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A bit confused about whether this grammar is ambiguous or not

C' -> C
C -> d C u C
C -> d C
C -> ε

I tried building the DFA for this but I get this in one of the states:

C -> d C DOT u C, $
    C -> d C DOT, $

Isn't this a shift-reduce conflict, so surely it means the grammar is not LR(1)? Or does it reduce regardless since $ and u are both in the follow set of C? Is this not a reduce-reduce conflict since it goes to C regardless?

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    $\begingroup$ Is your question about being LR(1) or about being ambiguous. A CF grammar may be unambiguous, but not LR(1). $\endgroup$ – babou Mar 28 '15 at 13:41
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This grammar (which isn't ambiguous) isn't LR(k) due to the right-recursion, thus it isn't LR(1).

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