For my first round of Golf at the Monastery, here's a non-strict, non-polynomial approach.
sub assemble {
## Begin Golf
$w=join'',@_;t("",@_);$w}
sub t{my$s=shift;$w=$s if!@_ and length$s<length$w;
return if!@_;my@b=(@_,@_);
map{t($_,@b[0..$#_-1])}_($s,shift@b)while(@b>@_)}
sub _{my($a,$b)=@_;$l=length$a;for(0..$l){$x=substr($a,0,$_).$b;
return$x if substr($x,0,$l)eq$a}
## End Golf
}
print assemble qw(GATTACA ATTACA GATT AAGAT CCC)
emits
AAGATTACACCC
That's 248 by my count (less the extra newlines that I threw in to avoid ugly wrapping). There's a 20 character test that prunes the search space back, but not enough (I think) to make it a polynomial solution.
Update: This is polynomial after all. I was too lazy to work that out at first. Bah.