Minkowski decompositions for generalized associahedra of acyclic type

We give an explicit subword complex description of the generators type cone g-vector fan a finite cluster algebra with acyclic initial seed. This yields in particular Newton polytopes F-polynomials terms complexes as conjectured by S. Brodsky and third author. then show that is combinatorially isomorphic to totally positive part tropicalization variety D. Speyer L. Williams.