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We consider two instantiations of the SCC-recursive schema for argumentation semantics, cf2, using maximal conflict-free sets as base semantics, and stage2, using stage extensions as base semantics. Both of them have been shown to be in general of high complexity. We provide a detailed analysis of possible tractable fragments for these semantics. Moreover we present a labeling based algorithm for computing cf2 extension, which is complexity-sensitive w.r.t. one of the tractable fragments.
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