All intra-regular generalized hypersubstitutions of type (2)

A generalized hypersubstitution of type τ maps each operation symbol of the type to a term of the type, and can be extended to a mapping defined on the set of all terms of this type. The set of all such generalized hypersubstitutions forms a monoid. An element a of a semigroup S is intra-regular if there is b ∈ S such that a = baab. In this paper, we determine the set of all intra-regular elements of this monoid for type τ = (2).