Typeid not functioning correctly

The problem is that A has no virtual functions, so is not treated as a polymorphic type. As a result, typeid looks up the declared type of the pointer, not the actual type of the object that it points to.

The object it points to must be polymorphic for this to work as you expect. If A had virtual methods than your code would have work as expected, for example adding a virtual destructor, which I demo live here using gcc.

Quote form the C++ draft standard section 5.2.8 Type identification paragraph 2 says:

When typeid is applied to a glvalue expression whose type is a polymorphic class type (10.3), the result refers to a std::type_info object representing the type of the most derived object (1.8) [...]

Which applies to the case where we have a virtual method, in your case you do not have a polymorphic type so paragraph 3 applies:

When typeid is applied to an expression other than a glvalue of a polymorphic class type, the result refers to a std::type_info object representing the static type of the expression

So you will get the static type back which is A.

Just to be a little more complete section 10.3 Virtual functions says:

Virtual functions support dynamic binding and object-oriented programming. A class that declares or inherits a virtual function is called a polymorphic class.