A superexponential lower bound for Gröbner bases and Church-Rosser commutative thue systems

Abstract

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 (2^2nC) for the production length and cardinality of Church-Rosser commutative Thue systems, and the degree and cardinality of Gröbner bases.