if the lower bound price is greater than said difference, summing the lower bound price with the sum of {HEAD ~ the prices} of {TAIL ~ the bid} that lie on the search path connected to said subtree and replacing the current price of the best allocation with said sum; and 
if the lower bound price is greater than said difference , summing the lower bound price with the sum of { HEAD ~ the prices } of { TAIL ~ the bid } that lie on the search path connected to said subtree and replacing the current price of the best allocation with said sum ; and
OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH HEAD HEAD HEAD HEAD HEAD HEAD REL TAIL TAIL TAIL TAIL TAIL TAIL OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH