  Most known results on avoiding the occur-check are based on the notion of
"not subject to occur-check" (NSTO). It means that unification is performed
only on such pairs of atoms for which the occur-check never succeeds in any run
of a nondeterministic unification algorithm. Here we show that this requirement
is too strong. We show how to weaken it, and present some related sufficient
conditions under which the occur-check may be safely omitted. We show examples
for which the proposed approach provides more general results than the
approaches based on well-moded and nicely moded programs (this includes cases
to which the latter approaches are inapplicable).
