  We extend the theory of initial conflicts in the framework of M-adhesive
categories to transformation rules with ACs. We first show that for rules with
ACs, conflicts are in general neither inherited from a bigger context any more,
nor is it possible to find a finite and complete subset of finite conflicts as
illustrated for the category of graphs. We define initial conflicts to be
special so-called symbolic transformation pairs, and show that they are
minimally complete (and in the case of graphs also finite) in this symbolic
way. We show that initial conflicts represent a proper subset of critical pairs
again. We moreover demonstrate that (analogous to the case of rules without
ACs) for each conflict a unique initial conflict exists representing it. We
conclude with presenting a sufficient condition illustrating important special
cases for rules with ACs, where we do not only have initial conflicts being
complete in a symbolic way, but also find complete (and in the case of graphs
also finite) subsets of conflicts in the classical sense.
