gradually eat away

See: erode
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The global growth in oil demand this year, while weaker than initially expected, could gradually eat away at the global oversupply of crude oil, which itself is steadily shrinking.
Rather, what it had done and what it did was the result of precise calculation and of a plan carefully designed in Tehran and Damascus to allow Hezbollah to gradually eat away at the authority of the Lebanese state and take control of its institutions, as the Assad family had done in Syria.
The play then revolves around the consequences of these actions, in particular the guilt that begins to gradually eat away inside Macbeth, and also the response these actions prompt from those around him.
If I read all the negative stuff I know it would gradually eat away at me and I cannot afford that to happen.