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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Church-Rosser Theorem
A property of a reduction system that states that
if an expression can be reduced by zero or more reduction
steps to either expression M or expression N then there exists
some other expression to which both M and N can be reduced.
This implies that there is a unique normal form for any
expression since M and N cannot be different normal forms
because the theorem says they can be reduced to some other
expression and normal forms are irreducible by definition. It
does not imply that a normal form is reachable, only that if
reduction terminates it will reach a unique normal form.
(1995-01-25)