We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a framework which includes the tropical and arctic type graphs of  and a new variant of arithmetic type graphs. These type graphs can be used to assign weights to graphs and to show that these weights decrease in every rewriting step in order to prove termination. We present an example involving counters and discuss the implementation in the tool Grez.
|Title of host publication||Graph Transformation (8th International Conference, ICGT 2015, Held as Part of STAF 2015, L'Aquila, Italy, July 21-23, 2015. Proceedings)|
|Editors||F. Parisi-Presicce, B. Westfechtel|
|Place of Publication||Cham|
|Publication status||Published - 2015|
|Name||Lecture Notes in Computer Science|
Bruggink, H. J. S., König, B., Nolte, D., & Zantema, H. (2015). Proving termination of graph transformation systems using weighted type graphs over semirings. In F. Parisi-Presicce, & B. Westfechtel (Eds.), Graph Transformation (8th International Conference, ICGT 2015, Held as Part of STAF 2015, L'Aquila, Italy, July 21-23, 2015. Proceedings) (pp. 52-68). (Lecture Notes in Computer Science; Vol. 9151). Cham: Springer. https://doi.org/10.1007/978-3-319-21145-9_4