Does "Undefined Behavior" really permit *anything* to happen? [duplicate]

Yes, it permits anything to happen. The note is just giving examples. The definition is pretty clear:

Undefined behavior: behavior for which this International Standard imposes no requirements.

Frequent point of confusion:

You should understand that "no requirement" also means means the implementation is NOT required to leave the behavior undefined or do something bizarre/nondeterministic!

The implementation is perfectly allowed by the C++ standard to document some sane behavior and behave accordingly.¹ So, if your compiler claims to wrap around on signed overflow, logic (sanity?) would dictate that you're welcome to rely on that behavior on that compiler. Just don't expect another compiler to behave the same way if it doesn't claim to.

_{¹Heck, it's even allowed to document one thing and do another. That'd be stupid, and it'd probably make you toss it into the trash—why would you trust a compiler whose documentation lies to you?—but it's not against the C++ standard.}

One of the historical purposes of Undefined Behavior was to allow for the possibility that certain actions may have different potentially-useful effects on different platforms. For example, in the early days of C, given

int i=INT_MAX;i++;printf("%d",i);

some compilers could guarantee that the code would print some particular value (for a two's-complement machine it would typically be INT_MIN), while others would guarantee that the program would terminate without reaching the printf. Depending upon the application requirements, either behavior could be useful. Leaving the behavior undefined meant that an application where abnormal program termination was an acceptable consequence of overflow but producing seemingly-valid-but-wrong output would not be, could forgo overflow checking if run on a platform which would reliably trap it, and an application where abnormal termination in case of overflow would not be acceptable, but producing arithmetically-incorrect output would be, could forgo overflow checking if run on a platform where overflows weren't trapped.

Recently, however, some compiler authors seem to have gotten into a contest to see who can most efficiently eliminate any code whose existence would not be mandated by the standard. Given, for example...

#include <stdio.h>int main(void){  int ch = getchar();  if (ch < 74)    printf("Hey there!");  else    printf("%d",ch*ch*ch*ch*ch);}

a hyper-modern compiler may conclude that if ch is 74 or greater, the computation of ch*ch*ch*ch*ch would yield Undefined Behavior, and as aconsequence the program should print "Hey there!" unconditionally regardlessof what character was typed.

Nitpicking: You have not quoted a standard.

These are the sources used to generate drafts of the C++ standard. These sources should not be considered an ISO publication, nor should documents generated from them unless officially adopted by the C++ working group (ISO/IEC JTC1/SC22/WG21).

Interpretation: Notes are not normative according to the ISO/IEC Directives Part 2.

Notes and examples integrated in the text of a document shall only be used for giving additional information intended to assist the understanding or use of the document. They shall not contain requirements ("shall"; see 3.3.1 and Table H.1) or any information considered indispensable for the use of the document e.g. instructions (imperative; see Table H.1), recommendations ("should"; see 3.3.2 and Table H.2) or permission ("may"; see Table H.3). Notes may be written as a statement of fact.

Emphasis mine. This alone rules out "comprehensive list of options". Giving examples however does count as "additional information intended to assist the understanding .. of the document".

Do keep in mind that the "nasal demon" meme is not meant to be taken literally, just as using a balloon to explain how universe expansion works holds no truth in physical reality. It's to illustrate that it's foolhardy to discuss what "undefined behavior" should do when it's permissible to do anything. Yes, this means that there isn't an actual rubber band in outer space.