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We present a canonical term rewriting system RX whose ground normal forms can directly be mapped to integral polynomials in distributive normal form. Completing RX and a set of ground equations simulates the Grobner base computation for the ideal presented by the ground equations. With our approach, we can clearly show the correspondences of the key features of algebraic completion procedures for integral polynomial ideals ([Lau76], [Buc84]) and their simulation in a term rewriting environment.

Completion of integral polynomials by AC-term completion