degree: 10, num pairs: 4
Basis total mons: 18732, average length: 307.082
Number of pair polynomials: 4, at 187 column(s), 0.000[r]
Average length for reductees: 33.75 [4], reductors: 27.20 [20]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 20 = 24 rows / 227 columns out of 3003 (7.559%)
Density: 12.463% / 13.38% (28.292/r), total: 679 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 3 (75.0%), min deg: 8 [2], av deg: 8.7
Degree counts: 8:2 10:1
Queue insertion time: 0.000
Step 52 time: 0.003[r], [0.005], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 53
Basis length: 64, queue length: 51, step degree: 9, num pairs: 1
Basis total mons: 18951, average length: 296.109
Number of pair polynomials: 1, at 109 column(s), 0.000
Average length for reductees: 63.00 [1], reductors: 35.50 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 145 columns out of 2002 (7.243%)
Density: 26.207% / 27.718% (38/r), total: 418 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 53 time: 0.000, [0.002], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 54
Basis length: 65, queue length: 58, step degree: 10, num pairs: 4
Basis total mons: 19048, average length: 293.046
Number of pair polynomials: 4, at 278 column(s), 0.000
Average length for reductees: 73.75 [4], reductors: 37.09 [57]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 57 = 61 rows / 485 columns out of 3003 (16.151%)
Density: 8.1426% / 8.9572% (39.492/r), total: 2409 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 4
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 54 time: 0.000, [0.003], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 55
Basis length: 65, queue length: 54, step degree: 11, num pairs: 6
Basis total mons: 19048, average length: 293.046
1 pair eliminated
Number of pair polynomials: 5, at 380 column(s), 0.000
Average length for reductees: 72.60 [5], reductors: 40.02 [55]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 55 = 60 rows / 554 columns out of 4368 (12.683%)
Density: 7.7136% / 8.6483% (42.733/r), total: 2564 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 1 (20.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 55 time: 0.000, [0.004], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 56
Basis length: 66, queue length: 53, step degree: 12, num pairs: 4
Basis total mons: 19172, average length: 290.485
Number of pair polynomials: 4, at 488 column(s), 0.000
Average length for reductees: 101.00 [4], reductors: 43.15 [96]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 96 = 100 rows / 656 columns out of 6188 (10.601%)
Density: 6.9299% / 7.8836% (45.46/r), total: 4546 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 18
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 2 (50.0%), min deg: 10 [2], av deg: 10.0
Degree counts: 10:2
Queue insertion time: 0.000
Step 56 time: 0.000, [0.004], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 57
Basis length: 68, queue length: 59, step degree: 11, num pairs: 3
Basis total mons: 19340, average length: 284.412
Number of pair polynomials: 3, at 323 column(s), 0.000
Average length for reductees: 103.67 [3], reductors: 38.06 [63]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 63 = 66 rows / 671 columns out of 4368 (15.362%)
Density: 6.1171% / 7.2324% (41.045/r), total: 2709 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 13
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 2 (66.7%), min deg: 11 [2], av deg: 11.0
Degree counts: 11:2
Queue insertion time: 0.000
Step 57 time: 0.000, [0.003], mat/total: 0.550/0.740, mem: 64.1MB, max: 99.9MB

*******
STEP 58
Basis length: 70, queue length: 72, step degree: 12, num pairs: 5
Basis total mons: 19835, average length: 283.357
Number of pair polynomials: 5, at 1080 column(s), 0.000
Average length for reductees: 199.00 [5], reductors: 51.85 [178]
Symbolic reduction time: 0.000, column sort time: 0.000[r]
5 + 178 = 183 rows / 1399 columns out of 6188 (22.608%)
Density: 3.9939% / 4.6978% (55.874/r), total: 10225 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 27
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 3 (60.0%), min deg: 12 [3], av deg: 12.0
Degree counts: 12:3
Queue insertion time: 0.000
Step 58 time: 0.009[r], [0.009], mat/total: 0.550/0.750, mem: 64.1MB, max: 99.9MB

*******
STEP 59
Basis length: 73, queue length: 86, step degree: 13, num pairs: 12
Basis total mons: 20828, average length: 285.315
1 pair eliminated
Number of pair polynomials: 11, at 1676 column(s), 0.000
Average length for reductees: 182.00 [11], reductors: 65.86 [465]
Symbolic reduction time: 0.000, column sort time: 0.000
11 + 465 = 476 rows / 2375 columns out of 8568 (27.719%)
Density: 2.8862% / 3.485% (68.548/r), total: 32629 (0.1MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.006[r] [3]
Number of unused reductors: 107
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 3 (27.3%), min deg: 11 [2], av deg: 11.7
Degree counts: 11:2 13:1
Queue insertion time: 0.000
Step 59 time: 0.010, [0.016], mat/total: 0.560/0.760, mem: 64.1MB, max: 99.9MB

*******
STEP 60
Basis length: 76, queue length: 97, step degree: 12, num pairs: 2
Basis total mons: 21531, average length: 283.303
Number of pair polynomials: 2, at 561 column(s), 0.000
Average length for reductees: 327.00 [2], reductors: 64.87 [89]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 89 = 91 rows / 1013 columns out of 6188 (16.370%)
Density: 6.972% / 7.6922% (70.626/r), total: 6427 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 22
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 60 time: 0.000, [0.007], mat/total: 0.560/0.760, mem: 64.1MB, max: 99.9MB

*******
STEP 61
Basis length: 76, queue length: 95, step degree: 13, num pairs: 1
Basis total mons: 21531, average length: 283.303
Number of pair polynomials: 1, at 133 column(s), 0.000
Average length for reductees: 99.00 [1], reductors: 107.21 [29]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 29 = 30 rows / 805 columns out of 8568 (9.395%)
Density: 13.284% / 14.118% (106.93/r), total: 3208 (0.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 10
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 61 time: 0.000, [0.006], mat/total: 0.560/0.760, mem: 64.1MB, max: 99.9MB

*******
STEP 62
Basis length: 76, queue length: 94, step degree: 14, num pairs: 16
Basis total mons: 21531, average length: 283.303
Number of pair polynomials: 16, at 2330 column(s), 0.000[r]
Average length for reductees: 168.88 [16], reductors: 55.50 [784]
Symbolic reduction time: 0.000, column sort time: 0.000
16 + 784 = 800 rows / 3756 columns out of 11628 (32.301%)
Density: 1.538% / 2.0028% (57.767/r), total: 46214 (0.2MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [1]
Number of unused reductors: 116
After ech memory: 64.1MB, max: 99.9MB
Num new polynomials: 1 (6.2%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 62 time: 0.019, [0.024], mat/total: 0.570/0.780, mem: 64.1MB, max: 99.9MB

*******
STEP 63
Basis length: 77, queue length: 84, step degree: 15, num pairs: 17
Basis total mons: 21804, average length: 283.169
3 pairs eliminated
Number of pair polynomials: 14, at 2062 column(s), 0.000
Average length for reductees: 156.14 [14], reductors: 68.15 [1362]
Symbolic reduction time: 0.005[r], column sort time: 0.000
14 + 1362 = 1376 rows / 5134 columns out of 15504 (33.114%)
Density: 1.3449% / 1.8096% (69.049/r), total: 95011 (0.4MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.017[r] + 0.000 + 0.000 = 0.019[r] [0]
Number of unused reductors: 502
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 63 time: 0.030, [0.033], mat/total: 0.590/0.810, mem: 64.1MB, max: 99.9MB

*******
STEP 64
Basis length: 77, queue length: 67, step degree: 16, num pairs: 17
Basis total mons: 21804, average length: 283.169
6 pairs eliminated
Number of pair polynomials: 11, at 2592 column(s), 0.000
Average length for reductees: 202.55 [11], reductors: 90.15 [2807]
Symbolic reduction time: 0.009, column sort time: 0.003[r]
11 + 2807 = 2818 rows / 8426 columns out of 20349 (41.407%)
Density: 1.0751% / 1.5188% (90.586/r), total: 255271 (1.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.038[r] + 0.000 + 0.000 = 0.039[r] [0]
Number of unused reductors: 1271
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 64 time: 0.059, [0.062], mat/total: 0.630/0.870, mem: 64.1MB, max: 99.9MB

*******
STEP 65
Basis length: 77, queue length: 50, step degree: 17, num pairs: 18
Basis total mons: 21804, average length: 283.169
7 pairs eliminated
Number of pair polynomials: 11, at 2433 column(s), 0.000
Average length for reductees: 178.36 [11], reductors: 87.42 [2818]
Symbolic reduction time: 0.009, column sort time: 0.000
11 + 2818 = 2829 rows / 9074 columns out of 26334 (34.457%)
Density: 0.96726% / 1.4358% (87.77/r), total: 248300 (0.9MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.040 + 0.000 + 0.000 = 0.040 [0]
Number of unused reductors: 1310
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000[r]
Step 65 time: 0.060, [0.066], mat/total: 0.670/0.930, mem: 64.1MB, max: 99.9MB

*******
STEP 66
Basis length: 77, queue length: 32, step degree: 18, num pairs: 10
Basis total mons: 21804, average length: 283.169
6 pairs eliminated
Number of pair polynomials: 4, at 1297 column(s), 0.000
Average length for reductees: 269.25 [4], reductors: 83.68 [3043]
Symbolic reduction time: 0.009, column sort time: 0.000
4 + 3043 = 3047 rows / 9527 columns out of 33649 (28.313%)
Density: 0.88086% / 1.3291% (83.919/r), total: 255702 (1.0MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.030 + 0.000 + 0.000 = 0.039[r] [0]
Number of unused reductors: 1755
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 66 time: 0.049, [0.062], mat/total: 0.710/0.980, mem: 64.1MB, max: 99.9MB

*******
STEP 67
Basis length: 77, queue length: 22, step degree: 19, num pairs: 6
Basis total mons: 21804, average length: 283.169
2 pairs eliminated
Number of pair polynomials: 4, at 1880 column(s), 0.000
Average length for reductees: 237.25 [4], reductors: 97.07 [3386]
Symbolic reduction time: 0.014[r], column sort time: 0.000
4 + 3386 = 3390 rows / 10411 columns out of 42504 (24.494%)
Density: 0.93396% / 1.4038% (97.235/r), total: 329626 (1.3MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.049 + 0.000 + 0.000 = 0.057[r] [0]
Number of unused reductors: 1410
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 67 time: 0.080, [0.082], mat/total: 0.770/1.060, mem: 64.1MB, max: 99.9MB

*******
STEP 68
Basis length: 77, queue length: 16, step degree: 20, num pairs: 6
Basis total mons: 21804, average length: 283.169
3 pairs eliminated
Number of pair polynomials: 3, at 1912 column(s), 0.000
Average length for reductees: 232.33 [3], reductors: 86.53 [4410]
Symbolic reduction time: 0.017[r], column sort time: 0.005[r]
3 + 4410 = 4413 rows / 11958 columns out of 53130 (22.507%)
Density: 0.72446% / 1.1439% (86.63/r), total: 382300 (1.5MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.059 + 0.000 + 0.000 = 0.059 [0]
Number of unused reductors: 1799
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
Step 68 time: 0.098[r], [0.100], mat/total: 0.840/1.160, mem: 64.1MB, max: 99.9MB

*******
STEP 69
Basis length: 77, queue length: 10, step degree: 21, num pairs: 6
Basis total mons: 21804, average length: 283.169
5 pairs eliminated
Number of pair polynomials: 1, at 965 column(s), 0.000
Average length for reductees: 281.00 [1], reductors: 102.44 [6679]
Symbolic reduction time: 0.020, column sort time: 0.006[r]
1 + 6679 = 6680 rows / 15172 columns out of 65780 (23.065%)
Density: 0.67538% / 1.0823% (102.47/r), total: 684491 (2.6MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.000
0.139[r] + 0.000 + 0.000 = 0.144[r] [0]
Number of unused reductors: 2280
After ech memory: 64.1MB, max: 99.9MB
No new polynomials
Queue insertion time: 0.000
New max step: 69, time: 0.180
Step 69 time: 0.180, [0.189], mat/total: 0.990/1.340, mem: 64.1MB, max: 99.9MB

*******
STEP 70
Basis length: 77, queue length: 4, step degree: 22, num pairs: 2
Basis total mons: 21804, average length: 283.169
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 71
Basis length: 77, queue length: 2, step degree: 23, num pairs: 1
Basis total mons: 21804, average length: 283.169
Number of pair polynomials: 1, at 1290 column(s), 0.000
Average length for reductees: 281.00 [1], reductors: 103.68 [11864]
Symbolic reduction time: 0.049, column sort time: 0.009[r]
1 + 11864 = 11865 rows / 21407 columns out of 98280 (21.782%)
Density: 0.48438% / 0.83299% (103.69/r), total: 1230286 (4.7MB)
Before ech memory: 64.1MB, max: 99.9MB
Row sort time: 0.003[r]
0.200 + 0.000 + 0.000 = 0.207[r] [0]
Number of unused reductors: 5559
After ech memory: 64.1MB, max: 102.1MB
No new polynomials
Queue insertion time: 0.000
New max step: 71, time: 0.280
Step 71 time: 0.279, [0.281], mat/total: 1.210/1.620, mem: 64.1MB, max: 102.1MB

*******
STEP 72
Basis length: 77, queue length: 1, step degree: 24, num pairs: 1
Basis total mons: 21804, average length: 283.169
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

Do extern interreduction (length 42)
INTERREDUCE 38 polynomial(s)
Symbolic reduction time: 0.000
Column sort time: 0.000
38 + 144 = 182 rows / 2180 columns
Density: 3.9142% / 4.8889% (85.33/r), total: 15530 (0.1MB)
Row sort time: 0.000
0.000[r] + 0.000 = 0.000[r] [38]
Number of unused reductors: 14
Total reduction time: 0.005[r]
Reduction time: 0.006[r]
Final extern interreduction time: 0.006[r]

Final basis length: 38
Number of pairs: 264
Max step: 71, time: 0.280
Max num entries matrix: 14558 by 20206
Max num rows matrix: 14558 by 20206
Approx mat cost: 3.98003e+07, sym red cost: 6.41485e+06
Total pair setup time: 0.020
Total symbolic reduction time: 0.280
Total column sort time: 0.090
Total row sort time: 0.040
Total matrix time: 1.210
Total new polys time: 0.010
Total queue update time: 0.000
Total Faugere F4 time: 1.629, real time: 1.856
Time: 1.630
dregs = [ 9, 10, 11, 10, 11, 12, 15, 13, 14, 15, 14, 15, 17, 15, 16, 18, 19, 21, 16, 11, 10, 11, 12, 11, 12, 13, 14, 13, 14, 15, 14, 16, 13, 14, 13, 15, 16, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 45, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=4)
*****************
FGLM ORDER CHANGE
*****************

Coefficient ring: GF(2^15)
Rank: 5
Initial order: Graded Reverse Lexicographical
Final order: Lexicographical
Basis length: 38
Try rep mat lex method; E: Y0000
Get rep mat (dim: 10985)
Rep mat time: 117.869
Use Keller-Gehrig for spin
Keller-Gehrig matrix time: 2808.450
Get kernel for min poly
Kernel mat time: 139.589
Nullity: 1
Get relations for all variables
REDUCE 5 polynomial(s) by 38 polynomial(s)
Symbolic reduction time: 0.630
Column sort time: 0.033[r]
5 + 52616 = 52621 rows / 63601 columns
Density: 0.22485% / 0.45501% (143.01/r), total: 7525150 (28.7MB)
Row sort time: 0.009
0.190 = 0.195[r] [5]
Number of unused reductors: 6547
Total reduction time: 0.880
Reduction time: 0.890
Relations time: 141.970
Time: 3207.900
unideg = 10985
----------------------------------------------------------------------------------------------------
Starting UNIV SOLVING computation... (r=4)
Time: 0.430
nsols = 1
----------------------------------------------------------------------------------------------------
Starting MULTIPLICITY computation... (r=4)
nsols_mult = 1
====================================================================================================
n_r: 5, n_v: 6, n_e: 6, mdeg: 93
degs = [5, 9, 21, 45, 93, 31]
Multivariate Polynomial Ring in S0500, S0400, S0300, S0200, S0100, Y0000 over Finite Field in z15 of size 2^15
----------------------------------------------------------------------------------------------------
Starting GB computation... (r=5)
********************
FAUGERE F4 ALGORITHM
********************
Coefficient ring: GF(2^15)
Rank: 6
Order: Graded Reverse Lexicographical
NEW hash table
Matrix kind: Packed GF(2^k)
Datum size: 2
No queue sort
Initial length: 6
Inhomogeneous

Initial queue setup time: 0.000
Initial queue length: 5

*******
STEP 1
Basis length: 6, queue length: 5, step degree: 9, num pairs: 1
Basis total mons: 13347, average length: 2224.500
Number of pair polynomials: 1, at 28 column(s), 0.000
Average length for reductees: 27.00 [1], reductors: 5.00 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 41 columns out of 5005 (0.819%)
Density: 17.073% / 20.071% (7/r), total: 77 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
New max step: 1, time: 0.000
Step 1 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 2
Basis length: 7, queue length: 5, step degree: 10, num pairs: 1
Basis total mons: 13375, average length: 1910.714
Number of pair polynomials: 1, at 32 column(s), 0.000
Average length for reductees: 28.00 [1], reductors: 10.75 [8]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 8 = 9 rows / 48 columns out of 8008 (0.599%)
Density: 26.389% / 30.059% (12.667/r), total: 114 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000
Step 2 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 3
Basis length: 8, queue length: 5, step degree: 11, num pairs: 1
Basis total mons: 13414, average length: 1676.750
Number of pair polynomials: 1, at 46 column(s), 0.000
Average length for reductees: 39.00 [1], reductors: 18.70 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 55 columns out of 12376 (0.444%)
Density: 37.355% / 41.304% (20.545/r), total: 226 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 9 [1], av deg: 9.0
Degree counts: 9:1
Queue insertion time: 0.000
Step 3 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 4
Basis length: 9, queue length: 6, step degree: 10, num pairs: 2
Basis total mons: 13448, average length: 1494.222
Number of pair polynomials: 2, at 53 column(s), 0.000
Average length for reductees: 34.00 [2], reductors: 17.11 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 9 = 11 rows / 55 columns out of 8008 (0.687%)
Density: 36.694% / 41.188% (20.182/r), total: 222 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (100.0%), min deg: 10 [2], av deg: 10.0
Degree counts: 10:2
Queue insertion time: 0.000
Step 4 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 5
Basis length: 11, queue length: 7, step degree: 11, num pairs: 2
Basis total mons: 13536, average length: 1230.545
Number of pair polynomials: 2, at 62 column(s), 0.000
Average length for reductees: 44.00 [2], reductors: 26.00 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 14 = 16 rows / 65 columns out of 12376 (0.525%)
Density: 43.462% / 49.081% (28.25/r), total: 452 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
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, [0.001], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 6
Basis length: 12, queue length: 6, step degree: 12, num pairs: 2
Basis total mons: 13580, average length: 1131.667
1 pair eliminated
Number of pair polynomials: 1, at 65 column(s), 0.000
Average length for reductees: 44.00 [1], reductors: 26.44 [16]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 16 = 17 rows / 71 columns out of 18564 (0.382%)
Density: 38.691% / 45.136% (27.471/r), total: 467 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 6 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 7
Basis length: 12, queue length: 4, step degree: 21, num pairs: 1
Basis total mons: 13580, average length: 1131.667
Number of pair polynomials: 1, at 219 column(s), 0.000
Average length for reductees: 215.00 [1], reductors: 15.61 [281]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 281 = 282 rows / 596 columns out of 296010 (0.201%)
Density: 2.7381% / 4.2458% (16.319/r), total: 4602 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 29
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 7 time: 0.000, [0.003], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 8
Basis length: 13, queue length: 5, step degree: 16, num pairs: 1
Basis total mons: 13711, average length: 1054.692
Number of pair polynomials: 1, at 135 column(s), 0.000
Average length for reductees: 131.00 [1], reductors: 6.45 [20]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 20 = 21 rows / 191 columns out of 74613 (0.256%)
Density: 6.4822% / 8.3045% (12.381/r), total: 260 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 8 time: 0.000, [0.001], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 9
Basis length: 14, queue length: 6, step degree: 17, num pairs: 1
Basis total mons: 13881, average length: 991.500
Number of pair polynomials: 1, at 232 column(s), 0.000
Average length for reductees: 170.00 [1], reductors: 24.73 [22]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 22 = 23 rows / 276 columns out of 100947 (0.273%)
Density: 11.248% / 14.016% (31.043/r), total: 714 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 3
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 9 time: 0.000, [0.002], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 10
Basis length: 15, queue length: 7, step degree: 18, num pairs: 3
Basis total mons: 14110, average length: 940.667
Number of pair polynomials: 3, at 349 column(s), 0.000
Average length for reductees: 176.67 [3], reductors: 34.33 [64]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 64 = 67 rows / 426 columns out of 134596 (0.317%)
Density: 9.5543% / 12.481% (40.701/r), total: 2727 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 3 (100.0%), min deg: 16 [2], av deg: 16.7
Degree counts: 16:2 18:1
Queue insertion time: 0.000
Step 10 time: 0.000, [0.003], mat/total: 0.000/0.000, mem: 101.6MB, max: 1474.8MB

