Add to ORKGAbstract. String rewriting can not only be applied on strings, but also on cycles and even on general graphs. In this paper we investigate ter-mination of string rewriting applied on cycles, shortly denoted as cycle rewriting, which is a strictly stronger requirement than termination on strings. Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, but match bounds, arctic ma-trices and tropical matrices can be applied. Further we show how any terminating string rewriting system can be transformed to a terminating cycle rewriting system, preserving derivational complexity.