  Faugere's F5 algorithm computes a Groebner basis incrementally, by computing
a sequence of (non-reduced) Groebner bases. The authors describe a variant of
F5, called F5C, that replaces each intermediate Groebner basis with its reduced
Groebner basis. As a result, F5C considers fewer polynomials and performs
substantially fewer polynomial reductions, so that it terminates more quickly.
We also provide a generalization of Faugere's characterization theorem for
Groebner bases.
