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Rule 416.3

When Recycling is listed as a Cost, the action must be able to be completed for the cost to be paid. Example: Vi, Destructive has the ability "Recycle 1 from your trash: Give me +1 [M] this turn." Each time a player activates the ability, they must recycle 1 card from their trash to pay its cost. If they have no cards in their trash, they can't activate the ability, because they can't pay its cost.

Official Core Rules