With the recent question, How can sets be recursively concatenated when intersecting with each other, I ended up revisiting these solutions and providing a streamlined answer. I must say that I'm definitely a fan of jaredor's solution below, but I noticed a couple areas where yours could be improved efficiency wise and one potential bug:

• Efficiency: loop $j from $i+1 to $#array instead of the entire array.
• Efficiency: using redo instead of goto so that fully reduced elements don't need to be gone over again.
• bug: dedup will potentially drop numbers that are substrings of other numbers. ie 11 and 111.

Here's my suggested changes applied to your solution:

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

my @array = ("11 12","11 13", "9 8 7", "3 4", "11 4 111") ;

## combine
AGAIN: for my $i ( 0 .. $#array ) {
    for my $j ( $i+1 .. $#array ) {
        for my $n (split ' ', $array[ $j ]){
            if( $array[ $i ] =~ m[\b$n\b] ) {
                $array[ $i ] .= ' ' . splice @array, $j, 1;
                redo AGAIN;
            }
        }
    }
}
## dedup
for ( @array ) {
    1 while s[(\b\d+)\s(?=.*\b\1\b)][]g;
}

pp \@array;
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