At first glance, the problem of distinguishing complex words from similar free syntactic combinations does not exist.
But compound words are a reflection of "the diversity of linguistic activity." Therefore, one or more features sometimes is not enough to establish the identity of a compound word. And sometimes this is simply impossible, as some units correspond to all signs, while others do not.
There are other units in the language, consisting of two or more words and outwardly similar to complex words. Sometimes it is very difficult to distinguish complex words from outwardly similar syntactic combinations and phraseological units.
It is natural that you need to draw a line between complex words and free combinations, because if we take all units of two or more words that designate one concept (with varying degrees of semantic integrity) as complex, we will make a huge confusion in definition of complex words and phrases.
Multiple routes for compound word processing in the brain: Evidence from EEG
