I got the task as follows: you are given some dictionary, and some string of repeating letters.
The main goal: find unique, matched by all letters words out of the given dictionary and do it fast).
Here is my solution
(it works equally fast on either on the dogs or cars (takes about 0.1s))

@words = qw/toyota dorf honda audi ford/;
%hash=('adduhifoorndatoyota' => '');
$unique = 0;
foreach $word (@words){
 foreach $key (sort keys %hash){
  $length = 0; if($key=~m/\#/){$_ = $'} else {$_= $key}
  foreach $l (split //, $word){if(/$l/){$_ = "$`$'"; $length++;}}
    if($length == length($word)){
     $newKey = '#'.$_;
     if($key=~m/\#/){
       if($newKey eq '#'){$newKey .= $unique++}
       $hash{$newKey} = $hash{$key}; $hash{$newKey}.= ' '.$word;
     } else {
       $hash{$newKey} = $word;
     }
  }
 }
}

foreach (sort keys %hash){
        print $hash{$_},"\n" if /\#\d+/;
}
-----OUTPUT-----
toyota dorf honda audi
toyota honda audi ford
[download]

if you noticed I intentionally put dorf into dictionary,
so there would be two unique combinations.
Exactly the same works with the dogs.
It takes about 0.1 seconds to finish calculations.
:)
But requires at least two words being mixed in the string line.

Update:

@words = qw/toyota dorf honda audi ford/;
%hash=('adduhifoorndatoyota' => '');
$unique = 0;
foreach $word (@words){
 foreach $key (sort keys %hash){
  $length = 0; if($key=~m/\#/){$_ = $'} else {$_= $key}
  foreach $l (split //, $word){if(/$l/){$_ = "$`$'"; $length++;}}
    if($length == length($word)){
     $newKey = '#'.$_;
     if($key=~m/\#/){
       if($newKey eq '#'){$newKey .= $unique++}
       $hash{$newKey} = $hash{$key}; $hash{$newKey}.= ' '.$word;
     } else {
       $hash{$newKey} = $word;
     }
  }
 }
}

foreach (sort keys %hash){
        print $hash{$_},"\n" if /\#\d+/;
}
-----OUTPUT-----
toyota dorf honda audi
toyota honda audi ford
[download]