gap> ReadTest("test01.test");
-----------------------------------------------------------------------------
Loading  GBNP 0.9 (Non-commutative Gröbner bases)
by A.M. Cohen (http://www.win.tue.nl/~amc) and
   D.A.H. Gijsbers (D.A.H.Gijsbers@tue.nl).
-----------------------------------------------------------------------------
true
[ [ [ [ 1, 2 ], [ 2, 1 ] ], [ 1, -1 ] ] ]
[ [ [ 1, 1, 2 ], [  ] ], [ 1, -1 ] ]
[ [ [ 1, 2, 2 ], [  ] ], [ 1, -1 ] ]
 a^2b - 1
 ab - ba
 ab^2 - 1
#I  number of entered polynomials is 3
#I  number of polynomials after reduction is 3
#I  End of fase I
#I  End of fase II
.
#I  length of G =2
#I  length of todo is 0
#I  List of todo lengths is [ 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 30
[ [ [ [ 2 ], [ 1 ] ], [ 1, -1 ] ], [ [ [ 1, 1, 1 ], [  ] ], [ 1, -1 ] ] ]
 b - a
 a^3 - 1
3
[ [ [ [  ] ], [ 1 ] ], [ [ [ 1 ] ], [ 1 ] ], [ [ [ 1, 1 ] ], [ 1 ] ] ]
 1
 a
 a^2
test01
GAP4stones: 200
true
gap> ReadTest("test02.test");
true
function( n, q ) ... end
651/25
function( l ) ... end
#I  number of entered polynomials is 258
#I  number of polynomials after reduction is 114
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 1, 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 5370
 ba^3 - 651/25aba^2 + 651/25a^2ba - a^3b
 b^3a - 651/25b^2ab + 651/25bab^2 - ab^3
 b^2a^2ba - bab^2a^2 - baba^2b + ba^2bab + ab^2aba - abab^2a - aba^2b^2 + a^2b\
^2ab
 b^2ab^2a^2 - 651/25b^2ababa + b^2aba^2b + 626/25bab^2aba - bab^2a^2b + babab^\
2a - ba^2b^2ab + ba^2bab^2 - 651/25ab^2ab^2a + ab^2abab + 423176/625abab^2ab -\
 423801/625ababab^2 + 626/25aba^2b^3 - 406901/625a^2b^2ab^2 + 423176/625a^2bab\
^3 - 651/25a^3b^4
 a^8
 a^7b
 a^6ba
 a^6b^2
 a^5ba^2
 a^5bab
 a^5b^2a
 a^5b^3
 a^4ba^2b
 a^4baba
 a^4bab^2
 a^4b^2a^2
 a^4b^2ab
 a^4b^4
 a^3ba^2ba
 a^3ba^2b^2
 a^3baba^2
 a^3babab
 a^3bab^2a
 a^3bab^3
 a^3b^2a^2b
 a^3b^2aba
 a^3b^2ab^2
 a^3b^5
 a^2ba^2ba^2
 a^2ba^2bab
 a^2ba^2b^2a
 a^2ba^2b^3
 a^2baba^2b
 a^2bababa
 a^2babab^2
 a^2bab^2a^2
 a^2bab^2ab
 a^2bab^4
 a^2b^2a^2b^2
 a^2b^2aba^2
 a^2b^2abab
 a^2b^2ab^2a
 a^2b^2ab^3
 a^2b^6
 aba^2ba^2b
 aba^2baba
 aba^2bab^2
 aba^2b^2a^2
 aba^2b^2ab
 aba^2b^4
 ababa^2ba
 ababa^2b^2
 abababa^2
 abababab
 ababab^2a
 ababab^3
 abab^2a^2b
 abab^2aba
 abab^2ab^2
 abab^5
 ab^2a^2b^2a
 ab^2a^2b^3
 ab^2aba^2b
 ab^2ababa
 ab^2abab^2
 ab^2ab^2ab
 ab^2ab^4
 ab^7
 ba^2ba^2ba
 ba^2ba^2b^2
 ba^2baba^2
 ba^2babab
 ba^2bab^2a
 ba^2bab^3
 ba^2b^2a^2b
 ba^2b^2aba
 ba^2b^2ab^2
 ba^2b^5
 baba^2ba^2
 baba^2bab
 baba^2b^2a
 baba^2b^3
 bababa^2b
 babababa
 bababab^2
 babab^2a^2
 babab^2ab
 babab^4
 bab^2a^2b^2
 bab^2aba^2
 bab^2abab
 bab^2ab^2a
 bab^2ab^3
 bab^6
 b^2a^2b^2a^2
 b^2a^2b^2ab
 b^2a^2b^4
 b^2aba^2ba
 b^2aba^2b^2
 b^2ababa^2
 b^2ababab
 b^2abab^2a
 b^2abab^3
 b^2ab^2aba
 b^2ab^2ab^2
 b^2ab^5
 b^8
#I  The computation took 0 msecs.
157
test02
GAP4stones: 1
true
gap> ReadTest("test03.test");
true
 aca - cac
 dcd - cdc
 dbd - bdb
 ded - ede
 fef - efe
 ab - ba
 ad - da
 ae - ea
 af - fa
 bc - cb
 be - eb
 bf - fb
 ce - ec
 cf - fc
 df - fd
 a^2 - 1
 b^2 - 1
 c^2 - 1
 d^2 - 1
 e^2 - 1
