Avodah Zarah 49 - Mixture of Forbidden and Permitted Causes is Permitted
One should not sit in the shadow of a tree that was worshipped, but if he did sit in the shadow, though not under the tree itself, he is still pure. If he sat directly under branches or foliage - he is ritually impure, because he was under "the same roof" with offerings to an idol.
One may plant vegetables under a worshipped tree in the winter, when shade is harmful to them, but not in the summer. Rabbi Yose forbids it even in winter, because the leaves becomes fertilizer for the vegetables. But the exact opposite should be true! Rabbi Yose considers the combination of two causes - forbidden leaves of the worshipped tree and permitted other fertilizers - permitted! Rabbi Yose is only answering the Sages. According to him it is indeed permitted, but he is saying that the Sages should forbid it! And the Sages? The don't prohibit it because the shade is detrimental anyway.
The branches of the worshipped tree are forbidden for benefit. It he fired a new oven with them, it must be broken. If he baked bread with them, that bread is forbidden. If forbidden bread mixed with other permitted bread, then Rabbi Eliezer says that he may take the monetary value of the benefit to the Dead Sea, and everything becomes permitted.
Art: Camille Pissarro - Old Peasant with Cabbage - c1890