  We prove that the existence of a term $s$ satisfying $s(r,a,r,e) =
s(a,r,e,a)$ in a general algebraic structure is equivalent to an existence of a
term $t$ satisfying $t(x,x,y,y,z,z)=t(y,z,z,x,x,y)$. As a consequence of a
general version of this theorem and previous results we get that each strongly
connected digraph of algebraic length one, which is compatible with an
operation $t$ satisfying an identity of the from $t(\ldots)=t(\ldots)$, has a
loop.
