In 1986, Niwi nski 13] showed that the alternation hierarchy of the-calculus on binary trees without intersection was strict. But the xed-point terms he considered for proving this result are all equivalent to coB uchi terms (i.e. in 2) with intersection. Since then, the question of the strictness of the hierarchy of the-calculus on binary trees with intersection was open 4, 14]. Recently, and ...