Right-linear overlay TRSs terminate if and only if they are innermost terminating, because absence of infinite minimal dependency-pair chains is equivalent to absence of infinite innermost minimal dependency-pair chains.
Proceedings of the 22nd International Conference on Rewriting Techniques and Applications , optbooktitle =
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Termination of Innermost-Terminating Right-Linear Overlay Term Rewrite Systems (Full Version)
Right-linear overlay TRSs terminate if and only if they are innermost terminating, because absence of infinite minimal dependency-pair chains is equivalent to absence of infinite innermost minimal dependency-pair chains.