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The Homeomorphic Embedding relation has been amply used for definingtermination criteria of symbolic methods for program analysis, transformation,and verification. However, homeomorphic embedding has never been investigatedin the context of order-sorted rewrite theories that support symbolic executionmethods modulo equational axioms. This paper generalizes the symbolichomeomorphic embedding relation to order-sorted rewrite theories that maycontain various combinations of associativity and/or commutativity axioms fordifferent binary operators. We systematically measure the performance ofincreasingly efficient formulations of the homeomorphic embedding relationmodulo associativity and commutativity axioms. From our experimental results,we conclude that our most efficient version indeed pays off in practice.

Homeomorphic Embedding modulo Combinations of Associativity and Commutativity Axioms