ambiguity of grammar and LR(k)

It is well-known the following grammar is ambiguous so that it is
not LR(k) for any k.
    S -> iEtSeS | iEtS | a
    ('a' is not important, maybe just some assigning statement)


But it can be written in an umambiguous way. I devised the following
grammar(maybe incorrect).
    S -> M | U
    M -> iEtMeM | a
    U -> iEtS


I guess it LR(1). Any correction will be welcomed.


What I cannot figure out is whether there is any language that is not
inherently ambiguous but cannot be LR(k) for any k. I'd appreciate if
anyone can give me some hints.


thanks,


Linlist
--
-------------------------
Linlist Leo
linlist@fudan.edu
-------------------------
[Sure. Construct one along these lines:


S -> aX | bY
a -> A | aA;
b -> A | bA;


The idea is that you need to look past an arbitrarily large number of
A's which need to reduce to an arbitrarily large number of a's or b's
to find the disambiguating X or Y. -John]

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