The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting.

A new compilation technique for left-linear term rewriting systems is presented, where rewrite rules are transformed into so-called minimal rewrite rules. These minimal rules have such a simple form that they can be viewed as instructions for an abstract rewriting machine ARM.

Formally well-founded compilation techniques for T erm Rewriting Systems (TRSs) are presented. TRSs are compiled into Minimal Term Rewriting Systems (MTRSs), a subclass of TRSs in which all rules have an extremely simple form. A notion of simulation of (rewrite) relations is presented, under which an MTRSs can be said to simulate a TRS. The MTRS rules can be directly interpreted as instructions for an extremely simple Abstract Rewriting Machine (ARM). Favourable practical results have already been obtained with an earlier version of ARM.

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