e =~ u|uae|edefe|ebe|ec

It should be doable in more up-to-date perl. The expression e must start with token u, so let's rewrite it using e => uE?

e =~ u|uauE?|uE?defe|uE?be|uE?c
E =~ auE?|E?defe|E?be|E?c

It should be evident that E? simplifies as

E =~ (au)*(defe|be|c)*

Putting things together:

#! /usr/bin/perl

my $g3 = "( d(?1)f(?1) | b(?1) | c )";      # (defe|be|c)
my $g2 = "( (?:au)* (?3)* )";               # E?
my $g1 = "( u | uau(?2) | u(?2)(?3) )";     # e

my $re = qr/ $g1 (?(DEFINE) $g2 $g3 ) /x;

warn "$re\n";
/^$re$/ and print while <>;
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But of course, this won't work with perl5.6 ...

Update. It looks this simplifies to just

my $re = qr/(u(?:au)*(?:d(?-1)f(?-1)|b(?-1)|c)*)/;