[R-sig-ME] meaning of lmer formula

[Don Cohen]

Ben Bolker writes:

 > > Does (input1 + input2 | group) mean the same as
 > > (input1 | group) + (input2 | group) or does it also include a 
 > > correlation between input1 and input2 ?
 >   The latter.

It occurred to me after I wrote the questions that 
(input1 | group) + (input2 | group) might also include that
correlation between input1 and input2 - I gather now it does not.

 > > Back to my question about additive shifts, is that extra correlation 
 > > required in order to maintain invariance over additive shifts?
 >   Yes.

One more question (so far):
If there are two different groupings, would
 (input1 + input2 | group1) + (input1 + input2 | group2)
involve correlations between group1 and group2 ?

If I think of (1+input1 | group) as a 2x2 matrix, and
(1+input1+input2 | group) as 3x3
then is (1+input1+input2 | group1)+(1+input1+input2 | group2)
two independent 3x3's or a full 6x6 (or something else) ?