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.

@article{paperbot2711,
  title = {Termination of Graph Transformation Systems Using Weighted Subgraph Counting},
  author = {Roy Overbeek and Jörg Endrullis},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 20, Issue 4},
  year = {2024},
  doi = {10.46298/lmcs-20(4:12)2024}
}