minimum reduced string made up of a,b,c

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This is an interview questions asked from me.

An input string is made up of only a, b and c. You have to reduce the string to minimum possible length. Reducing criteria is:

if ab or ba comes together, it can be replaced by c

if bc or cb comes together, it can be replaced by a

if ac or ca comes together, it can be replaced by b

For example,

abcbca --> abaca --> caca --> cba --> cc or aa

abcbca --> ccbca --> caca --> same as above

I could not even think of any proper logic. I started thinking in terms of odd and even place occurrence, but it did not help. Please help me in buildinga logic for it

Thanks

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