*******
STEP 11
Basis length: 18, queue length: 12, step degree: 17, num pairs: 1
Basis total mons: 14866, average length: 825.889
Number of pair polynomials: 1, at 346 column(s), 0.000
Average length for reductees: 221.00 [1], reductors: 44.22 [32]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 32 = 33 rows / 391 columns out of 100947 (0.387%)
Density: 12.679% / 15.463% (49.576/r), total: 1636 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000[r] [1]
Number of unused reductors: 4
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
New max step: 11, time: 0.002[r]
Step 11 time: 0.002[r], [0.003], mat/total: 0.010/0.010, mem: 101.6MB, max: 1474.8MB

*******
STEP 12
Basis length: 19, queue length: 13, step degree: 18, num pairs: 2
Basis total mons: 15167, average length: 798.263
Number of pair polynomials: 2, at 455 column(s), 0.000
Average length for reductees: 261.00 [2], reductors: 37.53 [106]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 106 = 108 rows / 518 columns out of 134596 (0.385%)
Density: 8.0438% / 10.35% (41.667/r), total: 4500 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 4
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 12 time: 0.000, [0.003], mat/total: 0.010/0.010, mem: 101.6MB, max: 1474.8MB

*******
STEP 13
Basis length: 19, queue length: 11, step degree: 19, num pairs: 5
Basis total mons: 15167, average length: 798.263
1 pair eliminated
Number of pair polynomials: 4, at 527 column(s), 0.000
Average length for reductees: 263.50 [4], reductors: 49.27 [166]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 166 = 170 rows / 646 columns out of 177100 (0.365%)
Density: 8.4065% / 10.719% (54.306/r), total: 9232 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 19
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (50.0%), min deg: 17 [1], av deg: 18.0
Degree counts: 17:1 19:1
Queue insertion time: 0.000
Step 13 time: 0.000, [0.002], mat/total: 0.010/0.010, mem: 101.6MB, max: 1474.8MB

*******
STEP 14
Basis length: 21, queue length: 12, step degree: 20, num pairs: 5
Basis total mons: 15785, average length: 751.667
Number of pair polynomials: 5, at 758 column(s), 0.000
Average length for reductees: 296.20 [5], reductors: 49.22 [310]
Symbolic reduction time: 0.000, column sort time: 0.000
5 + 310 = 315 rows / 860 columns out of 230230 (0.374%)
Density: 6.1787% / 8.0051% (53.137/r), total: 16738 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.003[r] [2]
Number of unused reductors: 30
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (40.0%), min deg: 18 [1], av deg: 19.0
Degree counts: 18:1 20:1
Queue insertion time: 0.000
New max step: 14, time: 0.007[r]
Step 14 time: 0.006[r], [0.007], mat/total: 0.020/0.019, mem: 101.6MB, max: 1474.8MB

*******
STEP 15
Basis length: 23, queue length: 11, step degree: 19, num pairs: 1
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 1, at 483 column(s), 0.000
Average length for reductees: 392.00 [1], reductors: 61.66 [105]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 105 = 106 rows / 574 columns out of 177100 (0.324%)
Density: 11.285% / 14.178% (64.774/r), total: 6866 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 22
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 15 time: 0.000, [0.003], mat/total: 0.020/0.019, mem: 101.6MB, max: 1474.8MB

*******
STEP 16
Basis length: 23, queue length: 10, step degree: 20, num pairs: 1
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 1, at 554 column(s), 0.000
Average length for reductees: 449.00 [1], reductors: 77.77 [135]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 135 = 136 rows / 648 columns out of 230230 (0.281%)
Density: 12.423% / 15.266% (80.5/r), total: 10948 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 14
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 16 time: 0.000, [0.005], mat/total: 0.020/0.019, mem: 101.6MB, max: 1474.8MB

*******
STEP 17
Basis length: 23, queue length: 9, step degree: 21, num pairs: 2
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 2, at 610 column(s), 0.000
Average length for reductees: 247.50 [2], reductors: 64.24 [335]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 335 = 337 rows / 914 columns out of 296010 (0.309%)
Density: 7.147% / 9.1901% (65.323/r), total: 22014 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.005[r] + 0.000 + 0.000 = 0.006[r] [0]
Number of unused reductors: 20
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 17 time: 0.006[r], [0.008], mat/total: 0.030/0.030, mem: 101.6MB, max: 1474.8MB

*******
STEP 18
Basis length: 23, queue length: 7, step degree: 22, num pairs: 2
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 2, at 641 column(s), 0.000
Average length for reductees: 346.50 [2], reductors: 74.09 [449]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 449 = 451 rows / 1070 columns out of 376740 (0.284%)
Density: 7.0375% / 9.0611% (75.302/r), total: 33961 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.009[r] + 0.000 + 0.000 = 0.009[r] [0]
Number of unused reductors: 15
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
New max step: 18, time: 0.010
Step 18 time: 0.009, [0.012], mat/total: 0.040/0.039, mem: 101.6MB, max: 1474.8MB

*******
STEP 19
Basis length: 23, queue length: 5, step degree: 23, num pairs: 1
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 1, at 677 column(s), 0.000
Average length for reductees: 392.00 [1], reductors: 74.82 [476]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 476 = 477 rows / 1100 columns out of 475020 (0.232%)
Density: 6.8618% / 8.956% (75.48/r), total: 36004 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.008[r] + 0.000 + 0.000 = 0.008[r] [0]
Number of unused reductors: 32
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
New max step: 19, time: 0.010
Step 19 time: 0.010, [0.012], mat/total: 0.050/0.050, mem: 101.6MB, max: 1474.8MB

*******
STEP 20
Basis length: 23, queue length: 4, step degree: 27, num pairs: 1
Basis total mons: 16626, average length: 722.870
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 21
Basis length: 23, queue length: 3, step degree: 31, num pairs: 1
Basis total mons: 16626, average length: 722.870
Number of pair polynomials: 1, at 168 column(s), 0.000
Average length for reductees: 164.00 [1], reductors: 40.22 [396]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 396 = 397 rows / 1263 columns out of 2324784 (0.054%)
Density: 3.2095% / 4.0969% (40.537/r), total: 16093 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 155
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 21 time: 0.000, [0.006], mat/total: 0.050/0.050, mem: 101.6MB, max: 1474.8MB

*******
STEP 22
Basis length: 24, queue length: 8, step degree: 17, num pairs: 1
Basis total mons: 16893, average length: 703.875
Number of pair polynomials: 1, at 271 column(s), 0.000
Average length for reductees: 267.00 [1], reductors: 17.13 [108]
Symbolic reduction time: 0.000[r], column sort time: 0.000
1 + 108 = 109 rows / 959 columns out of 100947 (0.950%)
Density: 2.0252% / 2.3503% (19.422/r), total: 2117 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 22 time: 0.003[r], [0.003], mat/total: 0.050/0.059, mem: 101.6MB, max: 1474.8MB

*******
STEP 23
Basis length: 25, queue length: 11, step degree: 18, num pairs: 1
Basis total mons: 17511, average length: 700.440
Number of pair polynomials: 1, at 767 column(s), 0.000
Average length for reductees: 618.00 [1], reductors: 45.97 [72]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 72 = 73 rows / 1151 columns out of 134596 (0.855%)
Density: 4.6749% / 5.1298% (53.808/r), total: 3928 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 13
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000
Step 23 time: 0.000, [0.004], mat/total: 0.050/0.059, mem: 101.6MB, max: 1474.8MB

*******
STEP 24
Basis length: 26, queue length: 14, step degree: 19, num pairs: 1
Basis total mons: 18269, average length: 702.654
Number of pair polynomials: 1, at 1005 column(s), 0.000
Average length for reductees: 758.00 [1], reductors: 40.46 [114]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 114 = 115 rows / 1248 columns out of 177100 (0.705%)
Density: 3.7416% / 4.1825% (46.696/r), total: 5370 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 14
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 24 time: 0.000, [0.004], mat/total: 0.050/0.059, mem: 101.6MB, max: 1474.8MB

*******
STEP 25
Basis length: 27, queue length: 16, step degree: 18, num pairs: 2
Basis total mons: 19036, average length: 705.037
Number of pair polynomials: 2, at 1211 column(s), 0.000
Average length for reductees: 767.00 [2], reductors: 35.55 [129]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 129 = 131 rows / 1269 columns out of 134596 (0.943%)
Density: 3.6814% / 4.1064% (46.718/r), total: 6120 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.001[r] + 0.000 + 0.000 = 0.002[r] [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000
Step 25 time: 0.005[r], [0.005], mat/total: 0.060/0.070, mem: 101.6MB, max: 1474.8MB

*******
STEP 26
Basis length: 28, queue length: 18, step degree: 19, num pairs: 1
Basis total mons: 20013, average length: 714.750
Number of pair polynomials: 1, at 1258 column(s), 0.000
Average length for reductees: 977.00 [1], reductors: 42.98 [212]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 212 = 213 rows / 1596 columns out of 177100 (0.901%)
Density: 2.9675% / 3.4011% (47.362/r), total: 10088 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 41
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 26 time: 0.000, [0.005], mat/total: 0.060/0.070, mem: 101.6MB, max: 1474.8MB

*******
STEP 27
Basis length: 28, queue length: 17, step degree: 20, num pairs: 1
Basis total mons: 20013, average length: 714.750
Number of pair polynomials: 1, at 383 column(s), 0.000
Average length for reductees: 267.00 [1], reductors: 64.82 [184]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 184 = 185 rows / 2320 columns out of 230230 (1.008%)
Density: 2.8409% / 3.1228% (65.908/r), total: 12193 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 96
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000[r]
Step 27 time: 0.006[r], [0.007], mat/total: 0.060/0.079, mem: 101.6MB, max: 1474.8MB

*******
STEP 28
Basis length: 29, queue length: 21, step degree: 21, num pairs: 6
Basis total mons: 20640, average length: 711.724
Number of pair polynomials: 6, at 2073 column(s), 0.000
Average length for reductees: 387.00 [6], reductors: 55.89 [1099]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 1099 = 1105 rows / 5963 columns out of 296010 (2.014%)
Density: 0.9675% / 1.1456% (57.692/r), total: 63750 (0.2MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.016[r] + 0.000 + 0.000 = 0.019[r] [4]
Number of unused reductors: 206
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 4 (66.7%), min deg: 17 [2], av deg: 18.0
Degree counts: 17:2 19:2
Queue insertion time: 0.000
New max step: 28, time: 0.020
Step 28 time: 0.019, [0.028], mat/total: 0.080/0.099, mem: 101.6MB, max: 1474.8MB

*******
STEP 29
Basis length: 33, queue length: 29, step degree: 18, num pairs: 1
Basis total mons: 23722, average length: 718.848
Number of pair polynomials: 1, at 739 column(s), 0.000
Average length for reductees: 473.00 [1], reductors: 387.00 [3]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 3 = 4 rows / 1063 columns out of 134596 (0.790%)
Density: 38.429% / 38.519% (408.5/r), total: 1634 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000
Step 29 time: 0.000, [0.004], mat/total: 0.080/0.099, mem: 101.6MB, max: 1474.8MB

*******
STEP 30
Basis length: 34, queue length: 31, step degree: 19, num pairs: 3
Basis total mons: 24479, average length: 719.971
Number of pair polynomials: 3, at 1892 column(s), 0.000
Average length for reductees: 734.33 [3], reductors: 14.44 [203]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 203 = 206 rows / 2097 columns out of 177100 (1.184%)
Density: 1.1885% / 1.4625% (24.922/r), total: 5134 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000[r]
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (33.3%), min deg: 19 [1], av deg: 19.0
Degree counts: 19:1
Queue insertion time: 0.000
Step 30 time: 0.005[r], [0.005], mat/total: 0.090/0.110, mem: 101.6MB, max: 1474.8MB

*******
STEP 31
Basis length: 35, queue length: 31, step degree: 20, num pairs: 3
Basis total mons: 25406, average length: 725.886
1 pair eliminated
Number of pair polynomials: 2, at 1940 column(s), 0.000
Average length for reductees: 700.00 [2], reductors: 34.44 [515]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 515 = 517 rows / 3736 columns out of 230230 (1.623%)
Density: 0.99088% / 1.2167% (37.019/r), total: 19139 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.005[r] [1]
Number of unused reductors: 156
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 20 [1], av deg: 20.0
Degree counts: 20:1
Queue insertion time: 0.000
Step 31 time: 0.009[r], [0.011], mat/total: 0.100/0.119, mem: 101.6MB, max: 1474.8MB

*******
STEP 32
Basis length: 36, queue length: 31, step degree: 21, num pairs: 4
Basis total mons: 26757, average length: 743.250
Number of pair polynomials: 4, at 3217 column(s), 0.000
Average length for reductees: 1049.50 [4], reductors: 29.53 [1234]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 1234 = 1238 rows / 6656 columns out of 296010 (2.249%)
Density: 0.49315% / 0.61061% (32.824/r), total: 40636 (0.2MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.011[r] + 0.000 + 0.000 = 0.013[r] [3]
Number of unused reductors: 239
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 3 (75.0%), min deg: 15 [1], av deg: 18.3
Degree counts: 15:1 19:1 21:1
Queue insertion time: 0.000
Step 32 time: 0.019, [0.022], mat/total: 0.120/0.139, mem: 101.6MB, max: 1474.8MB

*******
STEP 33
Basis length: 39, queue length: 37, step degree: 16, num pairs: 1
Basis total mons: 31838, average length: 816.359
Number of pair polynomials: 1, at 573 column(s), 0.000
Average length for reductees: 569.00 [1], reductors: 5.40 [72]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 72 = 73 rows / 785 columns out of 74613 (1.052%)
Density: 1.6718% / 2.1303% (13.123/r), total: 958 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 33 time: 0.000, [0.002], mat/total: 0.120/0.139, mem: 101.6MB, max: 1474.8MB

*******
STEP 34
Basis length: 40, queue length: 40, step degree: 17, num pairs: 1
Basis total mons: 32550, average length: 813.750
Number of pair polynomials: 1, at 1048 column(s), 0.000
Average length for reductees: 712.00 [1], reductors: 30.69 [51]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 51 = 52 rows / 1271 columns out of 100947 (1.259%)
Density: 3.4452% / 3.893% (43.788/r), total: 2277 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 3
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 34 time: 0.000, [0.003], mat/total: 0.120/0.139, mem: 101.6MB, max: 1474.8MB

*******
STEP 35
Basis length: 41, queue length: 43, step degree: 18, num pairs: 3
Basis total mons: 33547, average length: 818.220
Number of pair polynomials: 3, at 1610 column(s), 0.000
Average length for reductees: 759.33 [3], reductors: 42.11 [188]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 188 = 191 rows / 2360 columns out of 134596 (1.753%)
Density: 2.2617% / 2.6293% (53.377/r), total: 10195 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.003[r] [3]
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 3 (100.0%), min deg: 16 [2], av deg: 16.7
Degree counts: 16:2 18:1
Queue insertion time: 0.000
Step 35 time: 0.006[r], [0.008], mat/total: 0.130/0.150, mem: 101.6MB, max: 1474.8MB

*******
STEP 36
Basis length: 44, queue length: 56, step degree: 17, num pairs: 1
Basis total mons: 37762, average length: 858.227
Number of pair polynomials: 1, at 1992 column(s), 0.000
Average length for reductees: 1303.00 [1], reductors: 63.03 [114]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 114 = 115 rows / 2450 columns out of 100947 (2.427%)
Density: 3.0126% / 3.3695% (73.809/r), total: 8488 (0.0MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 5
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 36 time: 0.000, [0.006], mat/total: 0.130/0.150, mem: 101.6MB, max: 1474.8MB

*******
STEP 37
Basis length: 45, queue length: 59, step degree: 18, num pairs: 2
Basis total mons: 39579, average length: 879.533
Number of pair polynomials: 2, at 2739 column(s), 0.000
Average length for reductees: 1560.00 [2], reductors: 45.15 [444]
Symbolic reduction time: 0.000, column sort time: 0.001[r]
2 + 444 = 446 rows / 3358 columns out of 134596 (2.495%)
Density: 1.5467% / 1.8045% (51.939/r), total: 23165 (0.1MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 15
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 37 time: 0.009, [0.012], mat/total: 0.130/0.159, mem: 101.6MB, max: 1474.8MB

*******
STEP 38
Basis length: 45, queue length: 57, step degree: 19, num pairs: 5
Basis total mons: 39579, average length: 879.533
1 pair eliminated
Number of pair polynomials: 4, at 3411 column(s), 0.000
Average length for reductees: 1211.50 [4], reductors: 95.82 [370]
Symbolic reduction time: 0.003[r], column sort time: 0.000
4 + 370 = 374 rows / 5613 columns out of 177100 (3.169%)
Density: 1.9197% / 2.1396% (107.75/r), total: 40299 (0.2MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.009[r] + 0.000 + 0.000 = 0.009 [2]
Number of unused reductors: 60
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (50.0%), min deg: 17 [1], av deg: 18.0
Degree counts: 17:1 19:1
Queue insertion time: 0.000
Step 38 time: 0.018[r], [0.019], mat/total: 0.140/0.179, mem: 101.6MB, max: 1474.8MB

*******
STEP 39
Basis length: 47, queue length: 61, step degree: 20, num pairs: 7
Basis total mons: 43584, average length: 927.319
Number of pair polynomials: 7, at 7904 column(s), 0.000
Average length for reductees: 1688.00 [7], reductors: 74.07 [2466]
Symbolic reduction time: 0.009[r], column sort time: 0.006[r]
7 + 2466 = 2473 rows / 12588 columns out of 230230 (5.468%)
Density: 0.62472% / 0.73725% (78.64/r), total: 194476 (0.7MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.039 + 0.000 + 0.000 = 0.046[r] [2]
Number of unused reductors: 364
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (28.6%), min deg: 18 [1], av deg: 19.0
Degree counts: 18:1 20:1
Queue insertion time: 0.000
New max step: 39, time: 0.066[r]
Step 39 time: 0.065[r], [0.066], mat/total: 0.190/0.250, mem: 101.6MB, max: 1474.8MB

*******
STEP 40
Basis length: 49, queue length: 62, step degree: 19, num pairs: 2
Basis total mons: 47693, average length: 973.327
Number of pair polynomials: 2, at 3786 column(s), 0.000
Average length for reductees: 2390.00 [2], reductors: 87.59 [489]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
2 + 489 = 491 rows / 6013 columns out of 177100 (3.395%)
Density: 1.6127% / 1.8686% (96.969/r), total: 47612 (0.2MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [1]
Number of unused reductors: 102
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 19 [1], av deg: 19.0
Degree counts: 19:1
Queue insertion time: 0.000
Step 40 time: 0.019[r], [0.021], mat/total: 0.200/0.269, mem: 101.6MB, max: 1474.8MB

*******
STEP 41
Basis length: 50, queue length: 64, step degree: 20, num pairs: 3
Basis total mons: 51931, average length: 1038.620
Number of pair polynomials: 3, at 7031 column(s), 0.000
Average length for reductees: 3622.00 [3], reductors: 97.16 [986]
Symbolic reduction time: 0.006[r], column sort time: 0.000
3 + 986 = 989 rows / 7860 columns out of 230230 (3.414%)
Density: 1.3722% / 1.5804% (107.85/r), total: 106667 (0.4MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.029 + 0.000 + 0.000 = 0.029 [2]
Number of unused reductors: 57
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (66.7%), min deg: 20 [2], av deg: 20.0
Degree counts: 20:2
Queue insertion time: 0.000
Step 41 time: 0.046[r], [0.046], mat/total: 0.230/0.320, mem: 101.6MB, max: 1474.8MB

