  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 is inspired by the tropical and arctic type graphs of
[5] and introduces 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.
