Unique decomposition has been a subject of interest in process algebra for a long time (for example in BPP  or CCS [11,13]), as it provides a normal form with useful cancellation properties. We provide two parallel decomposition results for subsets of the Applied
-Calculus: we show that any closed normed (i.e. with a finite shortest complete trace) process
can be decomposed uniquely into prime factors
with respect to strong labeled bisimilarity, i.e. such that
. We also prove that closed finite processes can be decomposed uniquely with respect to weak labeled bisimilarity.
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