 f^2 - 1
#I  number of entered polynomials is 21
#I  number of polynomials after reduction is 21
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 7, 6, 6, 6, 6, 7, 6, 6, 9, 8, 8, 8, 7, 11, 13,
  13, 12, 9, 14, 20, 21, 28, 30, 23, 21, 16, 13, 13, 5, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 2440
 a^2 - 1
 ba - ab
 b^2 - 1
 cb - bc
 c^2 - 1
 da - ad
 d^2 - 1
 ea - ae
 eb - be
 ec - ce
 e^2 - 1
 fa - af
 fb - bf
 fc - cf
 fd - df
 f^2 - 1
 cab - bca
 cac - aca
 dbd - bdb
 dcd - cdc
 ede - ded
 fef - efe
 dcad - cdca
 edbe - dedb
 edce - dedc
 fedf - efed
 dbcdb - cdbcd
 dbcdc - bdbcd
 edbce - dedbc
 edcae - dedca
 fedbf - efedb
 fedcf - efedc
 dbcadb - cdbcad
 edbcae - dedbca
 fedbcf - efedbc
 fedcaf - efedca
 dbcadca - bdbcadc
 edbcded - dedbcde
 fedbcaf - efedbca
 fedbcdf - efedbcd
 edbcaded - dedbcade
 fedbcadf - efedbcad
 fedbcadcf - efedbcadc
 fedbcdefe - efedbcdef
 edbcadcedc - dedbcadced
 fedbcadefe - efedbcadef
 edbcadcedbc - dedbcadcedb
 fedbcadcefe - efedbcadcef
 fedbcadcedfed - efedbcadcedfe
 fedbcadcedbfedb - efedbcadcedbfed
#I  The computation took 2580 msecs.
51840
51840
test03
GAP4stones: 1
true
gap> ReadTest("test04.test");
true
[ [ [ 1 ], [  ] ], [ 1, 1 ] ]
[ [ [ 1 ], [  ] ], [ 1, 2 ] ]
[ [ [ [ 1 ], [  ] ], [ 1, 1 ] ], [ [ [ 1 ], [  ] ], [ 1, 2 ] ] ]
 a + 1
 a + 2
#I  number of entered polynomials is 2
#I  number of polynomials after reduction is 1
#I  End of fase I
#I  End of fase II
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 0
[ [ [ [  ] ], [ 1 ] ] ]
 1
test04
GAP4stones: infinity
true
gap> ReadTest("test05.test");
true
 a^3 + a + 1
 a^4 - a^2 + a
 - 10a^5 + 3a^4 + 14a^3 - 13a^2 + 7a + 4
 100a^6 - 60a^5 - 127a^4 + 172a^3 - 113a^2 - 15a + 12
 - 1000a^7 + 900a^6 + 1050a^5 - 2089a^4 + 1702a^3 - 241a^2 - 137a + 52
 10000a^8 - 12000a^7 - 7400a^6 + 23800a^5 - 23795a^4 + 8204a^3 + 195a^2 - 991a\
 + 204
 - 100000a^9 + 150000a^8 + 34000a^7 - 256600a^6 + 313550a^5 - 161781a^4 + 2947\
0a^3 + 9531a^2 - 5561a + 820
 1000000a^10 - 1800000a^9 + 150000a^8 + 2620000a^7 - 3934900a^6 + 2653660a^5 -\
 875223a^4 + 25916a^3 + 84983a^2 - 28847a + 3276
 - 10000000a^11 + 21000000a^10 - 7300000a^9 - 25150000a^8 + 47345000a^7 - 3936\
7700a^6 + 17967410a^5 - 3531953a^4 - 654202a^3 + 581543a^2 - 141545a + 13108
 100000000a^12 - 240000000a^11 + 140000000a^10 + 222400000a^9 - 548300000a^8 +\
 546192000a^7 - 313516800a^6 + 99836400a^5 - 7554731a^4 - 7674372a^3 + 3500011\
a^2 - 671103a + 52428
 - 1000000000a^13 + 2700000000a^12 - 2160000000a^11 - 1720000000a^10 + 6121000\
000a^9 - 7207420000a^8 + 4963124000a^7 - 2096385200a^6 + 446926150a^5 + 399517\
15a^4 - 60640034a^3 + 19537235a^2 - 3103769a + 209716
 10000000000a^14 - 30000000000a^13 + 30100000000a^12 + 9760000000a^11 - 658100\
00000a^10 + 91326800000a^9 - 73446700000a^8 + 38037992000a^7 - 12012484300a^6 \
+ 1340606900a^5 + 696036561a^4 - 407989940a^3 + 103649439a^2 - 14092879a + 838\
860
 - 100000000000a^15 + 330000000000a^14 - 395000000000a^13 + 3500000000a^12 + 6\
78740000000a^11 - 1117578000000a^10 + 1032931400000a^9 - 629549700000a^8 + 254\
