Crossword Genius

Tree cut up to make small bed (4)

Ross

I believe the answer is:

crib

I'm a little stuck... Click here to teach me more about this clue!

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

'tree cut up to make small' is the wordplay.
I cannot really understand how this works, but
'cut' could be 'rib' (cut of meat) and 'rib' is located in the answer.
A single letter 'c' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for crib that I've seen before include "Copy without acknowledgement" , "Cradle - manger" , "Cot - cattle stall - copy during an exam" , "Baby's bed" , "Child's cot" .)

I've seen this clue in The Hindu.
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