Can the application condition on the Merge rule in the computation of dag-solved forms of unification problems be improved?

The source page states the original problem together with its recorded qualifications and progress updates as follows.

Rules are given in [Jouannaud, 1991] for computing dag-solved forms of unification problems in equational theories. The Merge rule $x \approx s,x \approx t \Rightarrow x \approx s,s \approx t$ given there assumes that $s$ is not a variable and its size is less than or equal to that of $t$. Can this condition be improved by replacing it with the condition that the rule Check* does not apply? (In other words, is Check* complete for finding cycles when Merge is modified as above?)

Recorded progress.

The problem has been solved by Hubert Comon [Jouannaud, 1991] using an extended Check rule (requiring a congruence closure step). The original question---for whatever it may be worth---stands.