What would happen to the water cycle if there were no rain?

Well if the rain stopped coming then there would be nothing for the clouds to evaporate, so then there would be no rain and the water cycle would just completely stop

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No rain means no water cycle, but while the first answer is correct there, it shows complete misunderstanding of clouds and of basic meteorology generally. A cloud does NOT evaporate water, but is an accumulation of water that has ALREADY evaporated and then condensed into a visible aerosol of minute droplets. Rain results from the cloud's internal conditions allowing the droplets to coalesce so become too heavy to stay buoyant in the air.