No map required, but a hash sure helps:

use strict;
use warnings;

my @arg1   = split '', 'aaabbbccc';
my @arg2   = split '', 'abcabcabc';
my @result = split '', 'xyzrstmno';
my %rules;

die "Mismatched lengths in input arrays"
    if @arg1 != @arg2 or @arg1 != @result;

# Build the rules hash
$rules{$arg1[$_]}{$arg2[$_]} = $result[$_] for 0 .. $#result;

# Do da deed
my @test1 = qw(a b c b b c a a);
my @test2 = qw(a a b c c a b c);

print "$test1[$_]:$test2[$_] = $rules{$test1[$_]}{$test2[$_]}\n"
    for 0 .. $#test1;
[download]

Prints:

a:a = x
b:a = r
c:b = n
b:c = t
b:c = t
c:a = m
a:b = y
a:c = z
[download]