Church-Rosser on an example
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

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