I've been calculating some Gröbner bases in preparation for finding non-commutative Hilbert series (and, once I recreate that, characters of group actions). Specifically, I've been using the letterplace implementation, which I believe calculates to degree $d$ the Gröbner basis for an ideal in the non-commutative free algebra with $n$ generators by passing to something in a commutative ring with $nd$ generators.

In the two cases I've worked with, I can get to degree $5$ with a $9$-generator algebra or to degree $4$ with a $12$-generator algebra; doing one degree higher has led to exceeding the 24GB (8GB RAM + 16GB swap) of the Linux machine with the most memory I can access. This suggests that I can get somewhere in the 40s in terms of number of variables but not the 50s. How hopeless is the growth in memory access for this algorithm; would trying to jerry-rig in a different algorithm for the commutative algebra part be worthwhile?