Replace the "exact" b with a character class [bc]

Then Perl can't rule out the string because of the missing end and you'll see exponential growth.

use strict;
use warnings;

$\="\n";
$|=1;

redos($_) for 5..8;


sub redos {
    my ($length)=@_;


    my $futile = 'a' x $length;

    print "=== length=$length string=$futile";
    print 'start     ', my $start = scalar time;
    die 'huh?' if $futile =~
      /a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a
+*a*a*[bc]/
        ;
    print 'post rx 1 ',  time -$start," sec";
    die 'huh?' if $futile =~
      /(?:(?:(?:(?:(?:(?:(?:(?:(?:(?:(?:(?:(?:a*)*)*)*)*)*)*)*)*)*)*)*
+)*)*[bc]/
        ;
    print 'post rx 2 ',  time -$start," sec";
    print 'done      ',  time -$start," sec";
    print "\n" x2;
}
[download]

C:/Strawberry/perl/bin\perl.exe -w d:/tmp/pm/redos.pl 
=== length=5 string=aaaaa
start     1633643412
post rx 1 0 sec
post rx 2 0 sec
done      0 sec



=== length=6 string=aaaaaa
start     1633643412
post rx 1 1 sec
post rx 2 1 sec
done      1 sec



=== length=7 string=aaaaaaa
start     1633643413
post rx 1 4 sec
post rx 2 4 sec
done      4 sec



=== length=8 string=aaaaaaaa
start     1633643417
post rx 1 20 sec
post rx 2 20 sec
done      20 sec
[download]

it's the first regex which is obviously growing in an exponential manner...