Tosefta for Avodah Zarah 83:11
הני מילי דפחסה עובד כוכבים אבל פחסה ישראל לא בטלה
This rule only applies when an idolater defaced it in this manner, but if an Israelite did so it is not annulled.
Tosefta Demai
A Jew may not tie up his livestock beside the livestock of a Gentile (i.e., on the Gentile's property), for if his livestock [went there] to eat on its own [see Ab. Zar. 42a:9 (מאליה)], [the Gentile] is not required to return it. [Presumably, livestock that becomes accustomed to being brought onto someone else's property will eventually wander there on its own.]
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