Cycles in use statements can cause issues. Often hard-to-diagnose problems.

Breaking the cycle by making one of them a just-in-time require instead of a use is often a good solution.

# AAA.pm
package AAA;

use base 'Exporter';
our @EXPORT = qw(aaa);

use BBB qw(bbb);

sub aaa {
   my $arg = shift;
   return 0 if $arg <= 0;
   return 1 + bbb($arg - 1);
}

1;


# BBB.pm
package BBB;

use base 'Exporter';
our @EXPORT = qw(bbb);

# use AAA qw(aaa);

sub bbb {
   my $arg = shift;
   return 0 if $arg <= 0;
   require AAA;
   return 1 + AAA::aaa($arg - 1);
}

1;


# main.pl
use AAA;
use BBB;

print aaa(3) + bbb(4), "\n";
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