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We give in this paper a sufficient condition under which the least fixpoint of the equation X=a+f(X)X equals the least fixpoint of the equation X=a+f(a)X. We then apply that condition to recursive logic programs containing chain rules: we translate it into a sufficient condition under which a recursive logic program containing n驴 2 recursive calls in the bodies of the rules is equivalent to a linear program containing at most one recursive call in the bodies of the rules. We conclude with a discussion comparing our condition with the other approaches to linearization studied in the literature.