Acyclic rewriting system

Definition
A rewriting system is said to be acyclic if there is no cyclic sequence of non-identity reductions (that is, a sequence of reductions starting from a word and ending at the same word).

Note that a non-identity reduction means a reduction for which the underlying rewrite is not the identity rewrite.

Stronger properties

 * Length-reducing rewriting system
 * Length-cum-partial order-reducing rewriting system