Complexity of computing pseudo-ASL Gröbner bases

Determine the computational complexity of computing pseudo-ASL Gröbner bases for arbitrary finitely generated commutative algebras equipped with a pseudo-ASL term order, and ascertain whether such bases can always be computed using only exponential space.

Background

The paper develops a Gröbner basis theory intrinsic to finitely generated commutative algebras endowed with pseudo-ASL structures and term orders. Ordinary Gröbner bases are known to be EXPSPACE-hard, and the authors ask whether the same level of complexity is inherent to pseudo-ASL Gröbner bases, or whether better bounds exist.