  It is very fundamental to study irreducible plane curve singularities in
algebraic geometry. The contents of the paper consist of three parts, called
Part[A], Part[B] and Part[C] with Good Appendix. Our aim is to prove by Part[B]
and Part[C] that a complete irreducibility algorithm for the Weierstrass
polynomial of two complex variables and the Puiseux expansions in Part[A] can
be explicitly and rigorously computable in an elementary way, as follows. For
brevity, Weierstrass polynomials may be written by W-polys throughout this
paper.
