Decidability of AMPO Comparison for Fixed Parameters

Determine whether the applicative multiset path order comparison s >_ampo t is decidable for a fixed precedence and arity assignment, despite its definition by quantification over all grounding substitutions.

Background

The applicative multiset path order is defined by requiring s >_ampo t to hold for every grounding substitution of the terms s and t. Although the paper establishes decidability of whether a finite applicative term rewriting system can be oriented by AMPO for some arity assignment and precedence, it does not establish decidability of the underlying fixed-parameter comparison relation itself.

A decision procedure for fixed precedence and arity assignments would make AMPO more effective for completion and rewriting induction, as these techniques require repeated comparison of individual term pairs.