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

##</code><code>##

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

##</code><code>##

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

##</code><code>##

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

##</code><code>##

use Benchmark qw(cmpthese);

my $size = 5000;

my $orig = sub {
  for (my $i = 0; $i < ($size - 1); $i++) {
    for (my $j = $i + 1; $j < ($size - 1); $j++) {
    }
  }
};

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

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

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