A Superexponential Lower Bound for Gröbner Bases and Church-Rosser Commutative Thue Systems

The complexity of the normal form algorithms which transform a given polynomial ideal basis into a Gröbner basis or a given commutative Thue system into a Church-Rosser system is presently unknown. In this paper we derive a double-exponential lower bound (22") for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases