#2 leaks memory every time you call rec_helper. The sub you create references $recursive which references the sub, so you have a memory cycle. The simplest solution is to avoid using a lexical to hold the reference to the sub. It even simplifies the code a little.

sub rec_helper {
    my %state;
    local *recursive = sub {
        my( $arg ) = shift;
        ...
        if( ( $arg = $state{ $arg ) ) == ... ) {
             return recursive( $arg );
        }
        else {
             return 0;
        }
    };
}
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