This note presents a detailed proof of a result in the theory of concurrency semantics that is already considered folklore, namely that branching bisimilarity is an equivalence relation. The \simple proof," which in the literature is always assumed to exist, is shown to be incorrect. The proof in this note is based on the notion of a semi-branching bisimulation taken from [10]. Branching bisimi...

Slot and van Emde Boas’ weak invariance thesis states that reasonable machines can simulate each other within a polynomial overhead in time. Is λ-calculus a reasonable machine? Is there a way to measure the computational complexity of a λ-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is completely machine-independent and based o...