Problem: h 0 -> g (\x y. x (h y)) g (\x y. Z (\z. x z) y) -> Z (\z. 0) 0 Proof: Higher-Order Church Rosser Processor: h 0 -> g (\x y. x (h y)) g (\x y. Z (\z. x z) y) -> Z (\z. 0) 0 critical peaks: 0 Higher-Order Closedness Processor: all critical pairs are trivial Qed