NC.SetX("ab");
NC.SetOrdering("LLEX");
F1:=["aa", ""];
F2:=["bbb", ""];
F3:=["abababbabbabababbabb", ""];
G:=[F1,F2,F3]; -- a generalized triangle group
NC.GHF(G); -- G is a partial Groeber basis!!
[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 464, 614, 812,
1074, 1421, 1879, 2486, 3288, 4349, 5753, 7610, 10067, 13317]
-------------------------------
GB:=NC.GGB(G);
NC.GHF(GB);
[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 24, 27, 31, 35, 37, 38, 41, 43, 41, 34, 30, 32, 31, 23, 15, 9, 4, 1, 0]
-------------------------------
RGB:=NC.GReducedGB(G);
NC.GHF(RGB);
[1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 24, 27, 31, 35, 37, 38, 41, 43, 41, 34, 30, 32, 31, 23, 15, 9, 4, 1, 0]
-------------------------------
Sum(It); -- the order of the generalized triangle group
576
-------------------------------
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