  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.
