Church-Rosser on an example In lambda calculus, starting from $KII$ we can get by a single $\beta$-reduction to either

$\lambda y.II$

or $KI$

Now, according to Church-Rosser, these should be reducing into a common normal form. But the first reduces to $I$ and the second to $\lambda y.\lambda z.z$.

Am I doing wrong $\beta$-reductions or the theorem holds only on some condition? I do not see a common reduct here.
Remember that $1)$ application is left associative and $2)$ application has higher precedence than abstraction. This is: 

$1)$ $ A B C = (A B) C \neq A (B C)$
  $2)$ $ \lambda x. A B = \lambda x. (A B)  \neq (\lambda x. A) B$

So

$KII = (KI)I = ((\lambda x y. x) I) I = (\lambda y. I) I = I$