The criterion for confluence using decreasing diagrams is a generalization of several well-known confluence criteria in abstract rewriting, such as the strong confluence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of infinite reduction diagrams, arising from unsuccessful attempts to obtain a confluent diagram by tiling with elementary diagrams.

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CWI
Software Engineering [SEN]
Specification and Analysis of Embedded Systems

Klop, J.W, van Oostrom, V, & de Vrijer, R. (2000). A geometric proof of confluence by decreasing diagrams. Software Engineering [SEN]. CWI.