These icons are clear enough for me. Although, according to international standards, the red circle should be enough, in the UK we've never quite accepted its negative force,. So we tend to add a diagonal line to make sure.
But what I like about this is the additional prohibition: "It is an offence to damage this sign". I want to see that as a pictogram, please – the hand that was feeding the squirrel now attacking the sign with a hammer... all in a red circle with a line through it.
So we'd need a dog with no lead in the circle... perhaps accompanied by a permissive sign for dogs with leads (generally white on blue).