"Two open problems in rewriting"
Nachum

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Abstract

We describe two mature, challenging, partially open, partially closed
problems in the theory of rewriting. One problem deals with (criteria
for left-linear) confluence and the other with termination (of one
linear or string rule), the two paradigmatic properties of interest for
rewrite systems of any flavor. Both problems were formulated a
relatively long time ago, have seen considerable progress, but remain open.