Counterexamples in infinitary rewriting with non-fully-extended rules

Authors:
Jeroen Ketema
Affiliations:
Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Venue:
Information Processing Letters
Year:
2011

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Abstract

We show counterexamples exist to confluence modulo hypercollapsing subterms, fair normalisation, and the normal form property in orthogonal infinitary higher-order rewriting with non-fully-extended rules. This sets these systems apart from both fully-extended and finite systems, where no such counterexamples are possible.