  Reasoning in the presence of associativity and commutativity (AC) is well
known to be challenging due to prolific nature of these axioms. Specialised
treatment of AC axioms is mainly supported by provers for unit equality which
are based on Knuth-Bendix completion. The main ingredient for dealing with AC
in these provers are ground joinability criteria adapted for AC.
  In this paper we extend AC joinability from the context of unit equalities
and Knuth-Bendix completion to the superposition calculus and full first-order
logic. Our approach is based on an extension of the Bachmair-Ganzinger model
construction and a new redundancy criterion which covers ground joinability. A
by-product of our approach is a new criterion for applicability of demodulation
which we call encompassment demodulation. This criterion is useful in any
superposition theorem prover, independently of AC theories, and we demonstrate
that it enables demodulation in many more cases, compared to the standard
criterion.
