Abstract
We present a new technique to prove termination of Term Rewriting Systems, with full automation. A crucial task in this context is to find suitable well-founded orderings. A popular approach consists in interpreting terms into a domain equipped with an adequate well-founded ordering. In addition to the usual interpretations: natural numbers or polynomials over integer/rational numbers, the recently introduced matrix based interpretations have proved to be very efficient regarding termination of string rewriting and of term rewriting. In this spirit we propose to interpret terms as polynomials over integer matrices. Designed for term rewriting, our generalisation subsumes previous approaches allowing for more orderings without increasing the search space. Thus it performs better than the original version. Another advantage is that, interpreting terms to actual polynomials of matrices, it opens the way to matrix non linear interpretations. This result is implemented in the CiME3 rewriting toolkit.
Work partially supported by A3PAT project of the French ANR (ANR-05-BLAN-0146-01).
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Courtieu, P., Gbedo, G., Pons, O. (2010). Improved Matrix Interpretation. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_24
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