091315000a^7 - 57829062700a^6 - 1150840310a^5 + 6327815943a^4 - 2503024346a^3 \
+ 530026047a^2 - 63082313a + 3355444
13
#I  number of entered polynomials is 13
#I  number of polynomials after reduction is 1
#I  End of fase I
#I  End of fase II
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
[ [ [ [  ] ], [ 1 ] ] ]
 1
test05
GAP4stones: 1000
true
gap> ReadTest("test06.test");
true
 ea
 a^3 + fa
 a^9 + ca^3
 a^81 + ca^9 + da^3
 ca^81 + da^9 + ea^3
 a^27 + da^81 + ea^9 + fa^3
 b + ca^27 + ea^81 + fa^9
 cb + da^27 + fa^81
 a + db + ea^27
 ca + eb + fa^27
 da + fb
 b^3 - b
 ab - ba
 ac - ca
 ad - da
 ae - ea
 af - fa
 bc - cb
 bd - db
 be - eb
 bf - fb
 cd - dc
 ce - ec
 cf - fc
 de - ed
 df - fd
 ef - fe
27
true
#I  number of entered polynomials is 27
#I  number of polynomials after reduction is 8
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 5110
 a
 b
 dc - cd
 ec - ce
 ed - de
 fc - cf
 fd - df
 fe - ef
test06
GAP4stones: 1
true
gap> ReadTest("test07.test");
true
7
 d - 11/7a^2 - 11a + 11/7
 e - 11/7b^2 - 11b + 11/7
 f - 11/7c^2 - 11c + 11/7
 aba - bab
 bcb - cbc
 ac - ca
 ad - 1/11d
 be - 1/11e
 cf - 1/11f
 dbd - 11d
 eae - 11e
 ece - 11e
 fbf - 11f
 ded - d
 ede - e
 efe - e
 fef - f
17
#I  number of entered polynomials is 17
#I  number of polynomials after reduction is 17
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 18, 17, 21, 20, 19, 18, 19, 18, 21, 20, 19, 19,
  22, 20, 20, 23, 25, 26, 25, 24, 33, 33, 36, 39, 41, 40, 42, 43, 43, 43, 43,
  42, 42, 41, 40, 39, 39, 37, 34, 31, 30, 30, 29, 28, 28, 27, 26, 25, 24, 23,
  22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2,
  1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 1600
 a^2 - 7/11d + 7a - 1
 ad - 1/11d
 b^2 - 7/11e + 7b - 1
 be - 1/11e
 ca - ac
 c^2 - 7/11f + 7c - 1
 cf - 1/11f
 da - 1/11d
 dc - cd
 d^2 + 43/77d
 eb - 1/11e
 e^2 + 43/77e
 fa - af
 fc - 1/11f
 fd - df
 f^2 + 43/77f
 abd - ed
 acd - 1/11cd
 aed + 7ed - bd - 7d
 bab - aba
 bae - de
 bce - fe
 bdb - aea - 7ea + 7db + 7bd - 7ae - 49e + 49d
 bde + 7de - ae - 7e
 bfe + 7fe - ce - 7e
 cbc - bcb
 cbf - ef
 cdf - 1/11df
 cec - bfb - 7fb + 7ec + 7ce - 7bf - 49f + 49e
 cef + 7ef - bf - 7f
 dba - bae
 dbd - 11d
 dea + 7de - db - 7d
 ded - d
 eab - abd
 eae - 11e
 ecb - cbf
 ece - 11e
 edb + 7ed - ea - 7e
 ede - e
 efb + 7ef - ec - 7e
 efe - e
 fbc - bce
 fbf - 11f
 fec + 7fe - fb - 7f
 fef - f
 abcd - ecd
 acbd - ced
 aced + 7ced - cbd - 7cd
 aecd + 7ecd - bcd - 7cd
 afbd - fed
 afed + 7fed - fbd - 7df
 cbac - bcba
 cbaf - eaf
 cbdf - edf
 cdbf - def
 cdef + 7def - dbf - 7df
 ceac - bfba - 7fba + 7eac + 7cea - 7baf + 49ea - 49af
 ceaf + 7eaf - baf - 7af
 cedf + 7edf - bdf - 7df
 dbcb - cdbc
 dbcd - 11cd
 dbfb - cdec + 7dfb - 7dec + 7dbf - 7cde + 49df - 49de
 decd - cd
 dfba - dfe
 dfbd - 11df
 dfea + 7dfe - dfb - 7df
 dfed - df
 ecde - eafe
 edfe + 7eafe - eace - 77e
 fbac - fea
 fbaf - 11af
 fbdf - 11df
 feac + 7fea - fba - 7af
 feaf - af
 fedf - df
 abace - bafe
 abafe + 7bafe - bace - 7de
 abcbd - bfbd - 7fbd + 7ecd + 7ced - 7bdf + 49ed - 49df
