Shell Expansion

[robivad]

Hi help-bash members,

I noticed that books and online manuals report two different orders for the
recognition and the execution of expansions.

https://www.gnu.org/software/bash/manual/bash.html#Shell-Expansions

[diagram from a book][1]
[1]: <https://i.stack.imgur.com/b79Hw.jpg>

Considering the following:
```
$(((5+2)))
7: command not found
```

1) I think that the shell first recognizes the command substitution and
then the arithmetic substitution.
2) shell executes first the arithmetic substitution and then the command
substitution

Is the order of parsing different from the order of execution or is the
order on the image wrong? Why $((((5+2)))) gives 7: command not found just
like $(((5+2))) ?

Roberto