From Linear Term Rewriting to Graph Rewriting with Preservation of Termination

Roy Overbeek
(Vrije Universiteit Amsterdam)
Jörg Endrullis
(Vrije Universiteit Amsterdam)

Encodings of term rewriting systems (TRSs) into graph rewriting systems usually lose global termination, meaning the encodings do not terminate on all graphs. A typical encoding of the terminating TRS rule a(b(x)) -> b(a(x)), for example, may be indefinitely applicable along a cycle of a's and b's. Recently, we introduced PBPO+, a graph rewriting formalism in which rules employ a type graph to specify transformations and control rule applicability. In the present paper, we show that PBPO+ allows for a natural encoding of linear TRS rules that preserves termination globally. This result is a step towards modeling other rewriting formalisms, such as lambda calculus and higher order rewriting, using graph rewriting in a way that preserves properties like termination and confluence. We moreover expect that the encoding can serve as a guide for lifting TRS termination methods to PBPO+ rewriting.

In Berthold Hoffmann and Mark Minas: Proceedings Twelfth International Workshop on Graph Computational Models (GCM 2021), Online, 22nd June 2021, Electronic Proceedings in Theoretical Computer Science 350, pp. 19–34.
Published: 21st December 2021.

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