 abfbd + 7bfbd - bcbd + 7fed + 49fbd + 7edf - 7cbd + 49bdf - 7bcd + 343df - 49\
cd - 49bd - 350d
 aeace + 7eace - bdfe - 7bcde - 7dfe - 49cde + 77ae + 539e
 aeafe + 7eafe - bcde - 7cde
 bcdbc - aeacb - 7eacb + 7cdbc + 7bcdb + 49cdb - 7aef - 49ef
 bcdec - aeafb - 7eafb + 7cdec + 7bcde - 7aeaf - 49eaf + 49cde
 eacba - cbafb
 eacea - cbdfb - 7ecdb + 7eace - 7cbdf - 49ecd + 77ea + 539e
 eafba + 7eafb - eacb - 7ed
 eafea - ecdb + 7eafe - 7ecd
 ecdbc + 7ecdb - eacb - 7ef
105
test07
GAP4stones: 6
true
gap> ReadTest("test08.test");
true
 c - 3/2a^2 - 3a + 3/2
 d - 3/2b^2 - 3b + 3/2
 aba - bab
 ac - 1/3c
 bd - 1/3d
 cbc - 3c
 dad - 3d
 cdc - c
 dcd - d
#I  number of entered polynomials is 9
#I  number of polynomials after reduction is 9
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 8, 7, 6, 5, 4, 6, 4, 4, 4, 3, 3, 2, 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 160
 a^2 - 2/3c + 2a - 1
 ac - 1/3c
 b^2 - 2/3d + 2b - 1
 bd - 1/3d
 ca - 1/3c
 c^2 + 1/3c
 db - 1/3d
 d^2 + 1/3d
 abc - dc
 adc + 2dc - bc - 2c
 bab - aba
 bad - cd
 bcb - ada - 2da + 2cb + 2bc - 2ad - 4d + 4c
 bcd + 2cd - ad - 2d
 cba - bad
 cbc - 3c
 cda + 2cd - cb - 2c
 cdc - c
 dab - abc
 dad - 3d
 dcb + 2dc - da - 2d
 dcd - d
- 2/3G(1)
 G(4)
 3/7bG(1)adc - 3/7baG(1)dc - 9/7bG(1)bac + 3/7bcbG(1)bac + 6/7cbG(1)bac + 6/
7G(1)adc - 6/7aG(1)dc - 6/7bG(1)badc - 12/7G(1)badc - 18/7G(1)bac - 3/
7bcb^2aG(2)c - 6/7b^2aG(2)dc + 9/7b^2aG(2)c + 18/7baG(2)c - 6/7cb^2aG(2)c - 2/
7bcG(2)adc + 2/3G(2)adc + 6/7b^2aG(2)dc - 12/7baG(2)dc - 4/7cG(2)adc + 12/
7baG(2)dc + 9/14bcbaG(3)c - 9/7baG(3)dc - 27/7aG(3)c - 27/7bG(3)c - 27/14baG(
3)c + 9/7bcbG(3)c + 9/7cbaG(3)c + 9/14bcbG(3)bc + 9/7cbG(3)bc - 9/7bG(3)bdc -
18/7aG(3)dc - 18/7bG(3)dc - 36/7G(3)dc - 27/7G(3)bc + 18/7cbG(3)c - 54/7G(
3)c - 27/14bG(3)bc - 18/7G(3)bdc + 3/7bG(4)dc + 6/7G(4)dc - 9/7b^2abG(5)c -
18/7babG(5)c - 3b^2aG(5)c - 6baG(5)c - 3/7bG(6)bac - 6/7G(6)bac - 2/3G(7)c +
4/7cG(7)c + 2/7bcG(7)c + bG(8) + 2G(8)
test08
GAP4stones: 62
true
gap> ReadTest("test09.test");
true
[ [ [ 1, 2, 1 ], [ 2 ] ], [ 1, -1 ] ]
[ [ [ 2, 1, 2 ], [ 2 ] ], [ 1, -1 ] ]
[ [ [ [ 1, 2, 1 ], [ 2 ] ], [ 1, -1 ] ],
  [ [ [ 2, 1, 2 ], [ 2 ] ], [ 1, -1 ] ] ]
 aba - b
 bab - b
#I  number of entered polynomials is 2
#I  number of polynomials after reduction is 2
#I  End of fase I
#I  End of fase II
#I  j =2
#I  Current number of elements in todo is 1
#I  j =3
#I  Current number of elements in todo is 0
#I  List of todo lengths is [ 2, 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 0
[ rec( pol := [ [ [ 2, 1 ], [ 1, 2 ] ], [ 1, -1 ] ],
      trace := [ [ [  ], 1, [ 2 ], -1 ], [ [ 2 ], 1, [  ], 1 ],
          [ [ 1 ], 2, [  ], 1 ], [ [  ], 2, [ 1 ], -1 ] ] ),
  rec( pol := [ [ [ 2, 2 ], [ 2, 1 ] ], [ 1, -1 ] ],
      trace := [ [ [ 2 ], 1, [  ], -1 ], [ [  ], 2, [ 1 ], 1 ] ] ),
  rec( pol := [ [ [ 1, 1, 2 ], [ 2 ] ], [ 1, -1 ] ],
      trace := [ [ [  ], 1, [  ], 1 ], [ [ 1 ], 1, [ 2 ], 1 ],
          [ [ 1, 2 ], 1, [  ], -1 ], [ [ 1, 1 ], 2, [  ], -1 ],
          [ [ 1 ], 2, [ 1 ], 1 ] ] ) ]
 ba - ab
 b^2 - ba
 a^2b - b
- G(1)b + bG(1) + aG(2) - G(2)a

