Problem: f (\x. z x) -> z (z a) g x -> h x x Proof: Modularity Decomposition: 0:f (\x. z x) -> z (z a) 1:g x -> h x x ----- 0:f (\x. z x) -> z (z a) Higher-Order Church Rosser Processor: f (\x. z x) -> z (z a) critical peaks: 0 Higher-Order Closedness Processor: all critical pairs are trivial Qed 1:g x -> h x x Higher-Order Church Rosser Processor: g x -> h x x critical peaks: 0 Higher-Order Closedness Processor: all critical pairs are trivial Qed