my $str = "bea" x 100;
my $re  = qr/(?:be|ea|a)/;

sub atomic {
    use re 'debug';
    say 'Matched $re+\d' if $str =~ m/$re+\d/;
}

sub possessive {
    use re 'debug';
    say 'Matched $re++\d' if $str =~ m/$re++\d/;
}
atomic();
possessive();

##</code><code>##

# atomic
Compiling REx "(?-xism:(?:be|ea|a))+\d"
Final program:
   1: CURLYX[0] {1,32767} (14)
   3:   TRIE-EXACT[abe] (13)
        <be> 
        <ea> 
        <a> 
  13: WHILEM[1/1] (0)
  14: NOTHING (15)
  15: DIGIT (16)
  16: END (0)
minlen 2 

#possessive
Compiling REx "(?-xism:(?:be|ea|a))++\d"
Final program:
   1: SUSPEND (19)
   3:   CURLYX[0] {1,32767} (16)
   5:     TRIE-EXACT[abe] (15)
          <be> 
          <ea> 
          <a> 
  15:   WHILEM[1/1] (0)
  16:   NOTHING (17)
  17:   SUCCEED (0)
  18: TAIL (19)
  19: DIGIT (20)
  20: END (0)
minlen 2 

# regex.ato and regex.pos contain the output including
# the Compiling REx message
michael@lnx-main:working> wc regex.ato regex.pos
   10650    70471  1837158 regex.ato
  229368  1989603 47988305 regex.pos


##</code><code>##

michael@lnx-main:working> grep Detected regex.ato
whilem: Detected a super-linear match, switching on caching...
michael@lnx-main:working> grep Detected regex.pos
whilem: Detected a super-linear match, switching on caching...
# Now look for this line
# whilem: (cache) already tried at this position...
michael@lnx-main:working> grep '(cache)' regex.ato | wc
    298    2086   26426
michael@lnx-main:working> grep '(cache)' regex.pos | wc
      0       0       0

##</code><code>##

# Do nothing
NOTHING	no	Match empty string.
# A variant of above which delimits a group, thus stops optimizations
TAIL	no	Match empty string. Can jump here from outside.