*******
STEP 42
Basis length: 52, queue length: 69, step degree: 21, num pairs: 12
Basis total mons: 60358, average length: 1160.731
1 pair eliminated
Number of pair polynomials: 11, at 11477 column(s), 0.000
Average length for reductees: 2494.64 [11], reductors: 107.15 [3344]
Symbolic reduction time: 0.009, column sort time: 0.006[r]
11 + 3344 = 3355 rows / 15774 columns out of 296010 (5.329%)
Density: 0.72894% / 0.85545% (114.98/r), total: 385766 (1.5MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.099 + 0.000 + 0.000 = 0.099 [2]
Number of unused reductors: 385
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 2 (18.2%), min deg: 21 [2], av deg: 21.0
Degree counts: 21:2
Queue insertion time: 0.002[r]
New max step: 42, time: 0.130
Step 42 time: 0.129, [0.141], mat/total: 0.330/0.449, mem: 101.6MB, max: 1474.8MB

*******
STEP 43
Basis length: 54, queue length: 66, step degree: 22, num pairs: 23
Basis total mons: 67387, average length: 1247.907
1 pair eliminated
Number of pair polynomials: 22, at 14168 column(s), 0.000
Average length for reductees: 1536.50 [22], reductors: 101.10 [6688]
Symbolic reduction time: 0.028[r], column sort time: 0.009
22 + 6688 = 6710 rows / 21741 columns out of 376740 (5.771%)
Density: 0.48667% / 0.59547% (105.81/r), total: 709963 (2.7MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.179 + 0.000 + 0.000 = 0.190 [1]
Number of unused reductors: 715
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (4.5%), min deg: 22 [1], av deg: 22.0
Degree counts: 22:1
Queue insertion time: 0.000
New max step: 43, time: 0.230
Step 43 time: 0.230, [0.237], mat/total: 0.520/0.679, mem: 101.6MB, max: 1474.8MB

*******
STEP 44
Basis length: 55, queue length: 47, step degree: 23, num pairs: 23
Basis total mons: 71957, average length: 1308.309
4 pairs eliminated
Number of pair polynomials: 19, at 18135 column(s), 0.003[r]
Average length for reductees: 2035.16 [19], reductors: 132.00 [11363]
Symbolic reduction time: 0.059, column sort time: 0.014[r]
19 + 11363 = 11382 rows / 31593 columns out of 475020 (6.651%)
Density: 0.42787% / 0.52442% (135.18/r), total: 1538576 (5.9MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.351[r] + 0.000 + 0.000 = 0.362[r] [1]
Number of unused reductors: 2398
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (5.3%), min deg: 23 [1], av deg: 23.0
Degree counts: 23:1
Queue insertion time: 0.000
New max step: 44, time: 0.453[r]
Step 44 time: 0.453[r], [0.454], mat/total: 0.890/1.139, mem: 101.6MB, max: 1474.8MB

*******
STEP 45
Basis length: 56, queue length: 28, step degree: 24, num pairs: 12
Basis total mons: 76082, average length: 1358.607
3 pairs eliminated
Number of pair polynomials: 9, at 17737 column(s), 0.000
Average length for reductees: 3251.67 [9], reductors: 137.10 [13028]
Symbolic reduction time: 0.070, column sort time: 0.016[r]
9 + 13028 = 13037 rows / 34279 columns out of 593775 (5.773%)
Density: 0.40624% / 0.50771% (139.25/r), total: 1815456 (6.9MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.473[r] + 0.000 + 0.000 = 0.484[r] [0]
Number of unused reductors: 1639
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
New max step: 45, time: 0.580
Step 45 time: 0.579, [0.585], mat/total: 1.380/1.719, mem: 101.6MB, max: 1474.8MB

*******
STEP 46
Basis length: 56, queue length: 16, step degree: 25, num pairs: 7
Basis total mons: 76082, average length: 1358.607
2 pairs eliminated
Number of pair polynomials: 5, at 15655 column(s), 0.000
Average length for reductees: 4052.40 [5], reductors: 148.13 [13380]
Symbolic reduction time: 0.080, column sort time: 0.016[r]
5 + 13380 = 13385 rows / 35580 columns out of 736281 (4.832%)
Density: 0.42043% / 0.52521% (149.59/r), total: 2002238 (7.6MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.449 + 0.000 + 0.000 = 0.468[r] [0]
Number of unused reductors: 2704
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 46 time: 0.570, [0.577], mat/total: 1.850/2.289, mem: 101.6MB, max: 1474.8MB

*******
STEP 47
Basis length: 56, queue length: 9, step degree: 26, num pairs: 4
Basis total mons: 76082, average length: 1358.607
3 pairs eliminated
Number of pair polynomials: 1, at 6288 column(s), 0.001[r]
Average length for reductees: 4570.00 [1], reductors: 110.22 [12636]
Symbolic reduction time: 0.059, column sort time: 0.016[r]
1 + 12636 = 12637 rows / 32894 columns out of 906192 (3.630%)
Density: 0.33615% / 0.42884% (110.57/r), total: 1397320 (5.3MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.279[r] + 0.000 + 0.000 = 0.289 [0]
Number of unused reductors: 3113
After ech memory: 101.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 47 time: 0.378[r], [0.379], mat/total: 2.140/2.670, mem: 101.6MB, max: 1474.8MB

*******
STEP 48
Basis length: 56, queue length: 5, step degree: 27, num pairs: 1
Basis total mons: 76082, average length: 1358.607
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 49
Basis length: 56, queue length: 4, step degree: 28, num pairs: 1
Basis total mons: 76082, average length: 1358.607
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 50
Basis length: 56, queue length: 3, step degree: 29, num pairs: 1
Basis total mons: 76082, average length: 1358.607
1 pair eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 51
Basis length: 56, queue length: 2, step degree: 45, num pairs: 1
Basis total mons: 76082, average length: 1358.607
Number of pair polynomials: 1, at 1525 column(s), 0.000
Average length for reductees: 1521.00 [1], reductors: 46.11 [7863]
Symbolic reduction time: 0.014[r], column sort time: 0.000
1 + 7863 = 7864 rows / 11453 columns out of 18009460 (0.064%)
Density: 0.40423% / 0.69829% (46.297/r), total: 364076 (1.4MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.050 + 0.000 + 0.000 = 0.054[r] [1]
Number of unused reductors: 2594
After ech memory: 101.6MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 19 [1], av deg: 19.0
Degree counts: 19:1
Queue insertion time: 0.000
Step 51 time: 0.078[r], [0.080], mat/total: 2.200/2.750, mem: 101.6MB, max: 1474.8MB

*******
STEP 52
Basis length: 57, queue length: 8, step degree: 20, num pairs: 1
Basis total mons: 76606, average length: 1343.965
Number of pair polynomials: 1, at 697 column(s), 0.000
Average length for reductees: 524.00 [1], reductors: 120.52 [507]
Symbolic reduction time: 0.003[r], column sort time: 0.000
1 + 507 = 508 rows / 5640 columns out of 230230 (2.450%)
Density: 2.151% / 2.4219% (121.31/r), total: 61628 (0.2MB)
Before ech memory: 101.6MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 454
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 52 time: 0.010, [0.017], mat/total: 2.200/2.760, mem: 133.7MB, max: 1474.8MB

*******
STEP 53
Basis length: 58, queue length: 15, step degree: 15, num pairs: 1
Basis total mons: 76845, average length: 1324.914
Number of pair polynomials: 1, at 404 column(s), 0.000
Average length for reductees: 239.00 [1], reductors: 267.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 404 columns out of 54264 (0.745%)
Density: 62.624% / 62.624% (253/r), total: 506 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000[r] [1]
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 53 time: 0.002[r], [0.002], mat/total: 2.210/2.769, mem: 133.7MB, max: 1474.8MB

*******
STEP 54
Basis length: 59, queue length: 21, step degree: 15, num pairs: 1
Basis total mons: 77183, average length: 1308.186
Number of pair polynomials: 1, at 342 column(s), 0.000
Average length for reductees: 338.00 [1], reductors: 17.33 [135]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 135 = 136 rows / 1210 columns out of 54264 (2.230%)
Density: 1.6274% / 1.8527% (19.691/r), total: 2678 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 54 time: 0.000, [0.004], mat/total: 2.210/2.769, mem: 133.7MB, max: 1474.8MB

*******
STEP 55
Basis length: 60, queue length: 25, step degree: 16, num pairs: 3
Basis total mons: 77962, average length: 1299.367
Number of pair polynomials: 3, at 1602 column(s), 0.000
Average length for reductees: 452.00 [3], reductors: 41.94 [186]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 186 = 189 rows / 2806 columns out of 74613 (3.761%)
Density: 1.7265% / 1.9124% (48.444/r), total: 9156 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 18
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 3 (100.0%), min deg: 16 [3], av deg: 16.0
Degree counts: 16:3
Queue insertion time: 0.000
Step 55 time: 0.000, [0.008], mat/total: 2.210/2.769, mem: 133.7MB, max: 1474.8MB

*******
STEP 56
Basis length: 63, queue length: 37, step degree: 17, num pairs: 5
Basis total mons: 80270, average length: 1274.127
Number of pair polynomials: 5, at 3249 column(s), 0.000
Average length for reductees: 731.60 [5], reductors: 53.78 [325]
Symbolic reduction time: 0.002[r], column sort time: 0.000
5 + 325 = 330 rows / 4627 columns out of 100947 (4.584%)
Density: 1.3843% / 1.5197% (64.052/r), total: 21137 (0.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.006[r] [4]
Number of unused reductors: 50
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 4 (80.0%), min deg: 15 [2], av deg: 16.0
Degree counts: 15:2 17:2
Queue insertion time: 0.000
Step 56 time: 0.013[r], [0.013], mat/total: 2.220/2.789, mem: 133.7MB, max: 1474.8MB

*******
STEP 57
Basis length: 67, queue length: 53, step degree: 16, num pairs: 2
Basis total mons: 84401, average length: 1259.716
Number of pair polynomials: 2, at 1536 column(s), 0.000
Average length for reductees: 969.00 [2], reductors: 35.83 [161]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 161 = 163 rows / 1607 columns out of 74613 (2.154%)
Density: 2.9419% / 3.2164% (47.276/r), total: 7706 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 57 time: 0.000, [0.005], mat/total: 2.220/2.789, mem: 133.7MB, max: 1474.8MB

*******
STEP 58
Basis length: 68, queue length: 56, step degree: 17, num pairs: 1
Basis total mons: 85638, average length: 1259.382
Number of pair polynomials: 1, at 1596 column(s), 0.000
Average length for reductees: 1237.00 [1], reductors: 43.44 [263]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 263 = 264 rows / 2031 columns out of 100947 (2.012%)
Density: 2.3615% / 2.6297% (47.962/r), total: 12662 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.003[r] [0]
Number of unused reductors: 50
After ech memory: 133.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 58 time: 0.006[r], [0.008], mat/total: 2.230/2.800, mem: 133.7MB, max: 1474.8MB

*******
STEP 59
Basis length: 68, queue length: 55, step degree: 18, num pairs: 10
Basis total mons: 85638, average length: 1259.382
Number of pair polynomials: 10, at 8189 column(s), 0.000
Average length for reductees: 989.60 [10], reductors: 67.33 [1704]
Symbolic reduction time: 0.007[r], column sort time: 0.000
10 + 1704 = 1714 rows / 12376 columns out of 134596 (9.195%)
Density: 0.58755% / 0.66896% (72.715/r), total: 124633 (0.5MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.036[r] + 0.000 + 0.000 = 0.039 [7]
Number of unused reductors: 225
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 7 (70.0%), min deg: 16 [3], av deg: 17.1
Degree counts: 16:3 18:4
Queue insertion time: 0.000
Step 59 time: 0.049, [0.060], mat/total: 2.270/2.849, mem: 133.7MB, max: 1474.8MB

*******
STEP 60
Basis length: 75, queue length: 84, step degree: 17, num pairs: 5
Basis total mons: 94778, average length: 1263.707
Number of pair polynomials: 5, at 5889 column(s), 0.000
Average length for reductees: 1370.40 [5], reductors: 116.12 [254]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
5 + 254 = 259 rows / 7183 columns out of 100947 (7.116%)
Density: 1.9537% / 2.0882% (140.33/r), total: 36346 (0.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [3]
Number of unused reductors: 61
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 3 (60.0%), min deg: 17 [3], av deg: 17.0
Degree counts: 17:3
Queue insertion time: 0.000
Step 60 time: 0.019, [0.022], mat/total: 2.280/2.869, mem: 133.7MB, max: 1474.8MB

*******
STEP 61
Basis length: 78, queue length: 102, step degree: 18, num pairs: 3
Basis total mons: 101236, average length: 1297.897
Number of pair polynomials: 3, at 6030 column(s), 0.000
Average length for reductees: 1787.33 [3], reductors: 113.79 [598]
Symbolic reduction time: 0.005[r], column sort time: 0.000
3 + 598 = 601 rows / 9224 columns out of 134596 (6.853%)
Density: 1.3242% / 1.4424% (122.14/r), total: 73407 (0.3MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.019[r] + 0.000 + 0.000 = 0.023[r] [0]
Number of unused reductors: 219
After ech memory: 133.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 61 time: 0.036[r], [0.036], mat/total: 2.310/2.909, mem: 133.7MB, max: 1474.8MB

*******
STEP 62
Basis length: 78, queue length: 99, step degree: 19, num pairs: 25
Basis total mons: 101236, average length: 1297.897
1 pair eliminated
Number of pair polynomials: 24, at 13611 column(s), 0.000
Average length for reductees: 1037.62 [24], reductors: 75.33 [3749]
Symbolic reduction time: 0.016[r], column sort time: 0.009[r]
24 + 3749 = 3773 rows / 20074 columns out of 177100 (11.335%)
Density: 0.40575% / 0.47099% (81.45/r), total: 307309 (1.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.099[r] + 0.000 + 0.000 = 0.099 [17]
Number of unused reductors: 503
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 17 (70.8%), min deg: 15 [3], av deg: 17.2
Degree counts: 15:3 17:9 19:5
Queue insertion time: 0.002[r]
Step 62 time: 0.140, [0.140], mat/total: 2.410/3.050, mem: 133.7MB, max: 1474.8MB

*******
STEP 63
Basis length: 95, queue length: 181, step degree: 16, num pairs: 4
Basis total mons: 131862, average length: 1388.021
Number of pair polynomials: 4, at 2145 column(s), 0.000
Average length for reductees: 632.75 [4], reductors: 44.98 [195]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 195 = 199 rows / 2797 columns out of 74613 (3.749%)
Density: 2.0305% / 2.2222% (56.794/r), total: 11302 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 47
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 4 (100.0%), min deg: 14 [1], av deg: 15.5
Degree counts: 14:1 16:3
Queue insertion time: 0.000
Step 63 time: 0.000, [0.008], mat/total: 2.410/3.050, mem: 133.7MB, max: 1474.8MB

*******
STEP 64
Basis length: 99, queue length: 197, step degree: 15, num pairs: 2
Basis total mons: 134561, average length: 1359.202
Number of pair polynomials: 2, at 780 column(s), 0.000
Average length for reductees: 454.00 [2], reductors: 13.47 [53]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 53 = 55 rows / 885 columns out of 54264 (1.631%)
Density: 3.3323% / 3.7175% (29.491/r), total: 1622 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000
Step 64 time: 0.000, [0.003], mat/total: 2.410/3.050, mem: 133.7MB, max: 1474.8MB

*******
STEP 65
Basis length: 100, queue length: 199, step degree: 16, num pairs: 2
Basis total mons: 135117, average length: 1351.170
Number of pair polynomials: 2, at 1160 column(s), 0.000
Average length for reductees: 556.00 [2], reductors: 45.57 [37]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 37 = 39 rows / 1270 columns out of 74613 (1.702%)
Density: 5.6491% / 6.0303% (71.744/r), total: 2798 (0.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000[r] [1]
Number of unused reductors: 1
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 65 time: 0.003[r], [0.004], mat/total: 2.420/3.059, mem: 133.7MB, max: 1474.8MB

*******
STEP 66
Basis length: 101, queue length: 203, step degree: 17, num pairs: 13
Basis total mons: 135936, average length: 1345.901
1 pair eliminated
Number of pair polynomials: 12, at 6738 column(s), 0.000
Average length for reductees: 1080.42 [12], reductors: 71.04 [603]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
12 + 603 = 615 rows / 8136 columns out of 100947 (8.060%)
Density: 1.1153% / 1.2243% (90.74/r), total: 55805 (0.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [9]
Number of unused reductors: 113
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 9 (75.0%), min deg: 15 [5], av deg: 15.9
Degree counts: 15:5 17:4
Queue insertion time: 0.002[r]
Step 66 time: 0.030, [0.031], mat/total: 2.430/3.090, mem: 133.7MB, max: 1474.8MB

*******
STEP 67
Basis length: 110, queue length: 288, step degree: 16, num pairs: 2
Basis total mons: 148950, average length: 1354.091
Number of pair polynomials: 2, at 3351 column(s), 0.000
Average length for reductees: 1304.00 [2], reductors: 93.87 [181]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 181 = 183 rows / 4749 columns out of 74613 (6.365%)
Density: 2.2552% / 2.4091% (107.1/r), total: 19599 (0.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.006[r] [2]
Number of unused reductors: 50
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (100.0%), min deg: 16 [2], av deg: 16.0
Degree counts: 16:2
Queue insertion time: 0.000
Step 67 time: 0.009, [0.014], mat/total: 2.440/3.099, mem: 133.7MB, max: 1474.8MB

*******
STEP 68
Basis length: 112, queue length: 305, step degree: 17, num pairs: 7
Basis total mons: 151953, average length: 1356.723
Number of pair polynomials: 7, at 7828 column(s), 0.000
Average length for reductees: 1330.29 [7], reductors: 174.05 [654]
Symbolic reduction time: 0.007[r], column sort time: 0.000
7 + 654 = 661 rows / 10830 columns out of 100947 (10.728%)
Density: 1.7202% / 1.8362% (186.29/r), total: 123140 (0.5MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.029[r] + 0.000 + 0.000 = 0.033[r] [2]
Number of unused reductors: 264
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (28.6%), min deg: 17 [2], av deg: 17.0
Degree counts: 17:2
Queue insertion time: 0.000
Step 68 time: 0.050, [0.051], mat/total: 2.480/3.150, mem: 133.7MB, max: 1474.8MB

*******
STEP 69
Basis length: 114, queue length: 317, step degree: 18, num pairs: 32
Basis total mons: 155874, average length: 1367.316
4 pairs eliminated
Number of pair polynomials: 28, at 12753 column(s), 0.000
Average length for reductees: 1382.82 [28], reductors: 90.52 [2332]
Symbolic reduction time: 0.009, column sort time: 0.008[r]
28 + 2332 = 2360 rows / 17871 columns out of 134596 (13.278%)
Density: 0.5923% / 0.66164% (105.85/r), total: 249804 (1.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.070 + 0.000 + 0.000 = 0.079 [12]
Number of unused reductors: 406
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 12 (42.9%), min deg: 16 [4], av deg: 17.2
Degree counts: 16:4 17:1 18:7
Queue insertion time: 0.000
Step 69 time: 0.099, [0.112], mat/total: 2.560/3.250, mem: 133.7MB, max: 1474.8MB

*******
STEP 70
Basis length: 126, queue length: 359, step degree: 17, num pairs: 4
Basis total mons: 183560, average length: 1456.825
Number of pair polynomials: 4, at 7004 column(s), 0.000[r]
Average length for reductees: 1687.75 [4], reductors: 209.31 [524]
Symbolic reduction time: 0.000, column sort time: 0.006[r]
4 + 524 = 528 rows / 11989 columns out of 100947 (11.877%)
Density: 1.8393% / 1.9487% (220.51/r), total: 116430 (0.4MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.019 + 0.000 + 0.000 = 0.029[r] [1]
Number of unused reductors: 218
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (25.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 70 time: 0.046[r], [0.047], mat/total: 2.590/3.300, mem: 133.7MB, max: 1474.8MB

