Running the inner loop forward ensure earliest short-circuit and cut time to 1/4.

This will work regardless of the data and takes just under 2 minutes 35 seconds for a maximum sized AoA.

#! perl -slw
use strict;
use Time::HiRes qw[ time ];
use Data::Dump qw[ pp ];

## Generate test data
my @paths = map[ map chr(65+rand 26), 2 .. 2+rand(11) ], 1 .. 32448;

my $start = time;

## Sort by length of subarray; shortest last to facilitate deletion in
+ a loop
@paths = sort{ $#{ $b } <=> $#{ $a } } @paths;
#pp \@paths;

## Build an index to the elements in all the subarrays
my( $i, %index ) = 0;
for my $ref ( @paths ){
    $index{ $_ } //= ++$i for @$ref;
}
#pp \%index;

## Use the index to build bitmaps representing the subarrays
my @bitmaps = ( '' ) x @paths;
for my $n ( 0 .. $#paths ) {
    vec( $bitmaps[ $n ], $index{ $_ }, 1 ) = 1 for @{ $paths[ $n ] };
}
#pp \@bitmaps;

## bitwise OR the bitmaps to discover wholly contained subarrays and r
+emove them
OUTER:for my $i ( reverse 0 .. $#paths ) {
    for my $j ( 0 .. $i-1 ) {                            ## Remove rev
+erse; short-circuit earlier.
        if( ( $bitmaps[ $j ] | $bitmaps[ $i ] ) eq $bitmaps[ $j ] ) {
#            warn "deleting $i";
            delete $paths[ $i ];
            next OUTER;
        }
    }
}

## remove undefs
@paths = grep defined, @paths;

printf "Deleted %u subarrays\n", 32448 - @paths;
printf "Took %.6f seconds\nEnter to see results:", time() - $start;

<STDIN>;
pp \@paths;

__END__
C:\test>1169736.pl
Deleted 22228 subarrays
Took 107.267549 seconds
Enter to see results:Terminating on signal SIGINT(2)

C:\test>1169736.pl
Deleted 22024 subarrays
Took 108.820184 seconds
Enter to see results:Terminating on signal SIGINT(2)
[download]

It works by building an index to the items in the subarrays; uses that index to build bitmaps representing the subarrays; the cross compares the bitmaps using bitwise-OR to determine wholly contained subarrays and deletes them.