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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 aterm $t$ satisfying $t(x,x,y,y,z,z)=t(y,z,z,x,x,y)$. As a consequence of ageneral version of this theorem and previous results we get that each stronglyconnected digraph of algebraic length one, which is compatible with anoperation $t$ satisfying an identity of the from $t(\ldots)=t(\ldots)$, has aloop.

Loop conditions with strongly connected graphs