If all the elements of your arrays are single chars (as in your previous posts) then I think this would do the job. It does for the testcases provided:

#!/usr/bin/perl -w
use strict;
my @AR  = qw(a b c);   # First Case
my @ar  = qw(z a b c); # Second Case

my @ar2 = qw(b a);
my @ar3 = qw(a b);
my @ar4 = qw(a b c);
my @ar5 = qw(z a b c);

print "First case\n";
#                   L     R
print test_ordered(\@ar,\@ar2),"\n"; # Answer:False(0)
print test_ordered(\@ar,\@ar3),"\n"; # Answer:True(1)
print test_ordered(\@ar,\@ar4),"\n"; # Answer:True(1)
print test_ordered(\@ar,\@ar5),"\n"; # Answer:True(1)

print "Second case\n";
print test_ordered(\@AR,\@ar2),"\n"; # Answer: False(0)
print test_ordered(\@AR,\@ar3),"\n"; # Answer: True(1)
print test_ordered(\@AR,\@ar4),"\n"; # Answer: True(1)

sub test_ordered {
    my( $ar1, $ar2 ) = @_;
    my $re = join '.*?', @$ar2;
    $ar1 = join'', @$ar1;
    return $ar1 =~ $re ? 1 : 0;
}

__END__
P:\test>460234.pl
First case
0
1
1
1
Second case
0
1
1
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