TERMINATION OF GRAPH TRANSFORMATION SYSTEMS USING WEIGHTED SUBGRAPH COUNTING^∗

We introduce a termination method for the algebraic graph transformation framework PBPO⁺, in which we weigh objects by summing a class of weighted morphisms targeting them. The method is well-defined in rm-adhesive quasitoposes (which include toposes and therefore many graph categories of interest), and is applicable to non-linear rules. The method is also defined for other frameworks, including SqPO and left-linear DPO, because we have previously shown that they are naturally encodable into PBPO⁺ in the quasitopos setting. We have implemented our method, and the implementation includes a REPL that can be used for guiding relative termination proofs.