Decidability of termination for semi-constructor TRSs, left-linear shallow TRSs and related systems

Authors:
Yi Wang;Masahiko Sakai
Affiliations:
Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan;Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan
Venue:
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Year:
2006

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Abstract

We consider several classes of term rewriting systems and prove that termination is decidable for these classes. By showing the cycling property of infinite dependency chains, we prove that termination is decidable for semi-constructor case, which is a superclass of right-ground TRSs. By analyzing argument propagation cycles in the dependency graph, we show that termination is also decidable for left-linear shallow TRSs. Moreover we extend these by combining these two techniques.