Before revision:  We provide an extension of the decomposition approach for learning Bayesian networks (BNs) proposed by (Xie et. al.) to learn AMP CGs , which include BNs as a special case, under the faithfulness assumption and prove its correctness using the minimal separator results. The advantages of this decomposition approach hold in the more general setting: reduced complexity and increased power of computational independence tests. In addition, we show that the PC-like algorithm  is order-dependent, in the sense that the output can depend on the order in which the variables are given.
After revision:  To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order-dependent, in the sense that the output can depend on the order in which the variables are given.