Nested headers does not affect execution speed.
Nested headers will increase compile time. But so what?
You need to be sure tour headers all have inclusion guards to ptevent the contents from being include more than once. Otherwise you can get redefinition errors.
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#ifndef MYHEADER
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#define MYHEADER
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/*contents of header file here */
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#endif
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Lastly, your header files must contain nothing that occupies memory or generates instructions. If they do, you need to remove it and put it in an implementation file. Then change the header to refer to that implementation file.