- bG(1) + G(2)a

 G(1) + aG(1)b - abG(1) - a^2G(2) + aG(2)a
test09
GAP4stones: 1000
true
gap> ReadTest("test11.test");
true
[ [ [ [ 1, 1, 1, 2, 2 ], [ 1, 1, 1, 1, 1, 1 ], [ 2, 2, 2, 2 ] ], [ 1, -1, 1 ]
     ],
  [ [ [ 2, 2, 1, 1, 1 ], [ 1, 2, 1, 2, 1 ], [ 1, 1, 2, 1, 2 ] ], [ 1, 1, 1 ]
     ] ]
 a^3b^2 - a^6 + b^4
 b^2a^3 + ababa + a^2bab
#I  number of entered polynomials is 2
#I  number of polynomials after reduction is 2
#I  End of fase I
#I  Reached level 16
#I  end of the algorithm
#I  The computation took 0 msecs.
 b^2a^3 + ababa + a^2bab
 a^6 - a^3b^2 - b^4
 a^3b^2a - a^4b^2 + b^4a - ab^4
List of occuring arguments

Number of arguments is 2
The weigths of the arguments are [ 2, 3 ]

Level 0
Number of monomials this level is 1
Set [  ] occurs 1 times

Level 1
Number of monomials this level is 0
No monomials of this degree occur

Level 2
Number of monomials this level is 1
Set [ 1, 0 ] occurs 1 times

Level 3
Number of monomials this level is 1
Set [ 0, 1 ] occurs 1 times

Level 4
Number of monomials this level is 1
Set [ 2, 0 ] occurs 1 times

Level 5
Number of monomials this level is 2
Set [ 1, 1 ] occurs 2 times

Level 6
Number of monomials this level is 2
Set [ 3, 0 ] occurs 1 times
Set [ 0, 2 ] occurs 1 times

Level 7
Number of monomials this level is 3
Set [ 2, 1 ] occurs 3 times

Level 8
Number of monomials this level is 4
Set [ 4, 0 ] occurs 1 times
Set [ 1, 2 ] occurs 3 times

Level 9
Number of monomials this level is 5
Set [ 3, 1 ] occurs 4 times
Set [ 0, 3 ] occurs 1 times

Level 10
Number of monomials this level is 7
Set [ 5, 0 ] occurs 1 times
Set [ 2, 2 ] occurs 6 times

Level 11
Number of monomials this level is 9
Set [ 4, 1 ] occurs 5 times
Set [ 1, 3 ] occurs 4 times

Level 12
Number of monomials this level is 10
Set [ 3, 2 ] occurs 9 times
Set [ 0, 4 ] occurs 1 times

Level 13
Number of monomials this level is 16
Set [ 5, 1 ] occurs 6 times
Set [ 2, 3 ] occurs 10 times

Level 14
Number of monomials this level is 17
Set [ 4, 2 ] occurs 12 times
Set [ 1, 4 ] occurs 5 times

Level 15
Number of monomials this level is 24
Set [ 6, 1 ] occurs 5 times
Set [ 3, 3 ] occurs 18 times
Set [ 0, 5 ] occurs 1 times

