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I would guess their plumbing is downstream of the offending tree root. My GF is new to the area, her neighbours have been there for years. Their response (which sounds well rehearsed) is that they are not affected, it’s someone else’s problem even though it’s their negligence that has caused it. But that can’t be proved without first entering the house then digging up the garden and, well, you know what you can do with that idea, matey.
Presumably they’re thinking of leaving before it becomes a major problem? Wouldn’t it cost them more, and be far more unpleasant, if something happened to the pipe or the system?