*******
STEP 71
Basis length: 127, queue length: 360, step degree: 18, num pairs: 14
Basis total mons: 185571, average length: 1461.189
Number of pair polynomials: 14, at 13860 column(s), 0.000
Average length for reductees: 1839.64 [14], reductors: 94.91 [2753]
Symbolic reduction time: 0.016[r], column sort time: 0.009[r]
14 + 2753 = 2767 rows / 19481 columns out of 134596 (14.474%)
Density: 0.5325% / 0.59952% (103.74/r), total: 287037 (1.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.079 + 0.000 + 0.000 = 0.088[r] [4]
Number of unused reductors: 350
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 4 (28.6%), min deg: 16 [2], av deg: 17.0
Degree counts: 16:2 18:2
Queue insertion time: 0.000
Step 71 time: 0.119, [0.122], mat/total: 2.680/3.420, mem: 133.7MB, max: 1474.8MB

*******
STEP 72
Basis length: 131, queue length: 375, step degree: 17, num pairs: 5
Basis total mons: 194729, average length: 1486.481
Number of pair polynomials: 5, at 5960 column(s), 0.000
Average length for reductees: 1786.80 [5], reductors: 153.45 [382]
Symbolic reduction time: 0.004[r], column sort time: 0.000
5 + 382 = 387 rows / 9316 columns out of 100947 (9.229%)
Density: 1.8736% / 1.9846% (174.55/r), total: 67550 (0.3MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.019[r] + 0.000 + 0.000 = 0.023[r] [3]
Number of unused reductors: 170
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 3 (60.0%), min deg: 16 [1], av deg: 16.7
Degree counts: 16:1 17:2
Queue insertion time: 0.000
Step 72 time: 0.037[r], [0.038], mat/total: 2.710/3.460, mem: 133.7MB, max: 1474.8MB

*******
STEP 73
Basis length: 134, queue length: 393, step degree: 17, num pairs: 4
Basis total mons: 206836, average length: 1543.552
Number of pair polynomials: 4, at 7296 column(s), 0.000[r]
Average length for reductees: 2683.00 [4], reductors: 113.31 [482]
Symbolic reduction time: 0.000, column sort time: 0.004[r]
4 + 482 = 486 rows / 9095 columns out of 100947 (9.010%)
Density: 1.4784% / 1.5668% (134.46/r), total: 65348 (0.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [3]
Number of unused reductors: 62
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 3 (75.0%), min deg: 16 [2], av deg: 16.3
Degree counts: 16:2 17:1
Queue insertion time: 0.000
Step 73 time: 0.029, [0.035], mat/total: 2.720/3.489, mem: 133.7MB, max: 1474.8MB

*******
STEP 74
Basis length: 137, queue length: 406, step degree: 17, num pairs: 7
Basis total mons: 213567, average length: 1558.883
Number of pair polynomials: 7, at 5916 column(s), 0.000[r]
Average length for reductees: 1634.14 [7], reductors: 100.16 [385]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 385 = 392 rows / 7756 columns out of 100947 (7.683%)
Density: 1.6446% / 1.7369% (127.55/r), total: 50001 (0.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.015[r] [4]
Number of unused reductors: 37
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 4 (57.1%), min deg: 15 [2], av deg: 16.0
Degree counts: 15:2 17:2
Queue insertion time: 0.000
Step 74 time: 0.026[r], [0.028], mat/total: 2.740/3.519, mem: 133.7MB, max: 1474.8MB

*******
STEP 75
Basis length: 141, queue length: 435, step degree: 16, num pairs: 3
Basis total mons: 222049, average length: 1574.816
Number of pair polynomials: 3, at 5003 column(s), 0.000
Average length for reductees: 2248.33 [3], reductors: 335.41 [143]
Symbolic reduction time: 0.005[r], column sort time: 0.000
3 + 143 = 146 rows / 6623 columns out of 74613 (8.876%)
Density: 5.6578% / 5.8035% (374.72/r), total: 54709 (0.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [0]
Number of unused reductors: 54
After ech memory: 133.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 75 time: 0.019, [0.026], mat/total: 2.750/3.539, mem: 133.7MB, max: 1474.8MB

*******
STEP 76
Basis length: 141, queue length: 432, step degree: 18, num pairs: 16
Basis total mons: 222049, average length: 1574.816
Number of pair polynomials: 16, at 16653 column(s), 0.003[r]
Average length for reductees: 2926.25 [16], reductors: 118.64 [3222]
Symbolic reduction time: 0.019, column sort time: 0.009
16 + 3222 = 3238 rows / 24188 columns out of 134596 (17.971%)
Density: 0.54785% / 0.60451% (132.51/r), total: 429082 (1.6MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.001[r]
0.099 + 0.000 + 0.000 = 0.099 [5]
Number of unused reductors: 1248
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 5 (31.2%), min deg: 17 [1], av deg: 17.8
Degree counts: 17:1 18:4
Queue insertion time: 0.000
Step 76 time: 0.150, [0.156], mat/total: 2.860/3.690, mem: 133.7MB, max: 1474.8MB

*******
STEP 77
Basis length: 146, queue length: 450, step degree: 18, num pairs: 2
Basis total mons: 243270, average length: 1666.233
Number of pair polynomials: 2, at 10918 column(s), 0.002[r]
Average length for reductees: 5792.00 [2], reductors: 297.99 [802]
Symbolic reduction time: 0.010, column sort time: 0.008[r]
2 + 802 = 804 rows / 17759 columns out of 134596 (13.194%)
Density: 1.7549% / 1.8597% (311.66/r), total: 250572 (1.0MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.050 + 0.000 + 0.000 = 0.057[r] [0]
Number of unused reductors: 422
After ech memory: 133.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 77 time: 0.087[r], [0.087], mat/total: 2.920/3.780, mem: 133.7MB, max: 1474.8MB

*******
STEP 78
Basis length: 146, queue length: 448, step degree: 19, num pairs: 68
Basis total mons: 243270, average length: 1666.233
11 pairs eliminated
Number of pair polynomials: 57, at 28373 column(s), 0.008[r]
Average length for reductees: 2410.49 [57], reductors: 146.76 [7730]
Symbolic reduction time: 0.059, column sort time: 0.019[r]
57 + 7730 = 7787 rows / 39135 columns out of 177100 (22.098%)
Density: 0.41736% / 0.47431% (163.33/r), total: 1271870 (4.9MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.349 + 0.000 + 0.000 = 0.369 [19]
Number of unused reductors: 1163
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 19 (33.3%), min deg: 15 [1], av deg: 18.1
Degree counts: 15:1 16:1 17:5 18:1 19:11
Queue insertion time: 0.003[r]
Step 78 time: 0.467[r], [0.468], mat/total: 3.290/4.250, mem: 133.7MB, max: 1474.8MB

*******
STEP 79
Basis length: 165, queue length: 508, step degree: 16, num pairs: 2
Basis total mons: 314797, average length: 1907.861
Number of pair polynomials: 2, at 1992 column(s), 0.000
Average length for reductees: 977.00 [2], reductors: 72.61 [206]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 206 = 208 rows / 4762 columns out of 74613 (6.382%)
Density: 1.7073% / 1.8308% (81.303/r), total: 16911 (0.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.003[r] [1]
Number of unused reductors: 43
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (50.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 79 time: 0.010, [0.012], mat/total: 3.300/4.260, mem: 133.7MB, max: 1474.8MB

*******
STEP 80
Basis length: 166, queue length: 511, step degree: 17, num pairs: 5
Basis total mons: 315990, average length: 1903.554
Number of pair polynomials: 5, at 7395 column(s), 0.000
Average length for reductees: 1107.20 [5], reductors: 174.32 [518]
Symbolic reduction time: 0.007[r], column sort time: 0.000
5 + 518 = 523 rows / 11601 columns out of 100947 (11.492%)
Density: 1.5795% / 1.6766% (183.24/r), total: 95832 (0.4MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.023[r] + 0.000 + 0.000 = 0.027[r] [1]
Number of unused reductors: 201
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 1 (20.0%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 80 time: 0.046[r], [0.046], mat/total: 3.340/4.309, mem: 133.7MB, max: 1474.8MB

*******
STEP 81
Basis length: 167, queue length: 511, step degree: 18, num pairs: 18
Basis total mons: 317733, average length: 1902.593
Number of pair polynomials: 18, at 19289 column(s), 0.000
Average length for reductees: 3556.28 [18], reductors: 119.30 [3115]
Symbolic reduction time: 0.025[r], column sort time: 0.009
18 + 3115 = 3133 rows / 23555 columns out of 134596 (17.501%)
Density: 0.5903% / 0.65169% (139.04/r), total: 435625 (1.7MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.119 + 0.000 + 0.000 = 0.130 [9]
Number of unused reductors: 307
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 9 (50.0%), min deg: 14 [1], av deg: 16.9
Degree counts: 14:1 16:3 18:5
Queue insertion time: 0.000
Step 81 time: 0.170, [0.178], mat/total: 3.470/4.480, mem: 133.7MB, max: 1474.8MB

*******
STEP 82
Basis length: 176, queue length: 564, step degree: 17, num pairs: 5
Basis total mons: 346633, average length: 1969.506
Number of pair polynomials: 5, at 7427 column(s), 0.000
Average length for reductees: 1686.80 [5], reductors: 143.19 [590]
Symbolic reduction time: 0.007[r], column sort time: 0.005[r]
5 + 590 = 595 rows / 10902 columns out of 100947 (10.800%)
Density: 1.4324% / 1.5323% (156.16/r), total: 92918 (0.4MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.019 + 0.000 + 0.000 = 0.019 [2]
Number of unused reductors: 109
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (40.0%), min deg: 17 [2], av deg: 17.0
Degree counts: 17:2
Queue insertion time: 0.000
Step 82 time: 0.039, [0.045], mat/total: 3.490/4.519, mem: 133.7MB, max: 1474.8MB

*******
STEP 83
Basis length: 178, queue length: 570, step degree: 18, num pairs: 6
Basis total mons: 351184, average length: 1972.944
Number of pair polynomials: 6, at 10060 column(s), 0.000
Average length for reductees: 2035.50 [6], reductors: 95.93 [1700]
Symbolic reduction time: 0.013[r], column sort time: 0.008[r]
6 + 1700 = 1706 rows / 16501 columns out of 134596 (12.260%)
Density: 0.62268% / 0.69418% (102.75/r), total: 175289 (0.7MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.037[r] + 0.000 + 0.000 = 0.039 [2]
Number of unused reductors: 295
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (33.3%), min deg: 16 [1], av deg: 17.0
Degree counts: 16:1 18:1
Queue insertion time: 0.000
Step 83 time: 0.070, [0.071], mat/total: 3.530/4.590, mem: 133.7MB, max: 1474.8MB

*******
STEP 84
Basis length: 180, queue length: 583, step degree: 17, num pairs: 1
Basis total mons: 357076, average length: 1983.756
Number of pair polynomials: 1, at 3942 column(s), 0.000
Average length for reductees: 3731.00 [1], reductors: 195.14 [381]
Symbolic reduction time: 0.006[r], column sort time: 0.000
1 + 381 = 382 rows / 9265 columns out of 100947 (9.178%)
Density: 2.2061% / 2.3152% (204.39/r), total: 78078 (0.3MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.016[r] + 0.000 + 0.000 = 0.019 [0]
Number of unused reductors: 190
After ech memory: 133.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 84 time: 0.029, [0.035], mat/total: 3.550/4.619, mem: 133.7MB, max: 1474.8MB

*******
STEP 85
Basis length: 180, queue length: 582, step degree: 19, num pairs: 27
Basis total mons: 357076, average length: 1983.756
3 pairs eliminated
Number of pair polynomials: 24, at 28229 column(s), 0.006[r]
Average length for reductees: 3917.21 [24], reductors: 175.87 [5789]
Symbolic reduction time: 0.059, column sort time: 0.018[r]
24 + 5789 = 5813 rows / 36440 columns out of 177100 (20.576%)
Density: 0.52502% / 0.58657% (191.32/r), total: 1112129 (4.2MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.310 + 0.000 + 0.000 = 0.332[r] [7]
Number of unused reductors: 651
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 7 (29.2%), min deg: 17 [1], av deg: 18.6
Degree counts: 17:1 18:1 19:5
Queue insertion time: 0.003[r]
Step 85 time: 0.430[r], [0.432], mat/total: 3.890/5.059, mem: 133.7MB, max: 1474.8MB

*******
STEP 86
Basis length: 187, queue length: 610, step degree: 18, num pairs: 2
Basis total mons: 385946, average length: 2063.882
Number of pair polynomials: 2, at 10435 column(s), 0.000
Average length for reductees: 5711.00 [2], reductors: 201.63 [1362]
Symbolic reduction time: 0.019[r], column sort time: 0.010
2 + 1362 = 1364 rows / 18813 columns out of 134596 (13.977%)
Density: 1.1147% / 1.2028% (209.7/r), total: 286037 (1.1MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.059 + 0.000 + 0.000 = 0.069 [2]
Number of unused reductors: 544
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (100.0%), min deg: 18 [2], av deg: 18.0
Degree counts: 18:2
Queue insertion time: 0.000
Step 86 time: 0.099, [0.109], mat/total: 3.960/5.159, mem: 133.7MB, max: 1474.8MB

*******
STEP 87
Basis length: 189, queue length: 625, step degree: 19, num pairs: 5
Basis total mons: 397192, average length: 2101.545
Number of pair polynomials: 5, at 14439 column(s), 0.003[r]
Average length for reductees: 6052.20 [5], reductors: 157.38 [5471]
Symbolic reduction time: 0.049, column sort time: 0.018[r]
5 + 5471 = 5476 rows / 35977 columns out of 177100 (20.315%)
Density: 0.45241% / 0.51004% (162.76/r), total: 891298 (3.4MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.179 + 0.000 + 0.000 = 0.198[r] [3]
Number of unused reductors: 2337
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 3 (60.0%), min deg: 18 [1], av deg: 18.7
Degree counts: 18:1 19:2
Queue insertion time: 0.000
Step 87 time: 0.282[r], [0.282], mat/total: 4.170/5.449, mem: 133.7MB, max: 1474.8MB

*******
STEP 88
Basis length: 192, queue length: 635, step degree: 19, num pairs: 3
Basis total mons: 415089, average length: 2161.922
Number of pair polynomials: 3, at 12849 column(s), 0.000
Average length for reductees: 6203.67 [3], reductors: 134.83 [4963]
Symbolic reduction time: 0.039, column sort time: 0.016[r]
3 + 4963 = 4966 rows / 31556 columns out of 177100 (17.818%)
Density: 0.4389% / 0.49392% (138.5/r), total: 687784 (2.6MB)
Before ech memory: 133.7MB, max: 1474.8MB
Row sort time: 0.000
0.162[r] + 0.000 + 0.000 = 0.169 [2]
Number of unused reductors: 1810
After ech memory: 133.7MB, max: 1474.8MB
Num new polynomials: 2 (66.7%), min deg: 19 [2], av deg: 19.0
Degree counts: 19:2
Queue insertion time: 0.000
Step 88 time: 0.230, [0.241], mat/total: 4.340/5.679, mem: 133.7MB, max: 1474.8MB

*******
STEP 89
Basis length: 194, queue length: 646, step degree: 20, num pairs: 138
Basis total mons: 428584, average length: 2209.196
39 pairs eliminated
Number of pair polynomials: 99, at 47965 column(s), 0.019
Average length for reductees: 3390.97 [99], reductors: 249.30 [16175]
Symbolic reduction time: 0.237[r], column sort time: 0.030
99 + 16175 = 16274 rows / 67171 columns out of 230230 (29.176%)
Density: 0.39959% / 0.46159% (268.41/r), total: 4368102 (16.7MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.003[r]
1.173[r] + 0.000 + 0.000 = 1.190 [24]
Number of unused reductors: 2482
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 24 (24.2%), min deg: 14 [1], av deg: 18.5
Degree counts: 14:1 16:3 18:8 19:1 20:11
Queue insertion time: 0.004[r]
New max step: 89, time: 1.505[r]
Step 89 time: 1.504[r], [1.505], mat/total: 5.540/7.190, mem: 165.7MB, max: 1474.8MB

*******
STEP 90
Basis length: 218, queue length: 659, step degree: 15, num pairs: 1
Basis total mons: 545494, average length: 2502.266
Number of pair polynomials: 1, at 1150 column(s), 0.000
Average length for reductees: 990.00 [1], reductors: 482.00 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 1587 columns out of 54264 (2.925%)
Density: 34.945% / 35.309% (554.57/r), total: 3882 (0.0MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 2
After ech memory: 165.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 90 time: 0.000, [0.005], mat/total: 5.540/7.190, mem: 165.7MB, max: 1474.8MB

*******
STEP 91
Basis length: 218, queue length: 658, step degree: 16, num pairs: 1
Basis total mons: 545494, average length: 2502.266
Number of pair polynomials: 1, at 4261 column(s), 0.000
Average length for reductees: 990.00 [1], reductors: 249.55 [129]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
1 + 129 = 130 rows / 6089 columns out of 74613 (8.161%)
Density: 4.1919% / 4.3196% (255.25/r), total: 33182 (0.1MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.007[r] + 0.000 + 0.000 = 0.010 [1]
Number of unused reductors: 58
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 16 [1], av deg: 16.0
Degree counts: 16:1
Queue insertion time: 0.000
Step 91 time: 0.019[r], [0.021], mat/total: 5.550/7.210, mem: 165.7MB, max: 1474.8MB

*******
STEP 92
Basis length: 219, queue length: 665, step degree: 17, num pairs: 10
Basis total mons: 547482, average length: 2499.918
Number of pair polynomials: 10, at 8224 column(s), 0.000
Average length for reductees: 1164.10 [10], reductors: 101.90 [1188]
Symbolic reduction time: 0.009, column sort time: 0.006[r]
10 + 1188 = 1198 rows / 13041 columns out of 100947 (12.919%)
Density: 0.84937% / 0.92753% (110.77/r), total: 132698 (0.5MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.035[r] + 0.000 + 0.000 = 0.039[r] [5]
Number of unused reductors: 324
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 5 (50.0%), min deg: 13 [1], av deg: 15.4
Degree counts: 13:1 15:2 17:2
Queue insertion time: 0.000
Step 92 time: 0.059, [0.063], mat/total: 5.590/7.269, mem: 165.7MB, max: 1474.8MB

*******
STEP 93
Basis length: 224, queue length: 690, step degree: 14, num pairs: 2
Basis total mons: 555646, average length: 2480.562
Number of pair polynomials: 2, at 1346 column(s), 0.000
Average length for reductees: 551.00 [2], reductors: 614.50 [4]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 4 = 6 rows / 1346 columns out of 38760 (3.473%)
Density: 44.081% / 44.351% (593.33/r), total: 3560 (0.0MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 165.7MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 93 time: 0.000, [0.004], mat/total: 5.590/7.269, mem: 165.7MB, max: 1474.8MB

*******
STEP 94
Basis length: 224, queue length: 688, step degree: 15, num pairs: 1
Basis total mons: 555646, average length: 2480.562
Number of pair polynomials: 1, at 1527 column(s), 0.000
Average length for reductees: 1378.00 [1], reductors: 622.00 [3]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 3 = 4 rows / 1711 columns out of 54264 (3.153%)
Density: 47.399% / 47.492% (811/r), total: 3244 (0.0MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 1 (100.0%), min deg: 15 [1], av deg: 15.0
Degree counts: 15:1
Queue insertion time: 0.000[r]
Step 94 time: 0.003[r], [0.004], mat/total: 5.590/7.280, mem: 165.7MB, max: 1474.8MB

*******
STEP 95
Basis length: 225, queue length: 692, step degree: 16, num pairs: 6
Basis total mons: 556504, average length: 2473.351
Number of pair polynomials: 6, at 4333 column(s), 0.000
Average length for reductees: 840.83 [6], reductors: 68.08 [566]
Symbolic reduction time: 0.000, column sort time: 0.000
6 + 566 = 572 rows / 7411 columns out of 74613 (9.933%)
Density: 1.028% / 1.1211% (76.182/r), total: 43576 (0.2MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.010 + 0.000 + 0.000 = 0.014[r] [2]
Number of unused reductors: 129
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 2 (33.3%), min deg: 16 [2], av deg: 16.0
Degree counts: 16:2
Queue insertion time: 0.000
Step 95 time: 0.019, [0.026], mat/total: 5.610/7.300, mem: 165.7MB, max: 1474.8MB

