I was playing with Kanji Kentei exercises. The area: 熟語の構成.

> The word in question: 犯罪
>
> The correct answer: 下の文字が上の文字の目的語・補語になっているもの（着席）

Makes sense: 罪を犯す → 犯罪

* * *

Now the question: what makes it not fit the category 同じような意味の漢字を重ねたもの（岩石）?

I find the two characters meeting the criteria for 同じような意味:

罪＝法にふれる。  
犯＝しきりをふみこえる。法やおきてをやぶる。

Do these categories have an order like "first matched A so A")? Or are there
some other criteria?
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question
words kanji
Regarding the construction of 犯罪
In this case, 罪 and 犯 never make synonyms. Despite loose notion of word class
in Chinese grammar, people usually know a word's semantic category e.g. is an
object, quality, action etc.

罪 is usually considered an abstract entity: a _crime_ , _sin_ , or _guilt_
etc. 犯 represents action: _violate_ , _trespass_ , _infringe_ etc. Doesn't 犯
also mean "infringement"? Yes, but it's only "action of infringing" and not
"infringed state". In other words, 犯 could mean "crime-committing" but not
"crime".

You could argue that 犯人 "committer" and 罪人 "criminal" are synonyms, but not
for "commit" and "crime".

> Do these categories have an order like "first matched A so A")? Or are there
> some other criteria?

There is unfortunately no rule to deduce what construction a word has. You can
guess from kanji meaning, but its mostly lexical so that you have to memorize
one by one if you seek accuracy; for example, 作曲 "music composition" is verb-
object ("make music") type, but 作品 "art work" is adjective-noun ("made
goods").
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> 罪＝法にふれる。

罪 is a noun. Therefore, this explanation is not accurate.

> 罪＝法にふれる **行為** 、法にふれる **事**

This is more accurate.

> 犯＝しきりをふみこえる。法やおきてをやぶる。

This explanation is correct. 犯す is a verb.

In case of 岩石, 岩 and 石 are both nouns. Therefore the two words have the near-
the-same meaning and the same 品詞.

As you said, 罪 and 犯 may have the resembling meaning, however, according to
the 品詞の違い, the interpretation, 罪を犯す, seems much easier to understand.

Does this explanation make sense to you?

同じような意味 should include the premise that they are the 同じ品詞.
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answer