Extension of the Associative Path Ordering to a Chain of Associative Commutative Symbols

In this paper, we give a generalization of the associative path ordering. This ordering has been introduced by Bachmair and Plaisted [5] and is a restricted variant of the recursive path ordering which can be used for proving the termination of associative-commutative term rewriting systems. This ordering requires strong conditions on the precedence on the alphabet. In this article, we treat the case of a precedence which contains a chain of AC symbols. We also introduce some unary symbols comparable with AC symbols.