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Recursion can be conveniently modeled with left-linear positive/ negative-conditional term rewriting systems, provided that nontermination, non-trivial critical overlaps, non-right-stability, nonnormality, and extra variables are admitted. For such systems we present novel sufficient criteria for shallow confluence and arrive at the first decidable confluence criterion admitting nontrivial critical overlaps. To this end, we restrict the introduction of extra variables of right-hand sides todoi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq