Termination orders for three-dimensional rewriting

This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each system are studied. Finally, a convergent 3-polygraph for the (commutative) theory of image-vector spaces is given. In order to prove these results, it is explained how to craft a class of termination orders for 3-polygraphs.