Faction falling apart is hilarious (13)

I believe the answer is:

sidesplitting

'hilarious' is the definition.
(I've seen this before)

'faction falling apart' is the wordplay.
'faction' becomes 'side' (one side in a conflict or controversy).
'falling apart' becomes 'splitting' (splitting is a kind of falling apart).
'side'+'splitting'='SIDESPLITTING'

'is' acts as a link.

(Another definition for sidesplitting that I've seen is " Hilarious".)

I've seen this clue in The Irish Times.

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