Level 16
Number of monomials this level is 31
Set [ 5, 2 ] occurs 16 times
Set [ 2, 4 ] occurs 15 times

test11
GAP4stones: infinity
true
gap> ReadTest("test12.test");
true
[ [ [ [ 1, 1, 1, 2 ], [ 1, 1, 2, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ] ],
      [ 1, -651/25, 651/25, -1 ] ],
  [ [ [ 2, 2, 2, 1 ], [ 2, 2, 1, 2 ], [ 2, 1, 2, 2 ], [ 1, 2, 2, 2 ] ],
      [ 1, -651/25, 651/25, -1 ] ] ]
 a^3b - 651/25a^2ba + 651/25aba^2 - ba^3
 b^3a - 651/25b^2ab + 651/25bab^2 - ab^3
#I  number of entered polynomials is 2
#I  number of polynomials after reduction is 2
#I  End of fase I
#I  Reached level 7
#I  end of the algorithm
#I  The computation took 10 msecs.
 ba^3 - 651/25aba^2 + 651/25a^2ba - a^3b
 b^3a - 651/25b^2ab + 651/25bab^2 - ab^3
 b^2a^2ba - bab^2a^2 - baba^2b + ba^2bab + ab^2aba - abab^2a - aba^2b^2 + a^2b\
^2ab
 b^2ab^2a^2 - 651/25b^2ababa + b^2aba^2b + 626/25bab^2aba - bab^2a^2b + babab^\
2a - ba^2b^2ab + ba^2bab^2 - 651/25ab^2ab^2a + ab^2abab + 423176/625abab^2ab -\
 423801/625ababab^2 + 626/25aba^2b^3 - 406901/625a^2b^2ab^2 + 423176/625a^2bab\
^3 - 651/25a^3b^4
List of occuring arguments

Number of arguments is 2
The weigths of the arguments are [ 1, 1 ]

Level 0
Number of monomials this level is 1
Set [  ] occurs 1 times

Level 1
Number of monomials this level is 2
Set [ 1, 0 ] occurs 1 times
Set [ 0, 1 ] occurs 1 times

Level 2
Number of monomials this level is 4
Set [ 2, 0 ] occurs 1 times
Set [ 1, 1 ] occurs 2 times
Set [ 0, 2 ] occurs 1 times

Level 3
Number of monomials this level is 8
Set [ 3, 0 ] occurs 1 times
Set [ 2, 1 ] occurs 3 times
Set [ 1, 2 ] occurs 3 times
Set [ 0, 3 ] occurs 1 times

Level 4
Number of monomials this level is 14
Set [ 4, 0 ] occurs 1 times
Set [ 3, 1 ] occurs 3 times
Set [ 2, 2 ] occurs 6 times
Set [ 1, 3 ] occurs 3 times
Set [ 0, 4 ] occurs 1 times

Level 5
Number of monomials this level is 24
Set [ 5, 0 ] occurs 1 times
Set [ 4, 1 ] occurs 3 times
Set [ 3, 2 ] occurs 8 times
Set [ 2, 3 ] occurs 8 times
Set [ 1, 4 ] occurs 3 times
Set [ 0, 5 ] occurs 1 times

Level 6
Number of monomials this level is 40
Set [ 6, 0 ] occurs 1 times
Set [ 5, 1 ] occurs 3 times
Set [ 4, 2 ] occurs 9 times
Set [ 3, 3 ] occurs 14 times
Set [ 2, 4 ] occurs 9 times
Set [ 1, 5 ] occurs 3 times
Set [ 0, 6 ] occurs 1 times

Level 7
Number of monomials this level is 64
Set [ 7, 0 ] occurs 1 times
Set [ 6, 1 ] occurs 3 times
Set [ 5, 2 ] occurs 9 times
Set [ 4, 3 ] occurs 19 times
Set [ 3, 4 ] occurs 19 times
Set [ 2, 5 ] occurs 9 times
Set [ 1, 6 ] occurs 3 times
Set [ 0, 7 ] occurs 1 times

