# This will be our transitive closure.
my %is_winning_chain_over;
my @new_relations;

# First populate with the winners
for my $team (keys %play_result) {
    while (my ($other_team, $won) = each %{$play_result{$team}}) {
        if ($won) {
            $is_winning_chain_over{$team}{$other_team} = 1;
            push @new_relations, [$team, $other_team];
        }
    }
}

# Now compute the closure
while (@new_relations) {
    my $relation = shift @new_relations;
    my ($winner, $loser) = @$relation;
    my $winner_is_over = $is_winning_chain_over{$winner};
    my $loser_is_over = $is_winning_chain_over{$loser};
    for my $third_team (keys %$loser_is_over) {
        if (not $winner_is_over->{$third_team}) {
            $winner_is_over{$third_team} = 1;
            push @new_relations, [$winner, $third_team];
        }
    }
}