From Linear Term Rewriting to Graph Rewriting with Preservation of Termination.

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.