The pitfall that is hard to avoid when using the join-to-form-a-regexp solution is that, for example:

@b = (ab, c);
[download]

is probably not construable (depending on your exact view of the requirement) as being an ordered subset of:

@a = (a, bc, d);
[download]

My first reaction was therefore to use the standard join( $;, array ) approach ($; is a non-printable field separator often used for this purpose), while mulling over the possibility that the data might be binary and so accidentally contain a byte equal to $; (it's the ascii of decimal 19 and reassigning $; would just move the problem to a different false-positive), the following non-regexp approach drifted into my head - it does at least do about the minnimum necessary while being safe from the above join-delimitation problem:

sub isOrderedSublist{
    my ( $aref, $bref ) = @_; # references to arrays
    my @a = @$aref; # major - copy so we can safely destroy
    my @b = @$bref; # minor
    my $firstMatched = 0;
    while( not Empty( \@a ) ) {
        if ( $a[0] eq $b[0] ) {
            $firstMatched = 1;
            shift @b;
        else {
            $firstMatched and last;
        }
        shift @a;
    }
    return Empty( \@b ); # success if failure eliminated
}

sub Empty{
    my $aref = shift;
    return( not ( $#$aref + 1 ) );
}
[download]

update: factorised to reduce a couple of lines

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