*******
STEP 96
Basis length: 227, queue length: 696, step degree: 17, num pairs: 6
Basis total mons: 559337, average length: 2464.040
Number of pair polynomials: 6, at 6108 column(s), 0.000
Average length for reductees: 1278.00 [6], reductors: 90.98 [885]
Symbolic reduction time: 0.009[r], column sort time: 0.000
6 + 885 = 891 rows / 11532 columns out of 100947 (11.424%)
Density: 0.85822% / 0.93704% (98.97/r), total: 88182 (0.3MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.019[r] + 0.000 + 0.000 = 0.025[r] [3]
Number of unused reductors: 173
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 3 (50.0%), min deg: 17 [3], av deg: 17.0
Degree counts: 17:3
Queue insertion time: 0.000
Step 96 time: 0.039, [0.043], mat/total: 5.640/7.340, mem: 165.7MB, max: 1474.8MB

*******
STEP 97
Basis length: 230, queue length: 710, step degree: 18, num pairs: 23
Basis total mons: 565243, average length: 2457.578
1 pair eliminated
Number of pair polynomials: 22, at 18124 column(s), 0.000
Average length for reductees: 2216.86 [22], reductors: 121.75 [4117]
Symbolic reduction time: 0.036[r], column sort time: 0.009
22 + 4117 = 4139 rows / 27304 columns out of 134596 (20.286%)
Density: 0.48668% / 0.54217% (132.88/r), total: 550004 (2.1MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.140 + 0.000 + 0.000 = 0.150[r] [13]
Number of unused reductors: 1246
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 13 (59.1%), min deg: 16 [2], av deg: 17.6
Degree counts: 16:2 17:1 18:10
Queue insertion time: 0.000
Step 97 time: 0.210, [0.210], mat/total: 5.800/7.550, mem: 165.7MB, max: 1474.8MB

*******
STEP 98
Basis length: 243, queue length: 780, step degree: 17, num pairs: 3
Basis total mons: 605183, average length: 2490.465
Number of pair polynomials: 3, at 7186 column(s), 0.000
Average length for reductees: 1984.33 [3], reductors: 135.19 [533]
Symbolic reduction time: 0.008[r], column sort time: 0.000
3 + 533 = 536 rows / 9937 columns out of 100947 (9.844%)
Density: 1.4647% / 1.5659% (145.54/r), total: 78011 (0.3MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.018[r] + 0.000 + 0.000 = 0.021[r] [1]
Number of unused reductors: 204
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 1 (33.3%), min deg: 17 [1], av deg: 17.0
Degree counts: 17:1
Queue insertion time: 0.000
Step 98 time: 0.038[r], [0.039], mat/total: 5.830/7.590, mem: 165.7MB, max: 1474.8MB

*******
STEP 99
Basis length: 244, queue length: 787, step degree: 18, num pairs: 7
Basis total mons: 607934, average length: 2491.533
Number of pair polynomials: 7, at 14536 column(s), 0.000
Average length for reductees: 2690.57 [7], reductors: 148.68 [1756]
Symbolic reduction time: 0.019, column sort time: 0.009[r]
7 + 1756 = 1763 rows / 19681 columns out of 134596 (14.622%)
Density: 0.80674% / 0.87886% (158.78/r), total: 279921 (1.1MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.070 + 0.000 + 0.000 = 0.070 [3]
Number of unused reductors: 459
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 3 (42.9%), min deg: 17 [2], av deg: 17.3
Degree counts: 17:2 18:1
Queue insertion time: 0.000
Step 99 time: 0.099, [0.117], mat/total: 5.900/7.690, mem: 165.7MB, max: 1474.8MB

*******
STEP 100
Basis length: 247, queue length: 802, step degree: 18, num pairs: 4
Basis total mons: 619323, average length: 2507.381
Number of pair polynomials: 4, at 11198 column(s), 0.001[r]
Average length for reductees: 3869.50 [4], reductors: 183.70 [2760]
Symbolic reduction time: 0.030, column sort time: 0.013[r]
4 + 2760 = 2764 rows / 25981 columns out of 134596 (19.303%)
Density: 0.72757% / 0.79454% (189.03/r), total: 522479 (2.0MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.000
0.117[r] + 0.000 + 0.000 = 0.128[r] [1]
Number of unused reductors: 2012
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 1 (25.0%), min deg: 18 [1], av deg: 18.0
Degree counts: 18:1
Queue insertion time: 0.000
Step 100 time: 0.183[r], [0.184], mat/total: 6.030/7.880, mem: 165.7MB, max: 1474.8MB

*******
STEP 101
Basis length: 248, queue length: 805, step degree: 19, num pairs: 59
Basis total mons: 624392, average length: 2517.710
3 pairs eliminated
Number of pair polynomials: 56, at 32894 column(s), 0.009
Average length for reductees: 3365.89 [56], reductors: 206.61 [9450]
Symbolic reduction time: 0.127[r], column sort time: 0.019
56 + 9450 = 9506 rows / 48397 columns out of 177100 (27.327%)
Density: 0.46536% / 0.5241% (225.22/r), total: 2140957 (8.2MB)
Before ech memory: 165.7MB, max: 1474.8MB
Row sort time: 0.002[r]
0.579 + 0.000 + 0.000 = 0.599 [22]
Number of unused reductors: 1677
After ech memory: 165.7MB, max: 1474.8MB
Num new polynomials: 22 (39.3%), min deg: 16 [1], av deg: 18.3
Degree counts: 16:1 17:6 18:1 19:14
Queue insertion time: 0.009[r]
Step 101 time: 0.779, [0.783], mat/total: 6.640/8.659, mem: 174.6MB, max: 1474.8MB

*******
STEP 102
Basis length: 270, queue length: 894, step degree: 17, num pairs: 3
Basis total mons: 717166, average length: 2656.170
Number of pair polynomials: 3, at 7872 column(s), 0.000
Average length for reductees: 2972.00 [3], reductors: 296.89 [556]
Symbolic reduction time: 0.016[r], column sort time: 0.006[r]
3 + 556 = 559 rows / 14352 columns out of 100947 (14.217%)
Density: 2.1687% / 2.2691% (311.25/r), total: 173986 (0.7MB)
Before ech memory: 174.6MB, max: 1474.8MB
Row sort time: 0.000
0.045[r] + 0.000 + 0.000 = 0.049 [0]
Number of unused reductors: 291
After ech memory: 174.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 102 time: 0.078[r], [0.078], mat/total: 6.690/8.739, mem: 174.6MB, max: 1474.8MB

*******
STEP 103
Basis length: 270, queue length: 891, step degree: 18, num pairs: 15
Basis total mons: 717166, average length: 2656.170
Number of pair polynomials: 15, at 19338 column(s), 0.000
Average length for reductees: 3743.33 [15], reductors: 200.55 [3762]
Symbolic reduction time: 0.055[r], column sort time: 0.016[r]
15 + 3762 = 3777 rows / 31955 columns out of 134596 (23.741%)
Density: 0.67162% / 0.73344% (214.62/r), total: 810602 (3.1MB)
Before ech memory: 174.6MB, max: 1474.8MB
Row sort time: 0.000
0.209[r] + 0.000 + 0.000 = 0.210 [3]
Number of unused reductors: 1022
After ech memory: 174.6MB, max: 1474.8MB
Num new polynomials: 3 (20.0%), min deg: 17 [1], av deg: 17.7
Degree counts: 17:1 18:2
Queue insertion time: 0.001[r]
Step 103 time: 0.300, [0.301], mat/total: 6.900/9.039, mem: 174.6MB, max: 1474.8MB

*******
STEP 104
Basis length: 273, queue length: 898, step degree: 18, num pairs: 2
Basis total mons: 728701, average length: 2669.234
Number of pair polynomials: 2, at 5717 column(s), 0.000
Average length for reductees: 2444.00 [2], reductors: 221.59 [376]
Symbolic reduction time: 0.009[r], column sort time: 0.000
2 + 376 = 378 rows / 10980 columns out of 134596 (8.158%)
Density: 2.1252% / 2.2569% (233.35/r), total: 88205 (0.3MB)
Before ech memory: 174.6MB, max: 1474.8MB
Row sort time: 0.000
0.017[r] + 0.000 + 0.000 = 0.022[r] [0]
Number of unused reductors: 180
After ech memory: 174.6MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 104 time: 0.039, [0.041], mat/total: 6.930/9.079, mem: 174.6MB, max: 1474.8MB

*******
STEP 105
Basis length: 273, queue length: 896, step degree: 19, num pairs: 10
Basis total mons: 728701, average length: 2669.234
Number of pair polynomials: 10, at 20304 column(s), 0.000
Average length for reductees: 3372.20 [10], reductors: 185.66 [6431]
Symbolic reduction time: 0.085[r], column sort time: 0.019
10 + 6431 = 6441 rows / 41173 columns out of 177100 (23.248%)
Density: 0.46294% / 0.51755% (190.61/r), total: 1227697 (4.7MB)
Before ech memory: 174.6MB, max: 1474.8MB
Row sort time: 0.000
0.269[r] + 0.000 + 0.000 = 0.269 [5]
Number of unused reductors: 1889
After ech memory: 174.6MB, max: 1474.8MB
Num new polynomials: 5 (50.0%), min deg: 19 [5], av deg: 19.0
Degree counts: 19:5
Queue insertion time: 0.003[r]
Step 105 time: 0.389, [0.400], mat/total: 7.200/9.469, mem: 175.5MB, max: 1474.8MB

*******
STEP 106
Basis length: 278, queue length: 922, step degree: 20, num pairs: 92
Basis total mons: 748280, average length: 2691.655
11 pairs eliminated
Number of pair polynomials: 81, at 49685 column(s), 0.019
Average length for reductees: 3976.94 [81], reductors: 280.89 [19150]
Symbolic reduction time: 0.347[r], column sort time: 0.039[r]
81 + 19150 = 19231 rows / 75955 columns out of 230230 (32.991%)
Density: 0.39031% / 0.45187% (296.46/r), total: 5701187 (21.7MB)
Before ech memory: 207.5MB, max: 1474.8MB
Row sort time: 0.006[r]
1.549 + 0.000 + 0.000 = 1.579 [26]
Number of unused reductors: 3851
After ech memory: 207.5MB, max: 1474.8MB
Num new polynomials: 26 (32.1%), min deg: 18 [11], av deg: 19.2
Degree counts: 18:11 20:15
Queue insertion time: 0.000
New max step: 106, time: 2.000
Step 106 time: 2.000, [2.010], mat/total: 8.790/11.469, mem: 208.5MB, max: 1474.8MB

*******
STEP 107
Basis length: 304, queue length: 1004, step degree: 19, num pairs: 33
Basis total mons: 875716, average length: 2880.645
Number of pair polynomials: 33, at 28654 column(s), 0.009[r]
Average length for reductees: 3021.27 [33], reductors: 239.71 [8477]
Symbolic reduction time: 0.141[r], column sort time: 0.019
33 + 8477 = 8510 rows / 48504 columns out of 177100 (27.388%)
Density: 0.51645% / 0.58441% (250.5/r), total: 2131758 (8.1MB)
Before ech memory: 208.5MB, max: 1474.8MB
Row sort time: 0.000
0.480 + 0.000 + 0.000 = 0.501[r] [8]
Number of unused reductors: 2494
After ech memory: 208.5MB, max: 1474.8MB
Num new polynomials: 8 (24.2%), min deg: 17 [1], av deg: 18.8
Degree counts: 17:1 19:7
Queue insertion time: 0.000
Step 107 time: 0.684[r], [0.685], mat/total: 9.300/12.159, mem: 208.5MB, max: 1474.8MB

*******
STEP 108
Basis length: 312, queue length: 1021, step degree: 18, num pairs: 4
Basis total mons: 910289, average length: 2917.593
Number of pair polynomials: 4, at 8576 column(s), 0.000
Average length for reductees: 2155.00 [4], reductors: 332.47 [503]
Symbolic reduction time: 0.016[r], column sort time: 0.006[r]
4 + 503 = 507 rows / 13827 columns out of 134596 (10.273%)
Density: 2.5085% / 2.6241% (346.85/r), total: 175853 (0.7MB)
Before ech memory: 208.5MB, max: 1474.8MB
Row sort time: 0.000
0.042[r] + 0.000 + 0.000 = 0.046[r] [0]
Number of unused reductors: 213
After ech memory: 208.5MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.000
Step 108 time: 0.075[r], [0.076], mat/total: 9.350/12.239, mem: 208.5MB, max: 1474.8MB

*******
STEP 109
Basis length: 312, queue length: 1017, step degree: 20, num pairs: 37
Basis total mons: 910289, average length: 2917.593
3 pairs eliminated
Number of pair polynomials: 34, at 37199 column(s), 0.010
Average length for reductees: 4126.91 [34], reductors: 257.00 [16001]
Symbolic reduction time: 0.276[r], column sort time: 0.029
34 + 16001 = 16035 rows / 65515 columns out of 230230 (28.456%)
Density: 0.40481% / 0.46654% (265.21/r), total: 4252627 (16.2MB)
Before ech memory: 208.5MB, max: 1474.8MB
Row sort time: 0.004[r]
0.917[r] + 0.000 + 0.000 = 0.940 [5]
Number of unused reductors: 4330
After ech memory: 208.5MB, max: 1474.8MB
Num new polynomials: 5 (14.7%), min deg: 20 [5], av deg: 20.0
Degree counts: 20:5
Queue insertion time: 0.000
Step 109 time: 1.270, [1.275], mat/total: 10.300/13.510, mem: 209.6MB, max: 1474.8MB

*******
STEP 110
Basis length: 317, queue length: 1006, step degree: 21, num pairs: 271
Basis total mons: 949161, average length: 2994.199
111 pairs eliminated
Number of pair polynomials: 160, at 74300 column(s), 0.049
At 100000: 30642 rows, 105495 columns, 0.760
Average length for reductees: 4802.46 [160], reductors: 357.67 [35259]
Symbolic reduction time: 0.900, column sort time: 0.050
160 + 35259 = 35419 rows / 109280 columns out of 296010 (36.918%)
Density: 0.34567% / 0.41321% (377.75/r), total: 13379506 (51.0MB)
Before ech memory: 273.6MB, max: 1474.8MB
Row sort time: 0.010
3.629 + 0.000 + 0.000 = 3.668[r] [21]
Number of unused reductors: 6541
After ech memory: 305.7MB, max: 1474.8MB
Num new polynomials: 21 (13.1%), min deg: 19 [2], av deg: 20.8
Degree counts: 19:2 20:1 21:18
Queue insertion time: 0.009[r]
New max step: 110, time: 4.700
Step 110 time: 4.699, [4.706], mat/total: 13.980/18.210, mem: 306.8MB, max: 1474.8MB

*******
STEP 111
Basis length: 338, queue length: 867, step degree: 20, num pairs: 8
Basis total mons: 1139911, average length: 3372.518
Number of pair polynomials: 8, at 38428 column(s), 0.000
Average length for reductees: 9756.00 [8], reductors: 237.70 [14622]
Symbolic reduction time: 0.250, column sort time: 0.032[r]
8 + 14622 = 14630 rows / 64331 columns out of 230230 (27.942%)
Density: 0.37759% / 0.4355% (242.91/r), total: 3553765 (13.6MB)
Before ech memory: 306.8MB, max: 1474.8MB
Row sort time: 0.000
0.849 + 0.000 + 0.000 = 0.875[r] [1]
Number of unused reductors: 3208
After ech memory: 306.8MB, max: 1474.8MB
Num new polynomials: 1 (12.5%), min deg: 20 [1], av deg: 20.0
Degree counts: 20:1
Queue insertion time: 0.000
Step 111 time: 1.170, [1.177], mat/total: 14.860/19.380, mem: 306.8MB, max: 1474.8MB

*******
STEP 112
Basis length: 339, queue length: 864, step degree: 21, num pairs: 10
Basis total mons: 1160148, average length: 3422.265
Number of pair polynomials: 10, at 52125 column(s), 0.013[r]
Average length for reductees: 14745.40 [10], reductors: 310.81 [22574]
Symbolic reduction time: 0.479[r], column sort time: 0.039
10 + 22574 = 22584 rows / 82015 columns out of 296010 (27.707%)
Density: 0.38676% / 0.45588% (317.2/r), total: 7163730 (27.3MB)
Before ech memory: 306.8MB, max: 1474.8MB
Row sort time: 0.006[r]
1.690 + 0.000 + 0.000 = 1.710 [2]
Number of unused reductors: 5707
After ech memory: 306.8MB, max: 1474.8MB
Num new polynomials: 2 (20.0%), min deg: 21 [2], av deg: 21.0
Degree counts: 21:2
Queue insertion time: 0.006[r]
Step 112 time: 2.268[r], [2.268], mat/total: 16.580/21.650, mem: 308.1MB, max: 1474.8MB

*******
STEP 113
Basis length: 341, queue length: 864, step degree: 22, num pairs: 280
Basis total mons: 1199630, average length: 3517.977
125 pairs eliminated
Number of pair polynomials: 156, at 90552 column(s), 0.059
At 100000: 34794 rows, 129620 columns, 0.997[r]
Average length for reductees: 6867.17 [156], reductors: 412.69 [55450]
Symbolic reduction time: 1.639, column sort time: 0.077[r]
156 + 55450 = 55606 rows / 145428 columns out of 376740 (38.602%)
Density: 0.29622% / 0.3678% (430.79/r), total: 23954725 (91.4MB)
Before ech memory: 372.2MB, max: 1474.8MB
Row sort time: 0.018[r]
6.588[r] + 0.000 + 0.000 = 6.630 [15]
Number of unused reductors: 10598
After ech memory: 436.2MB, max: 1474.8MB
Num new polynomials: 15 (9.6%), min deg: 20 [2], av deg: 21.7
Degree counts: 20:2 22:13
Queue insertion time: 0.009
New max step: 113, time: 8.450
Step 113 time: 8.449, [8.458], mat/total: 23.230/30.099, mem: 439.2MB, max: 1474.8MB

*******
STEP 114
Basis length: 356, queue length: 663, step degree: 21, num pairs: 9
Basis total mons: 1349399, average length: 3790.447
Number of pair polynomials: 9, at 23885 column(s), 0.005[r]
Average length for reductees: 5711.56 [9], reductors: 269.25 [20083]
Symbolic reduction time: 0.359, column sort time: 0.039[r]
9 + 20083 = 20092 rows / 75265 columns out of 296010 (25.427%)
Density: 0.36097% / 0.42317% (271.69/r), total: 5458709 (20.8MB)
Before ech memory: 439.2MB, max: 1474.8MB
Row sort time: 0.005[r]
0.644[r] + 0.000 + 0.000 = 0.670 [2]
Number of unused reductors: 10101
After ech memory: 439.2MB, max: 1474.8MB
Num new polynomials: 2 (22.2%), min deg: 21 [2], av deg: 21.0
Degree counts: 21:2
Queue insertion time: 0.000
Step 114 time: 1.088[r], [1.090], mat/total: 23.910/31.190, mem: 439.2MB, max: 1474.8MB

*******
STEP 115
Basis length: 358, queue length: 664, step degree: 22, num pairs: 9
Basis total mons: 1366194, average length: 3816.184
Number of pair polynomials: 9, at 30899 column(s), 0.006[r]
Average length for reductees: 7575.33 [9], reductors: 310.60 [28640]
Symbolic reduction time: 0.590, column sort time: 0.049[r]
9 + 28640 = 28649 rows / 92091 columns out of 376740 (24.444%)
Density: 0.33976% / 0.40586% (312.89/r), total: 8963843 (34.2MB)
Before ech memory: 439.2MB, max: 1474.8MB
Row sort time: 0.009[r]
1.315[r] + 0.000 + 0.000 = 1.348[r] [1]
Number of unused reductors: 12852
After ech memory: 439.2MB, max: 1474.8MB
Num new polynomials: 1 (11.1%), min deg: 22 [1], av deg: 22.0
Degree counts: 22:1
Queue insertion time: 0.005[r]
Step 115 time: 2.015[r], [2.015], mat/total: 25.270/33.210, mem: 439.2MB, max: 1474.8MB

*******
STEP 116
Basis length: 359, queue length: 660, step degree: 23, num pairs: 249
Basis total mons: 1378668, average length: 3840.301
131 pairs eliminated
Number of pair polynomials: 118, at 95123 column(s), 0.059
At 100000: 37519 rows, 153680 columns, 1.205[r]
Average length for reductees: 7405.60 [118], reductors: 439.61 [76781]
Symbolic reduction time: 2.469, column sort time: 0.096[r]
118 + 76781 = 76899 rows / 178280 columns out of 475020 (37.531%)
Density: 0.25258% / 0.327% (450.3/r), total: 34627936 (132.1MB)
Before ech memory: 503.3MB, max: 1474.8MB
Row sort time: 0.025[r]
9.260 + 0.000 + 0.000 = 9.320 [5]
Number of unused reductors: 18067
After ech memory: 599.4MB, max: 1474.8MB
Num new polynomials: 5 (4.2%), min deg: 21 [1], av deg: 22.6
Degree counts: 21:1 23:4
Queue insertion time: 0.009[r]
New max step: 116, time: 11.990
Step 116 time: 11.989, [12.002], mat/total: 34.620/45.199, mem: 601.1MB, max: 1474.8MB

