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Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that determines if a given skew-symmetrizable matrix is of such type. This algorithm generalizes the one in WG. As a corollary, we use this algorithm to determine if a given skew-symmetrizable matrix has finite mutation type.arXiv:1202.0529v2 fatcat:4xos2i54eva5lpy6r3iffhfky4