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Given a family of (W) contractions $T_1,...,T_N$ on a reflexive Banach space X we discuss unrestricted sequences $T_{r_n}\circ ...\circ T_{r_1}\left(x\right)$. We show that they converge weakly to a common fixed point, which depends only on x and not on the order of the operators $T_{r_n}$ if and only if the weak operator closed semigroups generated by $T_1,...,T_N$ are right amenable.