Answer: Barberries are tenacious plants, it's true. Apart from yanking them out by the roots using a chain hooked to a powerful vehicle, the brute force method of chainsaw and then sawing/digging out the roots will also work.
Another option is to use an herbicide such as glyphosate according to the label instructions. Be sure to read and follow the instructions carefully and wait the prescribed time while the chemical is translocated to the roots where it actually does the job. Also take care not to contact desirable plants as this is a nonselective herbicide; it may require more than one spraying since this is such a sturdy plant with strong reserves.
As you already know, barberry forms an excellent barrier on a par with a fence. If all else fails, they do take clipping and trimming very well and can be managed as a sheared hedge. At least that might keep it out of your way on a daily basis.
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