Is it possible for two classes to inherit from each other

No it is not possible. compile time error is thrown

Circular base class dependency involving 'x' and 'y'

x & y are classes derived from each other.

No, it is not possible. One of the reasons is stated below.

In inheritance, if we create an object to child class, the base class constructor is by default called in derived class constructor as the first statement. Since there is cyclic dependency it will go into infinite loop.