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, The transformation ? assigns to each atom ? = p + (v 1 , . . . , v k , z) on ?(V) the atom ?(?) = p(v 1

.. .. , This means that for all body atom f B = p + (v 1 , . . . , v k , z) ? body(?(?)) we know that ?(f B ) ? so-chase n (I ? , ?(?)). Hence, by induction ?(?(f B )) ? so-chase n (I, ?). Then, the trigger (?, ? ? ) semi-oblivious, and the last component of a predicate never occurs in the frontier, ?(?(f )) is also of rank n + 1. So, let an instance I on V. Let us note that ?(?(I)) = I. By what precedes so-chase(I, ?) and so-chase(?(I), ?(?)) have the same rank. Now, let an instance I ? on ?(V) and I = ?(I ? ): by what precedes the rank of so-chase(I, ?) is at least the rank of so-chase(I ? , ?(?)). Furthermore, by embedding ?(I) in I ? , we can by using similar arguments prove that the rank of so-chase, so-chase i (I ? , ?(?)) generated by a trigger (?(?), ?), it holds that p