*******
STEP 117
Basis length: 364, queue length: 438, step degree: 22, num pairs: 5
Basis total mons: 1472487, average length: 4045.294
Number of pair polynomials: 5, at 47677 column(s), 0.009[r]
At 100000: 30462 rows, 102435 columns, 0.719
Average length for reductees: 19465.00 [5], reductors: 338.78 [32929]
Symbolic reduction time: 0.789, column sort time: 0.055[r]
5 + 32929 = 32934 rows / 105408 columns out of 376740 (27.979%)
Density: 0.32415% / 0.39179% (341.68/r), total: 11253053 (42.9MB)
Before ech memory: 601.1MB, max: 1474.8MB
Row sort time: 0.009[r]
2.449 + 0.000 + 0.000 = 2.487[r] [1]
Number of unused reductors: 10272
After ech memory: 601.1MB, max: 1474.8MB
Num new polynomials: 1 (20.0%), min deg: 22 [1], av deg: 22.0
Degree counts: 22:1
Queue insertion time: 0.000
Step 117 time: 3.360, [3.366], mat/total: 37.120/48.559, mem: 601.1MB, max: 1474.8MB

*******
STEP 118
Basis length: 365, queue length: 439, step degree: 23, num pairs: 6
Basis total mons: 1503803, average length: 4120.008
Number of pair polynomials: 6, at 71951 column(s), 0.016[r]
At 100000: 30307 rows, 124382 columns, 0.970
Average length for reductees: 29340.83 [6], reductors: 430.91 [58706]
Symbolic reduction time: 1.860, column sort time: 0.079[r]
6 + 58706 = 58712 rows / 149743 columns out of 475020 (31.524%)
Density: 0.28974% / 0.36565% (433.86/r), total: 25473081 (97.2MB)
Before ech memory: 601.1MB, max: 1474.8MB
Row sort time: 0.018[r]
6.069 + 0.000 + 0.000 = 6.119 [0]
Number of unused reductors: 16463
After ech memory: 665.2MB, max: 1474.8MB
No new polynomials
Queue insertion time: 0.008[r]
Step 118 time: 8.110, [8.112], mat/total: 43.260/56.670, mem: 667.1MB, max: 1474.8MB

*******
STEP 119
Basis length: 365, queue length: 433, step degree: 24, num pairs: 185
Basis total mons: 1503803, average length: 4120.008
117 pairs eliminated
Number of pair polynomials: 68, at 107800 column(s), 0.056[r]
At 100000: 41061 rows, 177471 columns, 1.440
At 200000: 93485 rows, 208741 columns, 3.469
Average length for reductees: 9818.07 [68], reductors: 475.57 [102973]
Symbolic reduction time: 3.860, column sort time: 0.118[r]
68 + 102973 = 103041 rows / 214332 columns out of 593775 (36.097%)
Density: 0.22476% / 0.3039% (481.74/r), total: 49638749 (189.4MB)
Before ech memory: 763.2MB, max: 1474.8MB
Row sort time: 0.032[r]
13.207[r] + 0.000 + 0.000 = 13.269 [5]
Number of unused reductors: 25947
After ech memory: 900.8MB, max: 1474.8MB
Num new polynomials: 5 (7.4%), min deg: 24 [5], av deg: 24.0
Degree counts: 24:5
Queue insertion time: 0.010
New max step: 119, time: 17.360
Step 119 time: 17.360, [17.367], mat/total: 56.570/74.030, mem: 893.4MB, max: 1474.8MB

*******
STEP 120
Basis length: 370, queue length: 276, step degree: 25, num pairs: 127
Basis total mons: 1582890, average length: 4278.081
79 pairs eliminated
Number of pair polynomials: 48, at 105955 column(s), 0.049[r]
At 100000: 42875 rows, 189956 columns, 1.519
At 200000: 95421 rows, 214016 columns, 3.549[r]
Average length for reductees: 11261.33 [48], reductors: 484.59 [117427]
Symbolic reduction time: 4.588[r], column sort time: 0.130
48 + 117427 = 117475 rows / 233604 columns out of 736281 (31.728%)
Density: 0.20932% / 0.2904% (488.99/r), total: 57443917 (219.1MB)
Before ech memory: 925.4MB, max: 1474.8MB
Row sort time: 0.037[r]
15.289[r] + 0.000 + 0.000 = 15.369 [2]
Number of unused reductors: 29808
After ech memory: 1064.3MB, max: 1477.9MB
Num new polynomials: 2 (4.2%), min deg: 25 [2], av deg: 25.0
Degree counts: 25:2
Queue insertion time: 0.009[r]
New max step: 120, time: 20.198[r]
Step 120 time: 20.197[r], [20.198], mat/total: 71.980/94.230, mem: 1053.6MB, max: 1477.9MB

*******
STEP 121
Basis length: 372, queue length: 161, step degree: 26, num pairs: 79
Basis total mons: 1654168, average length: 4446.688
48 pairs eliminated
Number of pair polynomials: 31, at 123751 column(s), 0.057[r]
At 100000: 44892 rows, 212611 columns, 1.849
At 200000: 96973 rows, 241632 columns, 3.970
Average length for reductees: 19719.55 [31], reductors: 496.24 [143450]
Symbolic reduction time: 5.940, column sort time: 0.150
31 + 143450 = 143481 rows / 269318 columns out of 906192 (29.720%)
Density: 0.1858% / 0.26625% (500.39/r), total: 71797076 (273.9MB)
Before ech memory: 1117.6MB, max: 1477.9MB
Row sort time: 0.048[r]
22.149 + 0.000 + 0.000 = 22.239 [0]
Number of unused reductors: 27653
After ech memory: 1323.0MB, max: 1799.8MB
No new polynomials
Queue insertion time: 0.009
New max step: 121, time: 28.470
Step 121 time: 28.469, [28.479], mat/total: 94.280/122.699, mem: 1312.1MB, max: 1799.8MB

*******
STEP 122
Basis length: 372, queue length: 82, step degree: 27, num pairs: 46
Basis total mons: 1654168, average length: 4446.688
42 pairs eliminated
Number of pair polynomials: 4, at 40786 column(s), 0.005[r]
At 100000: 42608 rows, 184290 columns, 1.409
At 200000: 95768 rows, 221495 columns, 3.539
Average length for reductees: 10340.75 [4], reductors: 483.27 [125618]
Symbolic reduction time: 4.920, column sort time: 0.134[r]
4 + 125618 = 125622 rows / 243725 columns out of 1107568 (22.005%)
Density: 0.19842% / 0.27817% (483.59/r), total: 60749329 (231.7MB)
Before ech memory: 1312.1MB, max: 1799.8MB
Row sort time: 0.040[r]
12.839 + 0.000 + 0.000 = 12.919 [0]
Number of unused reductors: 43947
After ech memory: 1419.8MB, max: 1851.2MB
No new polynomials
Queue insertion time: 0.009[r]
Step 122 time: 18.050, [18.053], mat/total: 107.250/140.750, mem: 1408.2MB, max: 1851.2MB

*******
STEP 123
Basis length: 372, queue length: 36, step degree: 28, num pairs: 21
Basis total mons: 1654168, average length: 4446.688
19 pairs eliminated
Number of pair polynomials: 2, at 16867 column(s), 0.002[r]
At 100000: 42217 rows, 191188 columns, 1.519
At 200000: 95836 rows, 240057 columns, 3.750
Average length for reductees: 6559.00 [2], reductors: 504.64 [166589]
Symbolic reduction time: 7.139, column sort time: 0.159
2 + 166589 = 166591 rows / 298703 columns out of 1344904 (22.210%)
Density: 0.16897% / 0.24944% (504.71/r), total: 84080533 (320.7MB)
Before ech memory: 1504.3MB, max: 1851.2MB
Row sort time: 0.057[r]
19.739 + 0.000 + 0.000 = 19.839 [0]
Number of unused reductors: 59158
After ech memory: 1679.8MB, max: 2208.5MB
No new polynomials
Queue insertion time: 0.015[r]
Step 123 time: 27.246[r], [27.246], mat/total: 127.150/168.000, mem: 1667.0MB, max: 2208.5MB

*******
STEP 124
Basis length: 372, queue length: 15, step degree: 29, num pairs: 12
Basis total mons: 1654168, average length: 4446.688
11 pairs eliminated
Number of pair polynomials: 1, at 9506 column(s), 0.000
At 100000: 44729 rows, 232079 columns, 1.750
At 200000: 98748 rows, 282674 columns, 4.150
At 300000: 163935 rows, 330567 columns, 7.309
Average length for reductees: 5569.00 [1], reductors: 539.18 [224265]
Symbolic reduction time: 10.539, column sort time: 0.219[r]
1 + 224265 = 224266 rows / 378393 columns out of 1623160 (23.312%)
Density: 0.1425% / 0.22072% (539.2/r), total: 120925336 (461.3MB)
Before ech memory: 1827.2MB, max: 2208.5MB
Row sort time: 0.077[r]
26.028[r] + 0.000 + 0.000 = 26.150 [0]
Number of unused reductors: 93507
After ech memory: 2071.9MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.013[r]
New max step: 124, time: 37.030
Step 124 time: 37.030, [37.035], mat/total: 153.390/205.030, mem: 2051.4MB, max: 2741.8MB

*******
STEP 125
Basis length: 372, queue length: 3, step degree: 30, num pairs: 2
Basis total mons: 1654168, average length: 4446.688
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 126
Basis length: 372, queue length: 1, step degree: 93, num pairs: 1
Basis total mons: 1654168, average length: 4446.688
Number of pair polynomials: 1, at 11419 column(s), 0.000
At 100000: 56053 rows, 266183 columns, 1.819
At 200000: 125214 rows, 345515 columns, 3.899
At 300000: 200529 rows, 403909 columns, 6.149
At 400000: 283871 rows, 461127 columns, 8.579
At 500000: 371134 rows, 538097 columns, 11.919
At 600000: 454956 rows, 623643 columns, 15.989
At 700000: 536688 rows, 708411 columns, 20.259
At 800000: 630998 rows, 800296 columns, 24.829
Average length for reductees: 11415.00 [1], reductors: 416.25 [631410]
Symbolic reduction time: 24.839, column sort time: 0.470[r]
1 + 631410 = 631411 rows / 800534 columns out of 1120529256 (0.071%)
Density: 0.051999% / 0.11949% (416.27/r), total: 262835299 (1002.6MB), bv
Before ech memory: 2643.2MB, max: 2741.8MB
Row sort time: 0.228[r]
0.168[r] + 0.004[r] = 0.210 [1]
Number of unused reductors: 525050
After ech memory: 2704.2MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.007[r]
Step 126 time: 25.809, [25.824], mat/total: 153.840/230.840, mem: 2660.0MB, max: 2741.8MB

*******
STEP 127
Basis length: 373, queue length: 21, step degree: 13, num pairs: 2
Basis total mons: 1654250, average length: 4434.987
Number of pair polynomials: 2, at 404 column(s), 0.000
Average length for reductees: 82.00 [2], reductors: 27.36 [39]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 39 = 41 rows / 574 columns out of 27132 (2.116%)
Density: 5.2307% / 5.5928% (30.024/r), total: 1231 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 2
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (100.0%), min deg: 11 [1], av deg: 12.0
Degree counts: 11:1 13:1
Queue insertion time: 0.000
Step 127 time: 0.000, [0.003], mat/total: 153.840/230.840, mem: 2660.0MB, max: 2741.8MB

*******
STEP 128
Basis length: 375, queue length: 46, step degree: 12, num pairs: 1
Basis total mons: 1654533, average length: 4412.088
Number of pair polynomials: 1, at 135 column(s), 0.000
Average length for reductees: 89.00 [1], reductors: 82.00 [1]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 1 = 2 rows / 135 columns out of 18564 (0.727%)
Density: 63.333% / 63.333% (85.5/r), total: 171 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 10 [1], av deg: 10.0
Degree counts: 10:1
Queue insertion time: 0.000[r]
Step 128 time: 0.002[r], [0.002], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 129
Basis length: 376, queue length: 53, step degree: 11, num pairs: 1
Basis total mons: 1654648, average length: 4400.660
Number of pair polynomials: 1, at 119 column(s), 0.000
Average length for reductees: 115.00 [1], reductors: 5.00 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 10 = 11 rows / 145 columns out of 12376 (1.172%)
Density: 10.345% / 10.972% (15/r), total: 165 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 11 [1], av deg: 11.0
Degree counts: 11:1
Queue insertion time: 0.000
Step 129 time: 0.000, [0.003], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 130
Basis length: 377, queue length: 60, step degree: 12, num pairs: 1
Basis total mons: 1654782, average length: 4389.342
Number of pair polynomials: 1, at 218 column(s), 0.000
Average length for reductees: 134.00 [1], reductors: 29.44 [9]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 9 = 10 rows / 284 columns out of 18564 (1.530%)
Density: 14.049% / 14.821% (39.9/r), total: 399 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 130 time: 0.000, [0.003], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 131
Basis length: 378, queue length: 67, step degree: 13, num pairs: 4
Basis total mons: 1655016, average length: 4378.349
Number of pair polynomials: 4, at 452 column(s), 0.000
Average length for reductees: 143.00 [4], reductors: 31.26 [65]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 65 = 69 rows / 868 columns out of 27132 (3.199%)
Density: 4.3478% / 4.7269% (37.739/r), total: 2604 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 2
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 4 (100.0%), min deg: 11 [2], av deg: 12.0
Degree counts: 11:2 13:2
Queue insertion time: 0.000
Step 131 time: 0.000, [0.004], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 132
Basis length: 382, queue length: 123, step degree: 12, num pairs: 1
Basis total mons: 1656306, average length: 4335.880
Number of pair polynomials: 1, at 538 column(s), 0.000
Average length for reductees: 301.00 [1], reductors: 77.18 [22]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 22 = 23 rows / 730 columns out of 18564 (3.932%)
Density: 11.906% / 12.48% (86.913/r), total: 1999 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 1
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 12 [1], av deg: 12.0
Degree counts: 12:1
Queue insertion time: 0.000
Step 132 time: 0.000, [0.004], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 133
Basis length: 383, queue length: 142, step degree: 13, num pairs: 2
Basis total mons: 1656797, average length: 4325.841
Number of pair polynomials: 2, at 774 column(s), 0.000
Average length for reductees: 396.00 [2], reductors: 48.05 [93]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 93 = 95 rows / 1001 columns out of 27132 (3.689%)
Density: 5.5324% / 5.9565% (55.379/r), total: 5261 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 2
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 133 time: 0.000, [0.005], mat/total: 153.840/230.849, mem: 2660.0MB, max: 2741.8MB

*******
STEP 134
Basis length: 383, queue length: 140, step degree: 14, num pairs: 8
Basis total mons: 1656797, average length: 4325.841
1 pair eliminated
Number of pair polynomials: 7, at 1280 column(s), 0.000
Average length for reductees: 253.71 [7], reductors: 66.53 [93]
Symbolic reduction time: 0.000[r], column sort time: 0.000
7 + 93 = 100 rows / 1506 columns out of 38760 (3.885%)
Density: 5.2875% / 5.6737% (79.63/r), total: 7963 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [4]
Number of unused reductors: 6
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 4 (57.1%), min deg: 14 [4], av deg: 14.0
Degree counts: 14:4
Queue insertion time: 0.000
Step 134 time: 0.006[r], [0.007], mat/total: 153.840/230.860, mem: 2660.0MB, max: 2741.8MB

*******
STEP 135
Basis length: 387, queue length: 165, step degree: 15, num pairs: 12
Basis total mons: 1658073, average length: 4284.426
Number of pair polynomials: 12, at 3316 column(s), 0.000
Average length for reductees: 242.58 [12], reductors: 79.13 [313]
Symbolic reduction time: 0.000, column sort time: 0.000
12 + 313 = 325 rows / 4456 columns out of 54264 (8.212%)
Density: 1.9113% / 2.0895% (85.169/r), total: 27680 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [9]
Number of unused reductors: 49
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 9 (75.0%), min deg: 13 [7], av deg: 13.3
Degree counts: 13:7 14:1 15:1
Queue insertion time: 0.001[r]
Step 135 time: 0.018[r], [0.019], mat/total: 153.840/230.880, mem: 2660.0MB, max: 2741.8MB

*******
STEP 136
Basis length: 396, queue length: 250, step degree: 14, num pairs: 9
Basis total mons: 1662341, average length: 4197.831
Number of pair polynomials: 9, at 2961 column(s), 0.000
Average length for reductees: 460.67 [9], reductors: 86.97 [202]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 202 = 211 rows / 3700 columns out of 38760 (9.546%)
Density: 2.7812% / 3.0165% (102.91/r), total: 21713 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.005[r] + 0.000 + 0.000 = 0.006[r] [5]
Number of unused reductors: 27
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 5 (55.6%), min deg: 14 [5], av deg: 14.0
Degree counts: 14:5
Queue insertion time: 0.000
Step 136 time: 0.009, [0.014], mat/total: 153.850/230.889, mem: 2660.0MB, max: 2741.8MB

*******
STEP 137
Basis length: 401, queue length: 287, step degree: 15, num pairs: 18
Basis total mons: 1665337, average length: 4152.960
Number of pair polynomials: 18, at 6260 column(s), 0.000
Average length for reductees: 601.50 [18], reductors: 106.69 [601]
Symbolic reduction time: 0.007[r], column sort time: 0.000
18 + 601 = 619 rows / 7972 columns out of 54264 (14.691%)
Density: 1.5188% / 1.6669% (121.08/r), total: 74947 (0.3MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.019 + 0.000 + 0.000 = 0.019 [11]
Number of unused reductors: 98
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 11 (61.1%), min deg: 13 [2], av deg: 14.4
Degree counts: 13:2 14:3 15:6
Queue insertion time: 0.000
Step 137 time: 0.030, [0.039], mat/total: 153.870/230.920, mem: 2660.0MB, max: 2741.8MB

*******
STEP 138
Basis length: 412, queue length: 358, step degree: 14, num pairs: 3
Basis total mons: 1675817, average length: 4067.517
Number of pair polynomials: 3, at 1869 column(s), 0.000
Average length for reductees: 593.67 [3], reductors: 115.55 [86]
Symbolic reduction time: 0.002[r], column sort time: 0.000
3 + 86 = 89 rows / 2637 columns out of 38760 (6.803%)
Density: 4.9929% / 5.206% (131.66/r), total: 11718 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 45
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (66.7%), min deg: 13 [1], av deg: 13.5
Degree counts: 13:1 14:1
Queue insertion time: 0.000
Step 138 time: 0.008[r], [0.009], mat/total: 153.870/230.929, mem: 2660.0MB, max: 2741.8MB

*******
STEP 139
Basis length: 414, queue length: 373, step degree: 14, num pairs: 3
Basis total mons: 1677561, average length: 4052.080
Number of pair polynomials: 3, at 2389 column(s), 0.000
Average length for reductees: 788.00 [3], reductors: 167.13 [90]
Symbolic reduction time: 0.000, column sort time: 0.002[r]
3 + 90 = 93 rows / 3155 columns out of 38760 (8.140%)
Density: 5.9322% / 6.1513% (187.16/r), total: 17406 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 59
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (66.7%), min deg: 13 [2], av deg: 13.0
Degree counts: 13:2
Queue insertion time: 0.000
Step 139 time: 0.010, [0.011], mat/total: 153.870/230.940, mem: 2660.0MB, max: 2741.8MB

*******
STEP 140
Basis length: 416, queue length: 397, step degree: 14, num pairs: 3
Basis total mons: 1678592, average length: 4035.077
Number of pair polynomials: 3, at 1406 column(s), 0.000
Average length for reductees: 507.00 [3], reductors: 150.92 [85]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 85 = 88 rows / 2435 columns out of 38760 (6.282%)
Density: 6.6964% / 6.9166% (163.06/r), total: 14349 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.004[r] + 0.000 + 0.000 = 0.005[r] [1]
Number of unused reductors: 23
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (33.3%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 140 time: 0.009[r], [0.010], mat/total: 153.880/230.949, mem: 2660.0MB, max: 2741.8MB

