[valarauko]

My concern is not whether the nastika schools had valuable contributions to the advancement of Indian philosophy. The question was one of defining Hinduism. Within the ambit of that question, casting the net wide enough to include Ajivika and Charvaka is too broad, and one the Ancient Indians wouldn't likely have made either. For example, the Hindu acharyas were pretty clear that Buddhism and Jainism were heresies and beyond the pale, and their opinion of Charvakaism is well known. Therefore I suggest that the question is best answered by restricting to the Astika schools, a categorization the ancient commentators would likely agree with.