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In a recent work "Arc-presentation of links: Monotonic simplification" IvanDynnikov showed that each rectangular diagram of the unknot, composite link, orsplit link can be monotonically simplified into a trivial, composite, or splitdiagram, respectively. The following natural question arises: Is it alwayspossible to simplify monotonically a rectangular diagram of a satellite knot orlink into one where the satellite structure is seen? Here we give a negativeanswer to that question.

Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification