  B-terms are built from the B combinator alone defined by B f g x = f (g x),
which is well-known as a function composition operator. This paper investigates
an interesting property of B-terms, that is, whether repetitive right
applications of a B-term circulates or not. We discuss conditions for B-terms
to and not to have the property through a sound and complete equational
axiomatization. Specifically, we give examples of B-terms which have the
property and show that there are infinitely many B-terms which does not have
the property. Also, we introduce a canonical representation of B-terms that is
useful to detect cycles, or equivalently, to prove the property, with an
efficient algorithm.
