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Simple and minimal ground term equation systems

Vagvölgyi S.

Fundamenta Informaticae

1998

Vol. 36, nr 4

367-413

A ground term equation system (gtes for short) E is simple if there is no gtes E' equivalent to E consisting of less equations than E has. Moreover, a gtes E is minimal if for each equation e < E, the congruence generated by E - {e} is a proper subset of the congruence generated by E. Given a reduced ground term rewriting system R, we describe all simple gtes' E and minimal gtes' F equivalent to R. We show that for a reduced ground term rewriting system R, it is decidable whether or not there exist infinitely many simple (minimal) gtes' equivalent to R. Finally, we show that for a reduced ground term rewriting system R, and a gtes E, it is decidable if there is a simple gtes F equivalent to R such that E < F.