Very sorry about this situation. I am a cat owner and I can tell you they are pretty independent creatures and won't listen to or obey anything they are told. The probability of getting them to stop is pretty small, even if you speak CAT. However, this does not mean that you are required to put up with having cats ruin your property. It is the responsibility of the owner of a pet to control that pet. If it is getting out and ruining your carpet, you can bring a claim in Small Claims court for the value of the carpet. The limit is $10,000.00, which should cover your carpet.
You need to prepare for court by gathering lots of evidence, photos of the carpet, photos of the cats on your property, photos of the cat poo, replacement estimates and witness statements about seeing the cats on the property. Do not expect the Court to look at the carpet or poo. But you might want to think about this: wild animals can get on your property and leave scat that looks like cat poo, too. How do you prove it was from the cats? If the neighbor claims it was not the cats and was a Possum or other animal, you have the burden of proving it was cat poo. this sounds really silly but you may need a poo expert. I don't even know who that would be, a Vet maybe?
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