In the state of Arizona, a hair stylist is a duly licensed personal care professional qualified by professional training and certification to provide hair cutting, styling, dyeing, and treatment services. To qualify as a hair stylist, a person must complete a course of training at a state-approved educational facility, pass an examination, and complete a period of apprenticeship. These requirements are ostensibly intended to protect the public against incompetent, unsanitary, and unprofessional hair-care service providers. Felicia Robbins is a 37-year-old Arizona resident who has been cutting hair in her home salon for more than 15 years without a license. She has a large and happy group of satisfied customers and, because she has no student loans to pay off, charges slightly below the market rate for most services. According to one of her customers, "Felicia is the most talented hair artist I have ever seen and I have seen a lot." Recently the Arizona Board of Public Health sent Ms. Robbins a cease and desist notice ordering her to close her business or face a steep fine and possible criminal charges. Ms. Robbins in turn filed suit challenging Arizona's licensing laws as unconstitutional discrimination against qualified, unlicensed hair stylists in violation of the Equal Protection Clause. Is her suit likely to prevail?

What would be both parties arguments in a court of law?