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for ( my $i = $size; $i--; ) { ... }
for ( my $j = $i; $j--; ) { ... }

foreach my $i ( 0 .. $size-1 ) { ... }
foreach my $j ( $i+1 .. $size-1 ) { ... }

foreach my $i ( 0 .. $size-1 ) { ... }
foreach my $string2 { @{$arrayDocs}[ $i+1 .. $size-1 ] } {
  # change references to '$arrayDocs->[$j]' to '$string2'
}

#           s/iter      orig backwards   foreach
# orig        10.6        --      -45%      -55%
# backwards   5.80       83%        --      -18%
# foreach     4.75      123%       22%        --

use Benchmark qw(cmpthese);

my $size = 5000;
...
};

cmpthese ( 10 , { orig => $orig, backwards => $backwards, foreach => $
+foreach } );