查了下：
comply的名词形式是compliance.
compliment和comply是同一个词源，但是compliment受complement影响，被带偏了。

找了找，词源差不多，引伸后出了叉子：
The original sense was ‘fulfil, accomplish’, later ‘fulfil the requirements of courtesy’, hence ‘to be agreeable, to oblige ’or‘ obey’. Compare with compliment.