I'm having trouble understanding the difference between unspecified and undefined behavior.
Then let's start with the definitions of those terms from the Standard:
undefined behavior behavior, upon use of a nonportable or erroneous program construct or of erroneous data, for which this
International Standard imposes no requirements
NOTE Possible undefined behavior ranges from ignoring the situation completely with unpredictable results, to behaving during
translation or program execution in a documented manner characteristic
of the environment (with or without the issuance of a diagnostic
message), to terminating a translation or execution (with the issuance
of a diagnostic message).
EXAMPLE An example of undefined behavior is the behavior on integer overflow.
(C2011, 3.4.3)
unspecified behavior use of an unspecified value, or other behavior where this International Standard provides two or more
possibilities and imposes no further requirements on which is chosen
in any instance
EXAMPLE An example of unspecified behavior is the order in which the
arguments to a function are evaluated.
(C2011, 3.4.4)
You remark that
The doubt arised because sometimes it is argued that things in C are
UB by "default" are only valid you can justify that the construction
is valid.
It is perhaps over-aggrandizing that to call it an argument, as if there were some doubt about its validity. In truth, it reflects explicit language from the standard:
If a ''shall'' or ''shall not'' requirement that appears outside of a
constraint or runtime- constraint is violated, the behavior is
undefined. Undefined behavior is otherwise indicated in this
International Standard by the words ''undefined behavior'' or by the
omission of any explicit definition of behavior. There is no
difference in emphasis among these three; they all describe ''behavior
that is undefined''.
(C2011, 4/2; emphasis added)
When you posit
Assuming none of these rules existed and there are no other rules that
"invalidate" x = x++.
, that doesn't necessarily change anything. In particular, removing the explicit rule that the order of evaluation of the operands is unspecified does not make the order specified. I'd be inclined to argue that the order remains unspecified, but the alternative is that the behavior would be undefined. The primary purpose served by explicitly saying it's unspecified is to sidestep that question.
The rule explicitly declaring UB when an object is modified twice between sequence points is a little less clear, but falls in the same boat. One could argue that the standard still did not define behavior for your example case, leaving it undefined. I think that's a bit more of a stretch, but that's exactly why it is useful to have an explicit rule, one way or the other. It would be possible to define behavior for your case -- Java does, for example -- but C chooses not to do, for a variety of technical and historical reasons.
The value of x would then be unspecified, right?
That's not entirely clear.
Please understand, too, that the various provisions of the standard for the most part do not stand alone. They are designed to work together, as a (mostly) coherent whole. Removing or altering random provisions has considerable risk of producing inconsistencies or gaps, leaving it difficult to reason about the result.