## Four Equivalent Equivalences of Reductions (2002)

by
Vincent Van Oostrom
,
Roel De Vrijer

### BibTeX

@MISC{Oostrom02fourequivalent,

author = {Vincent Van Oostrom and Roel De Vrijer},

title = {Four Equivalent Equivalences of Reductions},

year = {2002}

}

### OpenURL

### Abstract

Two co-initial reductions in a term rewriting system are said to be equivalent if they perform the same steps, albeit maybe in a di#erent order. We present four characterisations of such a notion of equivalence, based on permutation, standardisation, labelling and projection, respectively. We prove that the characterisations all yield the same notion of equivalence, for the class of first-order left-linear term rewriting systems. A crucial role in our development is played by the notion of a proof term. 1