Click to reduce, both beta and alpha (if needed) steps will be shown.

• You may use \ for the λ symbol, and ( and ) to group lambda terms.
• A space is required to denote application.
• The scope of abstraction extends to the rightmost.
• Application is left associative.

Here are a few examples you can try:

1. (λx.λy.y) ((λx.x x) (λx.x x))
2. (λf.f (f x)) ((λx.λy.x) (λx.y))
3. (λf.λx.f (f x)) (λf.λx.f (f x)) (λx.x) (λx.x)