*******
STEP 141
Basis length: 417, queue length: 403, step degree: 15, num pairs: 7
Basis total mons: 1679638, average length: 4027.909
3 pairs eliminated
Number of pair polynomials: 4, at 3568 column(s), 0.000
Average length for reductees: 978.50 [4], reductors: 152.23 [281]
Symbolic reduction time: 0.000, column sort time: 0.003[r]
4 + 281 = 285 rows / 5383 columns out of 54264 (9.920%)
Density: 3.0434% / 3.2215% (163.82/r), total: 46690 (0.2MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.009 [1]
Number of unused reductors: 109
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (25.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 141 time: 0.019, [0.024], mat/total: 153.890/230.969, mem: 2660.0MB, max: 2741.8MB

*******
STEP 142
Basis length: 418, queue length: 404, step degree: 14, num pairs: 2
Basis total mons: 1680841, average length: 4021.151
Number of pair polynomials: 2, at 2262 column(s), 0.000
Average length for reductees: 1203.00 [2], reductors: 163.33 [87]
Symbolic reduction time: 0.000, column sort time: 0.001[r]
2 + 87 = 89 rows / 3091 columns out of 38760 (7.975%)
Density: 6.04% / 6.2856% (186.7/r), total: 16616 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 23
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (100.0%), min deg: 12 [1], av deg: 13.0
Degree counts: 12:1 14:1
Queue insertion time: 0.000
Step 142 time: 0.010, [0.012], mat/total: 153.890/230.980, mem: 2660.0MB, max: 2741.8MB

*******
STEP 143
Basis length: 420, queue length: 428, step degree: 13, num pairs: 3
Basis total mons: 1682689, average length: 4006.402
Number of pair polynomials: 3, at 1454 column(s), 0.000
Average length for reductees: 458.00 [3], reductors: 391.80 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 10 = 13 rows / 1604 columns out of 27132 (5.912%)
Density: 25.379% / 25.869% (407.08/r), total: 5292 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 1
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (100.0%), min deg: 13 [3], av deg: 13.0
Degree counts: 13:3
Queue insertion time: 0.000
Step 143 time: 0.006[r], [0.006], mat/total: 153.900/230.989, mem: 2660.0MB, max: 2741.8MB

*******
STEP 144
Basis length: 423, queue length: 473, step degree: 14, num pairs: 7
Basis total mons: 1683948, average length: 3980.965
Number of pair polynomials: 7, at 2483 column(s), 0.000
Average length for reductees: 417.71 [7], reductors: 143.85 [123]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 123 = 130 rows / 3205 columns out of 38760 (8.269%)
Density: 4.9483% / 5.1518% (158.59/r), total: 20617 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.007[r] [3]
Number of unused reductors: 20
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (42.9%), min deg: 12 [1], av deg: 13.3
Degree counts: 12:1 14:2
Queue insertion time: 0.000
Step 144 time: 0.010, [0.014], mat/total: 153.910/231.000, mem: 2660.0MB, max: 2741.8MB

*******
STEP 145
Basis length: 426, queue length: 487, step degree: 13, num pairs: 3
Basis total mons: 1685240, average length: 3955.962
Number of pair polynomials: 3, at 1046 column(s), 0.000
Average length for reductees: 339.00 [3], reductors: 336.60 [10]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 10 = 13 rows / 1240 columns out of 27132 (4.570%)
Density: 27.19% / 27.494% (337.15/r), total: 4383 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (66.7%), min deg: 13 [2], av deg: 13.0
Degree counts: 13:2
Queue insertion time: 0.000
Step 145 time: 0.000, [0.005], mat/total: 153.910/231.000, mem: 2660.0MB, max: 2741.8MB

*******
STEP 146
Basis length: 428, queue length: 520, step degree: 14, num pairs: 3
Basis total mons: 1686080, average length: 3939.439
Number of pair polynomials: 3, at 1474 column(s), 0.000
Average length for reductees: 427.33 [3], reductors: 242.09 [64]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 64 = 67 rows / 2851 columns out of 38760 (7.356%)
Density: 8.7825% / 9.0405% (250.39/r), total: 16776 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.004[r] [0]
Number of unused reductors: 13
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 146 time: 0.010, [0.011], mat/total: 153.920/231.010, mem: 2660.0MB, max: 2741.8MB

*******
STEP 147
Basis length: 428, queue length: 517, step degree: 15, num pairs: 10
Basis total mons: 1686080, average length: 3939.439
Number of pair polynomials: 10, at 4367 column(s), 0.000
Average length for reductees: 556.20 [10], reductors: 70.65 [548]
Symbolic reduction time: 0.006[r], column sort time: 0.000
10 + 548 = 558 rows / 6223 columns out of 54264 (11.468%)
Density: 1.2751% / 1.4024% (79.348/r), total: 44276 (0.2MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.010 + 0.000 + 0.000 = 0.010 [4]
Number of unused reductors: 110
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 4 (40.0%), min deg: 15 [4], av deg: 15.0
Degree counts: 15:4
Queue insertion time: 0.000
Step 147 time: 0.019, [0.025], mat/total: 153.930/231.030, mem: 2660.0MB, max: 2741.8MB

*******
STEP 148
Basis length: 432, queue length: 540, step degree: 16, num pairs: 65
Basis total mons: 1688685, average length: 3908.993
12 pairs eliminated
Number of pair polynomials: 53, at 13120 column(s), 0.005[r]
Average length for reductees: 561.58 [53], reductors: 122.81 [2166]
Symbolic reduction time: 0.019[r], column sort time: 0.000
53 + 2166 = 2219 rows / 16387 columns out of 74613 (21.963%)
Density: 0.81337% / 0.91513% (133.29/r), total: 295765 (1.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.088[r] + 0.000 + 0.000 = 0.089 [25]
Number of unused reductors: 295
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 25 (47.2%), min deg: 12 [1], av deg: 15.0
Degree counts: 12:1 14:10 15:1 16:13
Queue insertion time: 0.000
Step 148 time: 0.129, [0.132], mat/total: 154.020/231.159, mem: 2660.0MB, max: 2741.8MB

*******
STEP 149
Basis length: 457, queue length: 672, step degree: 13, num pairs: 3
Basis total mons: 1708604, average length: 3738.740
Number of pair polynomials: 3, at 956 column(s), 0.000
Average length for reductees: 161.00 [3], reductors: 193.94 [16]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 16 = 19 rows / 1169 columns out of 27132 (4.309%)
Density: 16.145% / 16.51% (188.74/r), total: 3586 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 4
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (33.3%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 149 time: 0.000, [0.006], mat/total: 154.020/231.159, mem: 2660.0MB, max: 2741.8MB

*******
STEP 150
Basis length: 458, queue length: 675, step degree: 14, num pairs: 4
Basis total mons: 1708853, average length: 3731.120
Number of pair polynomials: 4, at 1039 column(s), 0.000
Average length for reductees: 249.00 [4], reductors: 74.89 [37]
Symbolic reduction time: 0.001[r], column sort time: 0.000
4 + 37 = 41 rows / 1189 columns out of 38760 (3.068%)
Density: 7.7273% / 8.1177% (91.878/r), total: 3767 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (50.0%), min deg: 12 [1], av deg: 13.0
Degree counts: 12:1 14:1
Queue insertion time: 0.000
Step 150 time: 0.003[r], [0.004], mat/total: 154.020/231.170, mem: 2660.0MB, max: 2741.8MB

*******
STEP 151
Basis length: 460, queue length: 691, step degree: 13, num pairs: 2
Basis total mons: 1709424, average length: 3716.139
Number of pair polynomials: 2, at 1106 column(s), 0.000
Average length for reductees: 279.00 [2], reductors: 318.08 [12]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 12 = 14 rows / 1195 columns out of 27132 (4.404%)
Density: 26.151% / 26.457% (312.5/r), total: 4375 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 1
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 151 time: 0.000, [0.005], mat/total: 154.020/231.170, mem: 2660.0MB, max: 2741.8MB

*******
STEP 152
Basis length: 460, queue length: 689, step degree: 15, num pairs: 18
Basis total mons: 1709424, average length: 3716.139
Number of pair polynomials: 18, at 5070 column(s), 0.000
Average length for reductees: 527.56 [18], reductors: 105.73 [681]
Symbolic reduction time: 0.007[r], column sort time: 0.000
18 + 681 = 699 rows / 7706 columns out of 54264 (14.201%)
Density: 1.513% / 1.6598% (116.59/r), total: 81496 (0.3MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.009 + 0.000 + 0.000 = 0.019[r] [8]
Number of unused reductors: 173
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 8 (44.4%), min deg: 13 [1], av deg: 14.6
Degree counts: 13:1 14:1 15:6
Queue insertion time: 0.000
Step 152 time: 0.029, [0.035], mat/total: 154.040/231.199, mem: 2660.0MB, max: 2741.8MB

*******
STEP 153
Basis length: 468, queue length: 736, step degree: 14, num pairs: 2
Basis total mons: 1713883, average length: 3662.143
Number of pair polynomials: 2, at 899 column(s), 0.000
Average length for reductees: 401.00 [2], reductors: 229.25 [4]
Symbolic reduction time: 0.000, column sort time: 0.001[r]
2 + 4 = 6 rows / 962 columns out of 38760 (2.482%)
Density: 29.782% / 30.234% (286.5/r), total: 1719 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (50.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 153 time: 0.003[r], [0.004], mat/total: 154.040/231.210, mem: 2660.0MB, max: 2741.8MB

*******
STEP 154
Basis length: 469, queue length: 743, step degree: 15, num pairs: 2
Basis total mons: 1714355, average length: 3655.341
Number of pair polynomials: 2, at 1412 column(s), 0.000
Average length for reductees: 472.00 [2], reductors: 89.42 [380]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 380 = 382 rows / 4214 columns out of 54264 (7.766%)
Density: 2.1696% / 2.38% (91.427/r), total: 34925 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.003[r] + 0.000 + 0.000 = 0.004[r] [1]
Number of unused reductors: 163
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (50.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 154 time: 0.009, [0.014], mat/total: 154.050/231.219, mem: 2660.0MB, max: 2741.8MB

*******
STEP 155
Basis length: 470, queue length: 748, step degree: 14, num pairs: 1
Basis total mons: 1714723, average length: 3648.347
Number of pair polynomials: 1, at 372 column(s), 0.000
Average length for reductees: 368.00 [1], reductors: 5.00 [36]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 36 = 37 rows / 480 columns out of 38760 (1.238%)
Density: 3.0856% / 3.5675% (14.811/r), total: 548 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (100.0%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 155 time: 0.000, [0.002], mat/total: 154.050/231.219, mem: 2660.0MB, max: 2741.8MB

*******
STEP 156
Basis length: 471, queue length: 753, step degree: 15, num pairs: 4
Basis total mons: 1715166, average length: 3641.541
Number of pair polynomials: 4, at 2104 column(s), 0.000
Average length for reductees: 386.75 [4], reductors: 100.56 [231]
Symbolic reduction time: 0.000, column sort time: 0.000
4 + 231 = 235 rows / 3531 columns out of 54264 (6.507%)
Density: 2.9858% / 3.2212% (105.43/r), total: 24776 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.006[r] [3]
Number of unused reductors: 72
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (75.0%), min deg: 15 [3], av deg: 15.0
Degree counts: 15:3
Queue insertion time: 0.000
Step 156 time: 0.010, [0.014], mat/total: 154.060/231.230, mem: 2660.0MB, max: 2741.8MB

*******
STEP 157
Basis length: 474, queue length: 769, step degree: 16, num pairs: 41
Basis total mons: 1716724, average length: 3621.781
7 pairs eliminated
Number of pair polynomials: 34, at 9167 column(s), 0.000
Average length for reductees: 549.03 [34], reductors: 116.96 [1836]
Symbolic reduction time: 0.019[r], column sort time: 0.006[r]
34 + 1836 = 1870 rows / 14743 columns out of 74613 (19.759%)
Density: 0.84658% / 0.9574% (124.81/r), total: 233397 (0.9MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.053[r] + 0.000 + 0.000 = 0.059[r] [17]
Number of unused reductors: 389
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 17 (50.0%), min deg: 12 [1], av deg: 14.6
Degree counts: 12:1 13:1 14:8 16:7
Queue insertion time: 0.000
Step 157 time: 0.090, [0.092], mat/total: 154.120/231.320, mem: 2660.0MB, max: 2741.8MB

*******
STEP 158
Basis length: 491, queue length: 834, step degree: 13, num pairs: 2
Basis total mons: 1727576, average length: 3518.485
Number of pair polynomials: 2, at 1152 column(s), 0.000
Average length for reductees: 401.00 [2], reductors: 333.18 [11]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 11 = 13 rows / 1509 columns out of 27132 (5.562%)
Density: 22.771% / 23.109% (343.62/r), total: 4467 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [2]
Number of unused reductors: 1
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 2 (100.0%), min deg: 13 [2], av deg: 13.0
Degree counts: 13:2
Queue insertion time: 0.000
Step 158 time: 0.004[r], [0.006], mat/total: 154.120/231.329, mem: 2660.0MB, max: 2741.8MB

*******
STEP 159
Basis length: 493, queue length: 854, step degree: 14, num pairs: 7
Basis total mons: 1728522, average length: 3506.130
Number of pair polynomials: 7, at 2079 column(s), 0.000
Average length for reductees: 373.29 [7], reductors: 112.13 [149]
Symbolic reduction time: 0.000, column sort time: 0.000
7 + 149 = 156 rows / 3361 columns out of 38760 (8.671%)
Density: 3.685% / 3.9083% (123.85/r), total: 19321 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.004[r] + 0.000 + 0.000 = 0.005[r] [3]
Number of unused reductors: 29
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (42.9%), min deg: 12 [1], av deg: 13.3
Degree counts: 12:1 14:2
Queue insertion time: 0.000
Step 159 time: 0.010, [0.012], mat/total: 154.130/231.340, mem: 2660.0MB, max: 2741.8MB

*******
STEP 160
Basis length: 496, queue length: 881, step degree: 13, num pairs: 2
Basis total mons: 1730221, average length: 3488.349
Number of pair polynomials: 2, at 446 column(s), 0.000
Average length for reductees: 123.00 [2], reductors: 47.25 [16]
Symbolic reduction time: 0.000, column sort time: 0.000
2 + 16 = 18 rows / 490 columns out of 27132 (1.806%)
Density: 11.361% / 11.767% (55.667/r), total: 1002 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (50.0%), min deg: 13 [1], av deg: 13.0
Degree counts: 13:1
Queue insertion time: 0.000
Step 160 time: 0.000, [0.003], mat/total: 154.130/231.340, mem: 2660.0MB, max: 2741.8MB

*******
STEP 161
Basis length: 497, queue length: 887, step degree: 14, num pairs: 3
Basis total mons: 1730370, average length: 3481.630
Number of pair polynomials: 3, at 735 column(s), 0.000
Average length for reductees: 140.33 [3], reductors: 55.11 [28]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 28 = 31 rows / 860 columns out of 38760 (2.219%)
Density: 7.3668% / 7.6978% (63.355/r), total: 1964 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [1]
Number of unused reductors: 2
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 1 (33.3%), min deg: 14 [1], av deg: 14.0
Degree counts: 14:1
Queue insertion time: 0.000
Step 161 time: 0.000, [0.004], mat/total: 154.130/231.340, mem: 2660.0MB, max: 2741.8MB

*******
STEP 162
Basis length: 498, queue length: 892, step degree: 15, num pairs: 23
Basis total mons: 1730596, average length: 3475.092
2 pairs eliminated
Number of pair polynomials: 21, at 6241 column(s), 0.000
Average length for reductees: 486.38 [21], reductors: 102.77 [1057]
Symbolic reduction time: 0.009, column sort time: 0.005[r]
21 + 1057 = 1078 rows / 9573 columns out of 54264 (17.642%)
Density: 1.1516% / 1.2803% (110.24/r), total: 118843 (0.5MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.029[r] + 0.000 + 0.000 = 0.029 [10]
Number of unused reductors: 185
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 10 (47.6%), min deg: 13 [4], av deg: 14.2
Degree counts: 13:4 15:6
Queue insertion time: 0.000
Step 162 time: 0.049, [0.053], mat/total: 154.160/231.389, mem: 2660.0MB, max: 2741.8MB

*******
STEP 163
Basis length: 508, queue length: 953, step degree: 14, num pairs: 12
Basis total mons: 1738516, average length: 3422.276
Number of pair polynomials: 12, at 2807 column(s), 0.000
Average length for reductees: 275.50 [12], reductors: 108.55 [242]
Symbolic reduction time: 0.003[r], column sort time: 0.000
12 + 242 = 254 rows / 3811 columns out of 38760 (9.832%)
Density: 3.0554% / 3.2708% (116.44/r), total: 29576 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.006[r] + 0.000 + 0.000 = 0.007[r] [4]
Number of unused reductors: 44
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 4 (33.3%), min deg: 12 [2], av deg: 13.0
Degree counts: 12:2 14:2
Queue insertion time: 0.000
Step 163 time: 0.015[r], [0.017], mat/total: 154.170/231.409, mem: 2660.0MB, max: 2741.8MB

*******
STEP 164
Basis length: 512, queue length: 987, step degree: 13, num pairs: 3
Basis total mons: 1739419, average length: 3397.303
Number of pair polynomials: 3, at 886 column(s), 0.000
Average length for reductees: 191.00 [3], reductors: 295.25 [8]
Symbolic reduction time: 0.000, column sort time: 0.000
3 + 8 = 11 rows / 1028 columns out of 27132 (3.789%)
Density: 25.955% / 26.245% (266.82/r), total: 2935 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 164 time: 0.000, [0.004], mat/total: 154.170/231.409, mem: 2660.0MB, max: 2741.8MB

*******
STEP 165
Basis length: 512, queue length: 984, step degree: 14, num pairs: 1
Basis total mons: 1739419, average length: 3397.303
Number of pair polynomials: 1, at 664 column(s), 0.000
Average length for reductees: 189.00 [1], reductors: 250.83 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 705 columns out of 38760 (1.819%)
Density: 34.326% / 35.106% (242/r), total: 1694 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 165 time: 0.000, [0.004], mat/total: 154.170/231.409, mem: 2660.0MB, max: 2741.8MB

*******
STEP 166
Basis length: 512, queue length: 983, step degree: 15, num pairs: 9
Basis total mons: 1739419, average length: 3397.303
Number of pair polynomials: 9, at 1826 column(s), 0.000
Average length for reductees: 256.44 [9], reductors: 64.85 [174]
Symbolic reduction time: 0.000, column sort time: 0.000
9 + 174 = 183 rows / 2294 columns out of 54264 (4.227%)
Density: 3.2377% / 3.4705% (74.273/r), total: 13592 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [3]
Number of unused reductors: 36
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (33.3%), min deg: 13 [1], av deg: 14.3
Degree counts: 13:1 15:2
Queue insertion time: 0.000
Step 166 time: 0.000, [0.009], mat/total: 154.170/231.409, mem: 2660.0MB, max: 2741.8MB

*******
STEP 167
Basis length: 515, queue length: 1006, step degree: 14, num pairs: 3
Basis total mons: 1740578, average length: 3379.763
Number of pair polynomials: 3, at 1356 column(s), 0.000
Average length for reductees: 354.00 [3], reductors: 102.49 [72]
Symbolic reduction time: 0.001[r], column sort time: 0.000
3 + 72 = 75 rows / 1879 columns out of 38760 (4.848%)
Density: 5.9897% / 6.213% (112.55/r), total: 8441 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 16
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 167 time: 0.006[r], [0.008], mat/total: 154.170/231.420, mem: 2660.0MB, max: 2741.8MB

*******
STEP 168
Basis length: 515, queue length: 1003, step degree: 16, num pairs: 41
Basis total mons: 1740578, average length: 3379.763
2 pairs eliminated
Number of pair polynomials: 39, at 10742 column(s), 0.000
Average length for reductees: 666.72 [39], reductors: 105.44 [2325]
Symbolic reduction time: 0.019, column sort time: 0.008[r]
39 + 2325 = 2364 rows / 16463 columns out of 74613 (22.065%)
Density: 0.69674% / 0.79146% (114.7/r), total: 271160 (1.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.069[r] + 0.000 + 0.000 = 0.076[r] [7]
Number of unused reductors: 530
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 7 (17.9%), min deg: 10 [1], av deg: 14.0
Degree counts: 10:1 12:1 14:2 16:3
Queue insertion time: 0.000
Step 168 time: 0.110, [0.114], mat/total: 154.250/231.530, mem: 2660.0MB, max: 2741.8MB

