Abstract
We study OI and IO one-pass reduction sequences with term rewritesystems. We present second order decidability and undecidabilityresults on recognizable tree languages and one-pass reductions. Forleft-linear TRSs, the second order OI inclusion problem and the secondorder OI reachability problem are decidable, the second order OIjoinability problem is undecidable. For right-linear TRSs, the secondorder common IO ancestor problem is undecidable.
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