# A Knuth-Bendix-Like Ordering for Orienting Combinator Equations

@article{Bhayat2020AKO,
title={A Knuth-Bendix-Like Ordering for Orienting Combinator Equations},
author={Ahmed Bhayat and Giles Reger},
journal={Automated Reasoning},
year={2020},
volume={12166},
pages={259 - 277}
}
• Published 18 April 2020
• Mathematics
• Automated Reasoning
We extend the graceful higher-order basic Knuth-Bendix order (KBO) of Becker et al. to an ordering that orients combinator equations left-to-right. The resultant ordering is highly suited to parameterising the first-order superposition calculus when dealing with the theory of higher-order logic, as it prevents inferences between the combinator axioms. We prove a number of desirable properties about the ordering including it having the subterm property for ground terms, being transitive and…
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