*******
STEP 169
Basis length: 522, queue length: 1012, step degree: 12, num pairs: 1
Basis total mons: 1744969, average length: 3342.852
Number of pair polynomials: 1, at 150 column(s), 0.000
Average length for reductees: 96.00 [1], reductors: 74.50 [6]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 6 = 7 rows / 231 columns out of 18564 (1.244%)
Density: 33.581% / 34.303% (77.571/r), total: 543 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 169 time: 0.000, [0.002], mat/total: 154.250/231.530, mem: 2660.0MB, max: 2741.8MB

*******
STEP 170
Basis length: 522, queue length: 1011, step degree: 13, num pairs: 1
Basis total mons: 1744969, average length: 3342.852
Number of pair polynomials: 1, at 346 column(s), 0.000
Average length for reductees: 60.00 [1], reductors: 124.21 [14]
Symbolic reduction time: 0.000, column sort time: 0.000
1 + 14 = 15 rows / 579 columns out of 27132 (2.134%)
Density: 20.714% / 21.428% (119.93/r), total: 1799 (0.0MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.000 + 0.000 + 0.000 = 0.000 [0]
Number of unused reductors: 4
After ech memory: 2660.0MB, max: 2741.8MB
No new polynomials
Queue insertion time: 0.000
Step 170 time: 0.000, [0.004], mat/total: 154.250/231.530, mem: 2660.0MB, max: 2741.8MB

*******
STEP 171
Basis length: 522, queue length: 1010, step degree: 15, num pairs: 7
Basis total mons: 1744969, average length: 3342.852
Number of pair polynomials: 7, at 2289 column(s), 0.000
Average length for reductees: 347.57 [7], reductors: 61.85 [542]
Symbolic reduction time: 0.006[r], column sort time: 0.000
7 + 542 = 549 rows / 6929 columns out of 54264 (12.769%)
Density: 0.94516% / 1.0801% (65.49/r), total: 35954 (0.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.010 + 0.000 + 0.000 = 0.010 [3]
Number of unused reductors: 60
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (42.9%), min deg: 15 [3], av deg: 15.0
Degree counts: 15:3
Queue insertion time: 0.000
Step 171 time: 0.019, [0.026], mat/total: 154.260/231.550, mem: 2660.0MB, max: 2741.8MB

*******
STEP 172
Basis length: 525, queue length: 1027, step degree: 16, num pairs: 13
Basis total mons: 1752053, average length: 3337.244
Number of pair polynomials: 13, at 10169 column(s), 0.000[r]
Average length for reductees: 1028.15 [13], reductors: 124.78 [2184]
Symbolic reduction time: 0.019, column sort time: 0.009[r]
13 + 2184 = 2197 rows / 18918 columns out of 74613 (25.355%)
Density: 0.68782% / 0.78718% (130.12/r), total: 285876 (1.1MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.069 + 0.000 + 0.000 = 0.082[r] [3]
Number of unused reductors: 553
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 3 (23.1%), min deg: 16 [3], av deg: 16.0
Degree counts: 16:3
Queue insertion time: 0.000
Step 172 time: 0.122[r], [0.124], mat/total: 154.350/231.679, mem: 2660.0MB, max: 2741.8MB

*******
STEP 173
Basis length: 528, queue length: 1044, step degree: 17, num pairs: 177
Basis total mons: 1762198, average length: 3337.496
79 pairs eliminated
Number of pair polynomials: 98, at 27167 column(s), 0.010
Average length for reductees: 829.47 [98], reductors: 170.41 [7606]
Symbolic reduction time: 0.089[r], column sort time: 0.019[r]
98 + 7606 = 7704 rows / 37806 columns out of 100947 (37.451%)
Density: 0.47292% / 0.55949% (178.79/r), total: 1377408 (5.3MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.365[r] + 0.000 + 0.000 = 0.378[r] [6]
Number of unused reductors: 1695
After ech memory: 2660.0MB, max: 2741.8MB
Num new polynomials: 6 (6.1%), min deg: 17 [6], av deg: 17.0
Degree counts: 17:6
Queue insertion time: 0.000
Step 173 time: 0.500, [0.506], mat/total: 154.730/232.179, mem: 2660.0MB, max: 2741.8MB

*******
STEP 174
Basis length: 534, queue length: 907, step degree: 18, num pairs: 160
Basis total mons: 1768383, average length: 3311.579
60 pairs eliminated
Number of pair polynomials: 100, at 29345 column(s), 0.010
Average length for reductees: 577.20 [100], reductors: 190.23 [13408]
Symbolic reduction time: 0.174[r], column sort time: 0.027[r]
100 + 13408 = 13508 rows / 52495 columns out of 134596 (39.002%)
Density: 0.36784% / 0.45215% (193.1/r), total: 2608329 (9.9MB)
Before ech memory: 2660.0MB, max: 2741.8MB
Row sort time: 0.000
0.654[r] + 0.000 + 0.000 = 0.673[r] [6]
Number of unused reductors: 3915
After ech memory: 2660.0MB, max: 2753.0MB
Num new polynomials: 6 (6.0%), min deg: 16 [3], av deg: 16.8
Degree counts: 16:3 17:1 18:2
Queue insertion time: 0.000
Step 174 time: 0.898[r], [0.898], mat/total: 155.410/233.079, mem: 2660.0MB, max: 2753.0MB

*******
STEP 175
Basis length: 540, queue length: 783, step degree: 17, num pairs: 12
Basis total mons: 1776200, average length: 3289.259
Number of pair polynomials: 12, at 7667 column(s), 0.000
Average length for reductees: 1383.42 [12], reductors: 91.00 [2212]
Symbolic reduction time: 0.019[r], column sort time: 0.005[r]
12 + 2212 = 2224 rows / 13217 columns out of 100947 (13.093%)
Density: 0.74126% / 0.85144% (97.973/r), total: 217891 (0.8MB)
Before ech memory: 2660.0MB, max: 2753.0MB
Row sort time: 0.000
0.056[r] + 0.000 + 0.000 = 0.059 [3]
Number of unused reductors: 382
After ech memory: 2660.0MB, max: 2753.0MB
Num new polynomials: 3 (25.0%), min deg: 17 [3], av deg: 17.0
Degree counts: 17:3
Queue insertion time: 0.000
Step 175 time: 0.090, [0.093], mat/total: 155.470/233.170, mem: 2660.0MB, max: 2753.0MB

*******
STEP 176
Basis length: 543, queue length: 790, step degree: 18, num pairs: 16
Basis total mons: 1782558, average length: 3282.796
Number of pair polynomials: 16, at 13062 column(s), 0.000
Average length for reductees: 1864.12 [16], reductors: 121.56 [4221]
Symbolic reduction time: 0.039, column sort time: 0.009
16 + 4221 = 4237 rows / 21814 columns out of 134596 (16.207%)
Density: 0.58743% / 0.69084% (128.14/r), total: 542940 (2.1MB)
Before ech memory: 2660.0MB, max: 2753.0MB
Row sort time: 0.000
0.139 + 0.000[r] + 0.000 = 0.151[r] [4]
Number of unused reductors: 933
After ech memory: 2660.0MB, max: 2753.0MB
Num new polynomials: 4 (25.0%), min deg: 18 [4], av deg: 18.0
Degree counts: 18:4
Queue insertion time: 0.000
Step 176 time: 0.210, [0.211], mat/total: 155.630/233.380, mem: 2660.0MB, max: 2753.0MB

*******
STEP 177
Basis length: 547, queue length: 800, step degree: 19, num pairs: 167
Basis total mons: 1794150, average length: 3279.982
69 pairs eliminated
Number of pair polynomials: 98, at 42530 column(s), 0.019[r]
Average length for reductees: 1016.05 [98], reductors: 213.08 [22682]
Symbolic reduction time: 0.349, column sort time: 0.039[r]
98 + 22682 = 22780 rows / 74459 columns out of 177100 (42.043%)
Density: 0.29081% / 0.37429% (216.53/r), total: 4932606 (18.8MB)
Before ech memory: 2660.0MB, max: 2753.0MB
Row sort time: 0.007[r]
1.297[r] + 0.000 + 0.000 = 1.319 [4]
Number of unused reductors: 5704
After ech memory: 2660.0MB, max: 2791.8MB
Num new polynomials: 4 (4.1%), min deg: 19 [4], av deg: 19.0
Degree counts: 19:4
Queue insertion time: 0.000
Step 177 time: 1.739, [1.751], mat/total: 156.960/235.119, mem: 2660.0MB, max: 2791.8MB

*******
STEP 178
Basis length: 551, queue length: 665, step degree: 20, num pairs: 163
Basis total mons: 1803917, average length: 3273.897
76 pairs eliminated
Number of pair polynomials: 87, at 54719 column(s), 0.019
At 100000: 36379 rows, 102762 columns, 0.705[r]
Average length for reductees: 1210.10 [87], reductors: 270.15 [38490]
Symbolic reduction time: 0.750, column sort time: 0.055[r]
87 + 38490 = 38577 rows / 104241 columns out of 230230 (45.277%)
Density: 0.26119% / 0.34862% (272.27/r), total: 10503319 (40.1MB)
Before ech memory: 2660.0MB, max: 2791.8MB
Row sort time: 0.010
2.650 + 0.000[r] + 0.000 = 2.694[r] [4]
Number of unused reductors: 11355
After ech memory: 2660.0MB, max: 2844.5MB
Num new polynomials: 4 (4.6%), min deg: 20 [4], av deg: 20.0
Degree counts: 20:4
Queue insertion time: 0.000
Step 178 time: 3.544[r], [3.545], mat/total: 159.680/238.670, mem: 2660.0MB, max: 2844.5MB

*******
STEP 179
Basis length: 555, queue length: 528, step degree: 21, num pairs: 156
Basis total mons: 1828028, average length: 3293.744
71 pairs eliminated
Number of pair polynomials: 85, at 70734 column(s), 0.028[r]
At 100000: 38531 rows, 126751 columns, 0.920
Average length for reductees: 1961.24 [85], reductors: 343.09 [64705]
Symbolic reduction time: 1.690, column sort time: 0.078[r]
85 + 64705 = 64790 rows / 146639 columns out of 296010 (49.539%)
Density: 0.23541% / 0.3268% (345.21/r), total: 22366039 (85.3MB)
Before ech memory: 2660.0MB, max: 2844.5MB
Row sort time: 0.019
5.174[r] + 0.000 + 0.000 = 5.223[r] [2]
Number of unused reductors: 21323
After ech memory: 2660.0MB, max: 2919.6MB
Num new polynomials: 2 (2.4%), min deg: 21 [2], av deg: 21.0
Degree counts: 21:2
Queue insertion time: 0.000
Step 179 time: 7.049, [7.057], mat/total: 164.930/245.719, mem: 2660.0MB, max: 2919.6MB

*******
STEP 180
Basis length: 557, queue length: 385, step degree: 22, num pairs: 140
Basis total mons: 1847369, average length: 3316.641
80 pairs eliminated
Number of pair polynomials: 60, at 74018 column(s), 0.026[r]
At 100000: 40409 rows, 149175 columns, 1.059
Average length for reductees: 2693.03 [60], reductors: 387.97 [91334]
Symbolic reduction time: 2.849, column sort time: 0.099
60 + 91334 = 91394 rows / 185966 columns out of 376740 (49.362%)
Density: 0.20944% / 0.30323% (389.49/r), total: 35596791 (135.8MB)
Before ech memory: 2660.0MB, max: 2919.6MB
Row sort time: 0.029[r]
7.280 + 0.000[r] + 0.000 = 7.340 [0]
Number of unused reductors: 36391
After ech memory: 2668.3MB, max: 2997.6MB
No new polynomials
Queue insertion time: 0.000
Step 180 time: 10.360, [10.373], mat/total: 172.300/256.079, mem: 2660.0MB, max: 2997.6MB

*******
STEP 181
Basis length: 557, queue length: 245, step degree: 23, num pairs: 88
Basis total mons: 1847369, average length: 3316.641
62 pairs eliminated
Number of pair polynomials: 26, at 58037 column(s), 0.015[r]
At 100000: 38377 rows, 140131 columns, 1.010
Average length for reductees: 2544.15 [26], reductors: 388.80 [94588]
Symbolic reduction time: 3.098[r], column sort time: 0.103[r]
26 + 94588 = 94614 rows / 188432 columns out of 475020 (39.668%)
Density: 0.20665% / 0.29958% (389.4/r), total: 36842341 (140.5MB)
Before ech memory: 2660.0MB, max: 2997.6MB
Row sort time: 0.030
6.089 + 0.000 + 0.000 = 6.149 [0]
Number of unused reductors: 45333
After ech memory: 2668.7MB, max: 3002.2MB
No new polynomials
Queue insertion time: 0.007[r]
Step 181 time: 9.420, [9.423], mat/total: 178.480/265.500, mem: 2660.0MB, max: 3002.2MB

*******
STEP 182
Basis length: 557, queue length: 157, step degree: 24, num pairs: 60
Basis total mons: 1847369, average length: 3316.641
45 pairs eliminated
Number of pair polynomials: 15, at 60576 column(s), 0.013[r]
At 100000: 38693 rows, 164163 columns, 1.130
At 200000: 99944 rows, 213855 columns, 3.509[r]
Average length for reductees: 3443.13 [15], reductors: 426.31 [125430]
Symbolic reduction time: 4.468[r], column sort time: 0.128[r]
15 + 125430 = 125445 rows / 230155 columns out of 593775 (38.761%)
Density: 0.18538% / 0.28033% (426.67/r), total: 53523909 (204.2MB)
Before ech memory: 2660.0MB, max: 3002.2MB
Row sort time: 0.039
9.498[r] + 0.000 + 0.000 = 9.569 [0]
Number of unused reductors: 57779
After ech memory: 2671.5MB, max: 3078.9MB
No new polynomials
Queue insertion time: 0.009[r]
Step 182 time: 14.247[r], [14.248], mat/total: 188.090/279.750, mem: 2660.0MB, max: 3078.9MB

*******
STEP 183
Basis length: 557, queue length: 97, step degree: 25, num pairs: 46
Basis total mons: 1847369, average length: 3316.641
38 pairs eliminated
Number of pair polynomials: 8, at 74521 column(s), 0.010
At 100000: 42690 rows, 189280 columns, 1.332[r]
At 200000: 100147 rows, 224465 columns, 3.578[r]
Average length for reductees: 4548.50 [8], reductors: 437.31 [143921]
Symbolic reduction time: 5.509[r], column sort time: 0.139
8 + 143921 = 143929 rows / 253452 columns out of 736281 (34.423%)
Density: 0.17263% / 0.26812% (437.54/r), total: 62974689 (240.2MB)
Before ech memory: 2660.0MB, max: 3078.9MB
Row sort time: 0.047[r]
12.689 + 0.002[r] + 0.000 = 12.780 [0]
Number of unused reductors: 59570
After ech memory: 2673.2MB, max: 3121.8MB
No new polynomials
Queue insertion time: 0.010
Step 183 time: 18.510, [18.515], mat/total: 200.920/298.260, mem: 2660.0MB, max: 3121.8MB

*******
STEP 184
Basis length: 557, queue length: 51, step degree: 26, num pairs: 24
Basis total mons: 1847369, average length: 3316.641
21 pairs eliminated
Number of pair polynomials: 3, at 22386 column(s), 0.000
At 100000: 46606 rows, 200692 columns, 1.500
At 200000: 103118 rows, 235588 columns, 3.639
Average length for reductees: 4526.67 [3], reductors: 436.84 [159177]
Symbolic reduction time: 6.169, column sort time: 0.150
3 + 159177 = 159180 rows / 270328 columns out of 906192 (29.831%)
Density: 0.16162% / 0.25639% (436.92/r), total: 69548419 (265.3MB)
Before ech memory: 2660.0MB, max: 3121.8MB
Row sort time: 0.049
15.960 + 0.000 + 0.000 = 16.059[r] [0]
Number of unused reductors: 60324
After ech memory: 2674.6MB, max: 3153.1MB
No new polynomials
Queue insertion time: 0.000
Step 184 time: 22.449, [22.457], mat/total: 217.040/320.710, mem: 2660.0MB, max: 3153.1MB

*******
STEP 185
Basis length: 557, queue length: 27, step degree: 27, num pairs: 14
Basis total mons: 1847369, average length: 3316.641
12 pairs eliminated
Number of pair polynomials: 2, at 9828 column(s), 0.000
At 100000: 46596 rows, 208776 columns, 1.539[r]
At 200000: 104236 rows, 248870 columns, 3.812[r]
Average length for reductees: 334.00 [2], reductors: 464.80 [181227]
Symbolic reduction time: 7.429, column sort time: 0.166[r]
2 + 181227 = 181229 rows / 296393 columns out of 1107568 (26.761%)
Density: 0.15682% / 0.25177% (464.8/r), total: 84235545 (321.3MB)
Before ech memory: 2660.0MB, max: 3153.1MB
Row sort time: 0.059
18.605[r] + 0.000 + 0.000 = 18.707[r] [0]
Number of unused reductors: 72387
After ech memory: 2676.6MB, max: 3201.2MB
No new polynomials
Queue insertion time: 0.013[r]
Step 185 time: 26.392[r], [26.393], mat/total: 235.810/347.110, mem: 2662.8MB, max: 3201.2MB

*******
STEP 186
Basis length: 557, queue length: 13, step degree: 28, num pairs: 9
Basis total mons: 1847369, average length: 3316.641
9 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 187
Basis length: 557, queue length: 4, step degree: 29, num pairs: 2
Basis total mons: 1847369, average length: 3316.641
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

*******
STEP 188
Basis length: 557, queue length: 2, step degree: 30, num pairs: 2
Basis total mons: 1847369, average length: 3316.641
2 pairs eliminated
No pairs to reduce
Pair elimination time: 0.000

Do extern interreduction (length 145)
INTERREDUCE 133 polynomial(s)
Symbolic reduction time: 0.110
Column sort time: 0.028[r]
133 + 10977 = 11110 rows / 44867 columns
Density: 0.23972% / 0.31363% (107.56/r), total: 1194939 (4.6MB)
Row sort time: 0.000
0.029[r] + 0.000 = 0.030[r] [133]
Number of unused reductors: 2802
Total reduction time: 0.179
Reduction time: 0.215[r]
Final extern interreduction time: 0.230

Final basis length: 133
Number of pairs: 2436
Max step: 124, time: 37.030
Max num entries matrix: 631411 by 800534
Max num rows matrix: 631411 by 800534
Approx mat cost: 3.97504e+10, sym red cost: 1.26777e+09
Total pair setup time: 0.800
Total symbolic reduction time: 106.320
Total column sort time: 3.690
Total row sort time: 1.030
Total matrix time: 235.810
Total new polys time: 0.250
Total queue update time: 0.080
Total Faugere F4 time: 347.360, real time: 347.747
Time: 347.360
dregs = [ 9, 10, 11, 10, 11, 12, 21, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 23, 27, 31, 17, 18, 19, 18, 19, 20, 21, 18, 19, 20, 21, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 45, 20, 15, 15, 16, 17, 16, 17, 18, 17, 18, 19, 16, 15, 16, 17, 16, 17, 18, 17, 18, 17, 17, 17, 16, 18, 18, 19, 16, 17, 18, 17, 18, 17, 19, 18, 19, 19, 20, 15, 16, 17, 14, 15, 16, 17, 18, 17, 18, 18, 19, 17, 18, 18, 19, 20, 19, 18, 20, 21, 20, 21, 22, 21, 22, 23, 22, 23, 24, 25, 26, 27, 28, 29, 30, 93, 13, 12, 11, 12, 13, 12, 13, 14, 15, 14, 15, 14, 14, 14, 15, 14, 13, 14, 13, 14, 15, 16, 13, 14, 13, 15, 14, 15, 14, 15, 16, 13, 14, 13, 14, 15, 14, 13, 14, 15, 14, 16, 12, 13, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ]
----------------------------------------------------------------------------------------------------
Starting FGLM computation... (r=5)
slurmstepd-haswell378g0: error: *** STEP 373.0 ON haswell378g0 CANCELLED AT 2024-05-25T21:02:48 ***