Non-static member functions with no ref-qualifier

This is a follow-up to my previous post

With reference to Non-static member functions

Under

const-, volatile-, and ref-qualified member functions

A non-static member function can be declared with no ref-qualifier,... During overload resolution, non-static cv-qualified member function of class X is treated as follows:

no ref-qualifier: the implicit object parameter has type lvalue reference to cv-qualified X and is additionally allowed to bind rvalue implied object argument

To explore this further, I experimented with the source code provided in the above link, as shown below:

#include <utility>
#include <iostream>
using std::move;
using std::cout;
using std::endl;

struct S {
    void f() {cout << "no ref-qualifier: the implicit object parameter has type lvalue reference to cv-qualified S and is additionally allowed to bind rvalue implied object argument\n"; }

    //if only the below method signature were to be enabled,
    //the invocations using rvalue implicit object would fail
    //to compile with the error [-fpermissive]
    //void f() & {cout << "lvalue\n"; }

    //if only the below method signature were to be enabled,
    //the invocation using lvalue implicit object would fail
    //to complile with the error [-fpermissive]
    //void f() && {cout << "rvalue\n"; }
};

int main (void){

    S s;
    s.f();       // prints "lvalue"
    move(s).f(); // prints "rvalue"
    S().f();          // prints "rvalue"

    return 0;
}

I have provided relevant comments above each non-static member function overload based on reference qualifier, highlighting the compilation issue that would ensue if only that particular overload were to be enabled, in view of the source code in main().

My question is, what is happening under the hoods in order for the non-ref qualified non-static member function to be able to be agnostic to the implicit type of the object upon which it has been invoked? Does the compiler step in with the appropriate overload?

Appreciate your thoughts.