How to remove left-recursion in the following grammar?

Question

Unfortunately, it is not possible for ANTLR to support direct-left recursion when the rule has parameters passed. The only viable option is to remove the left recursion. Is there a way to remove the left-recursion in the following grammar ?

---

a[int x]
    : b a[$x] c
    | a[$x - 1] 
    (
          c a[$x - 1]
        | b c
    )
    ;

---

The problem is in the second alternative involving left recursion. Any kind of help would be much appreciated.

Answer 1

Without the parameters and easier formatting, it would look like this:

a
 : b a c
 | a (c a | b c)
 ;

When a's left recursive alternative is matched n times, it would just mean that (c a | b c) will be matched n times, pre-pended with the terminating b a c (the first alternative). That means that this rule will always start with b a c, followed by zero or more occurrences of (c a | b c):

a
 : b a c (c a | b c)*
 ;