I'm trying to define the computation of Grobner bases in some form of logic. In particular, this means that I should come up with a basis which is independent of the chosen order on terms/monomials.
My question is: are there known instances of ideals for which there is a set of generators such that Buchberger's algorithm outputs the same Grobner basis whatever the chosen term/monomial order?
I know it's quite a generic question, but let me know if you need more clarity wrt the background.