No. However, even after nuking the old lawn, bermuda will reinvade if the st augustine is not properly maintained. By proper maintenance, I am referring to height of cut, irrigation and fertilization. Bermuda has the upper hand in a lawn that is cut too short, dry and underfertilized. Here in Hawaii, because of the lack of rain and constant high temperatures, st augustine is only used in shady lawns that are irrigated. Bermuda tends to take over in sun exposed lawns, especially if a client's lawn service scalps the lawn and the client is trying to skimp on watering.
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Benjamin Franklin 1775
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Benjamin Franklin Poor Richard's Almanac1738