test12
GAP4stones: 1000
true
gap> ReadTest("test13.test");
true
 aca - cac
 dcd - cdc
 dbd - bdb
 ded - ede
 fef - efe
 ab - ba
 ad - da
 ae - ea
 af - fa
 bc - cb
 be - eb
 bf - fb
 ce - ec
 cf - fc
 df - fd
 a^2 - 1
 b^2 - 1
 c^2 - 1
 d^2 - 1
 e^2 - 1
 f^2 - 1
#I  number of entered polynomials is 21
#I  number of polynomials after reduction is 21
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 7, 6, 6, 6, 6, 7, 6, 6, 9, 8, 8, 8, 7, 11, 13,
  13, 12, 9, 14, 20, 21, 28, 30, 23, 21, 16, 13, 13, 5, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 2540
true
#I  The computation took 2280 msecs.
test13
GAP4stones: 1
Syntax error: fi expected in test13.test line 128
^
true
gap> ReadTest("test14.test");
true
#I  number of entered polynomials is 21
#I  number of polynomials after reduction is 21
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 7, 6, 6, 6, 6, 7, 6, 6, 9, 8, 8, 8, 7, 11, 13,
  13, 12, 9, 14, 20, 21, 28, 30, 23, 21, 16, 13, 13, 5, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 2740
true
#I  The computation took 2110 msecs.
51840
test14
GAP4stones: 2
true
gap> ReadTest("test15.test");
true
[ [ [ [ 2, 2, 2, 2 ], [ 2, 2 ] ], [ 1, -1 ] ],
  [ [ [ 1, 1, 2 ], [ 1, 2 ] ], [ 1, -1 ] ] ]
#I  number of entered polynomials is 2
#I  number of polynomials after reduction is 2
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
 a^2b - ab
 b^4 - b^2
[ [ 1, 1, 2 ], [ 2, 2, 2, 2 ] ]
false
"infinite: exponential growth"
test15
GAP4stones: 1000
true
gap> ReadTest("test16.test");
true
 ea
 a^3 + fa
 a^9 + ca^3
 a^81 + ca^9 + da^3
 ca^81 + da^9 + ea^3
 a^27 + da^81 + ea^9 + fa^3
 b + ca^27 + ea^81 + fa^9
 cb + da^27 + fa^81
 a + db + ea^27
 ca + eb + fa^27
 da + fb
 b^3 - b
 ab - ba
 ac - ca
 ad - da
 ae - ea
 af - fa
 bc - cb
 bd - db
 be - eb
 bf - fb
 cd - dc
 ce - ec
 cf - fc
 de - ed
 df - fd
 ef - fe
#I  number of entered polynomials is 27
#I  number of polynomials after reduction is 8
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 6170
[ [ [ [ 1 ] ], [ 1 ] ], [ [ [ 2 ] ], [ 1 ] ],
  [ [ [ 4, 3 ], [ 3, 4 ] ], [ 1, -1 ] ], [ [ [ 5, 3 ], [ 3, 5 ] ], [ 1, -1 ] ]
    , [ [ [ 5, 4 ], [ 4, 5 ] ], [ 1, -1 ] ],
  [ [ [ 6, 3 ], [ 3, 6 ] ], [ 1, -1 ] ], [ [ [ 6, 4 ], [ 4, 6 ] ], [ 1, -1 ] ]
    , [ [ [ 6, 5 ], [ 5, 6 ] ], [ 1, -1 ] ] ]
 a
 b
 dc - cd
 ec - ce
 ed - de
 fc - cf
 fd - df
 fe - ef
infinite: polynomial growth of degree d = 4
4
[ 1, 4, 10, 20, 35 ]
test16
GAP4stones: 1
true
gap> ReadTest("test20.test");
true
<algebra-with-one over GF(2), with 2 generators>
[ (Z(2)^0)*a, (Z(2)^0)*b ]
[ (Z(2)^0)*<identity ...>+(Z(2)^0)*a^2, (Z(2)^0)*<identity ...>+(Z(2)^0)*b^2,
  (Z(2)^0)*<identity ...>+(Z(2)^0)*a*b*a*b*a*b ]
 a^2 + Z(2)^0
 b^2 + Z(2)^0
 ababab + Z(2)^0
#I  number of entered polynomials is 3
#I  number of polynomials after reduction is 3
#I  End of fase I
#I  End of fase II
#I  length of G =3
#I  length of todo is 3
#I  length of G =3
#I  length of todo is 2
#I  length of G =3
#I  length of todo is 0
#I  List of todo lengths is [ 2, 3, 2, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 0
 a^2 + Z(2)^0
 b^2 + Z(2)^0
 bab + aba
6
 Z(2)^0
 a
 b
 ab
 ba
 aba
[ (Z(2)^0)*a^2+(Z(2)^0)*<identity ...>, (Z(2)^0)*b^2+(Z(2)^0)*<identity ...>,
  (Z(2)^0)*b*a*b+(Z(2)^0)*a*b*a ]
[ (Z(2)^0)*<identity ...>, (Z(2)^0)*a, (Z(2)^0)*b, (Z(2)^0)*a*b,
  (Z(2)^0)*b*a, (Z(2)^0)*a*b*a ]
test20
GAP4stones: 500
true
gap> ReadTest("test3l.test");
false
gap> ReadTest("test32.test");
true
<algebra-with-one over Rationals, with 2 generators>
#I  TWO-SIDED
#I  number of entered polynomials is 2 prefix and 3 two-sided.
#I  Generating a Gröbner basis of the two-sided relations.
#I  number of entered polynomials is 3
#I  number of polynomials after reduction is 3
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 2, 3, 2, 3, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 0
#I  Length of the Gröbner basis is 6
#I  PREFIX
#I  number of prefix relations after reduction is 2
#I  End of fase I
#I  End of fase II
Variable: 'GBset' must have an assigned value
Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

 Z(2)^0
 a
 b
 ab
 ba
 aba
Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

List Element: <list>[1] must have an assigned value
test32
GAP4stones: 250
true
gap> ReadTest("test33.test");
true
<algebra-with-one over Rationals, with 2 generators>
[ b - 1 , 0]
[ 0, b - 1 ]
[ ab + a^2 + a + 1 , - ab - a^2 - a - 1 ]
#I  TWO-SIDED
#I  number of entered polynomials is 3 prefix and 3 two-sided.
#I  Generating a Gröbner basis of the two-sided relations.
#I  number of entered polynomials is 3
#I  number of polynomials after reduction is 3
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 2, 3, 2, 3, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
#I  Length of the Gröbner basis is 6
#I  PREFIX
#I  number of prefix relations after reduction is 3
#I  End of fase I
#I  End of fase II
Variable: 'GBset' must have an assigned value
Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

List Element: <list>[1] must have an assigned value
test33
GAP4stones: 1000
true
gap> ReadTest("test34.test");
true
<algebra-with-one over Rationals, with 4 generators>
[ (-1)*<identity ...>+(1)*s1^2, (-1)*<identity ...>+(1)*s2^2,
  (-1)*<identity ...>+(1)*s3^2, (-1)*<identity ...>+(1)*s1*s2*s1*s2*s1*s2,
  (-1)*<identity ...>+(1)*s2*s3*s2*s3*s2*s3,
  (-1)*<identity ...>+(1)*s1*s3*s1*s3, (-1)*e+(1)*e^2, (1)*s1*e+(-1)*e*s1,
  (1)*s2*e+(-1)*e*s2, (1)*e*s3*e+(-1)*e*s3*e*s3, (1)*e*s3*e+(-1)*s3*e*s3*e ]
[ (1)*e, (-1)*<identity ...>+(1)*s1, (-1)*<identity ...>+(1)*s2,
  (-1)*s3+(1)*s3*e ]
#I  TWO-SIDED
#I  number of entered polynomials is 4 prefix and 11 two-sided.
#I  Generating a Gröbner basis of the two-sided relations.
#I  number of entered polynomials is 11
#I  number of polynomials after reduction is 11
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 8, 8, 5, 6, 5, 3, 5, 6, 6, 4, 6, 7, 8, 8, 9, 9,
  9, 8, 9, 9, 9, 8, 7, 6, 6, 6, 6, 5, 4, 4, 4, 3, 3, 2, 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 230
#I  Length of the Gröbner basis is 38
#I  PREFIX
#I  number of prefix relations after reduction is 4
#I  End of fase I
#I  End of fase II
Variable: 'GBset' must have an assigned value
Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

 Z(2)^0
 s1
 s2
 s1s2
 s2s1
 s1s2s1
Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

Variable: 'GBR' must have a value

List Element: <list>[1] must have an assigned value
test34
GAP4stones: 40
true
gap> ReadTest("test35.test");
true
<algebra-with-one over GF(3), with 3 generators>
[ (Z(3)^0)*<identity ...>+(Z(3))*x+(Z(3)^0)*x^2,
  (Z(3)^0)*<identity ...>+(Z(3))*y+(Z(3)^0)*y^2,
  (Z(3)^0)*<identity ...>+(Z(3))*z+(Z(3)^0)*z^2, (Z(3))*x*y*x+(Z(3)^0)*y*x*y,
  (Z(3))*y*z*y+(Z(3)^0)*z*y*z, (Z(3))*x*z+(Z(3)^0)*z*x ]
[ (Z(3)^0)*<identity ...>+(Z(3)^0)*x, (Z(3)^0)*<identity ...>+(Z(3)^0)*y ]
#I  TWO-SIDED
#I  number of entered polynomials is 2 prefix and 6 two-sided.
#I  Generating a Gröbner basis of the two-sided relations.
#I  number of entered polynomials is 6
#I  number of polynomials after reduction is 6
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 1, 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
#I  Length of the Gröbner basis is 7
#I  PREFIX
#I  number of prefix relations after reduction is 2
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
 s1^2 + Z(3)s1 + Z(3)^0
 s2^2 + Z(3)s2 + Z(3)^0
 s3s1 + Z(3)s1s3
 s3^2 + Z(3)s3 + Z(3)^0
 s2s1s2 + Z(3)s1s2s1
 s3s2s3 + Z(3)s2s3s2
 s3s2s1s3 + Z(3)s2s3s2s1
 s1 + Z(3)^0
 s2 + Z(3)^0
 Z(3)^0
 s3
 s3s2
 s3s2s1
[ [ (Z(3)^0)*<identity ...>+(Z(3)^0)*x ],
  [ (Z(3)^0)*<identity ...>+(Z(3)^0)*y ] ]
#I  TWO-SIDED
#I  number of entered polynomials is 2 prefix and 7 two-sided.
#I  Generating a Gröbner basis of the two-sided relations.
#I  number of entered polynomials is 7
#I  number of polynomials after reduction is 7
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
#I  Length of the Gröbner basis is 7
#I  PREFIX
#I  number of prefix relations after reduction is 2
#I  End of fase I
#I  End of fase II
#I  List of todo lengths is [ 0 ]
#I  End of fase III
#I  End of fase IV
#I  elapsed time is 10
[ s1 + Z(3)^0 ]
[ s2 + Z(3)^0 ]
[ Z(3)^0 ]
[ s3 ]
[ s3s2 ]
[ s3s2s1 ]
test35
GAP4stones: 166
true
gap> 