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We introduce techniques for proving uniform termination of graphtransformation systems, based on matrix interpretations for string rewriting.We generalize this technique by adapting it to graph rewriting instead ofstring rewriting and by generalizing to ordered semirings. In this way weobtain a framework which is inspired by the tropical and arctic type graphs of[5] and introduces a new variant of arithmetic type graphs. These type graphscan be used to assign weights to graphs and to show that these weights decreasein every rewriting step in order to prove termination. We present an exampleinvolving counters and discuss the implementation in the tool Grez.

Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings