A Higher-Order Iterative Path Ordering

The higher-order recursive path ordering ( HORPO ) defined by Jouannaud and Rubio provides a method to prove termination of higher-order rewriting. We present an iterative version of HORPO by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop. We study well-foundedness of the iterative definition, discuss its relationship with the original HORPO, and point out possible ways to strengthen the ordering.

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