LL(2) always factorable to LL(1)?

All:


I'm TA-ing a compilers course, and am looking for some good examples
of (for example) languages that are intrinsically LL(0,1,2) and same
for LR. It's clear that some languages can be expressed in an LL(2)
grammar, but the grammar can be further factored. For example:


        S -> id "=" Expr | id "(" Params ")"


is LL(2) but can be factored to


        S -> id rest
        rest -> "=" E | "(" Params ")"


Is this always possible?


Other useful things would be: an example of a trivial LL/LR(1) lauguage
and a simple addition that forces it to be (intrinsically) LL/LR(2). Or
a language that lives in the difference between LR(1) and LL(1). Any
suggestions?


Andrew Duncan
http://www.cs.ucsb.edu/~aduncan
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