Alonzo/factorial_2.txt at master · maxpohlmann/Alonzo · GitHub

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λ$ Y FACT 2
λ> (((λf.((λx.(f (x x))) (λx.(f (x x))))) (λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x)))))) (λf x.(f (f x))))
α> (((λf.((λx''.(f (x'' x''))) (λx''.(f (x'' x''))))) (λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x)))))) (λf x.(f (f x))))
β> (((λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x''))) (λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x'')))) (λf x.(f (f x))))
α> (((λx''.((λf'' x'''.((((λn'.((n' (λz' x'''' y'.y')) (λx'''' y'.x''''))) x''') (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) x''') (f'' ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) x'''))))) (x'' x''))) (λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x'')))) (λf x.(f (f x))))
β> (((λf'' x'''.((((λn'.((n' (λz' x'''' y'.y')) (λx'''' y'.x''''))) x''') (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) x''') (f'' ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) x'''))))) ((λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x''))) (λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x''))))) (λf x.(f (f x))))
β> ((λx'''.((((λn'.((n' (λz' x'''' y'.y')) (λx'''' y'.x''''))) x''') (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) x''') (((λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x''))) (λx''.((λf x.((((λn.((n (λz x' y.y)) (λx' y.x'))) x) (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x) (f ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) x'''))))) (λf x.(f (f x))))
α> ((λx'''.((((λn'.((n' (λz' x'''' y'.y')) (λx'''' y'.x''''))) x''') (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) x''') (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) x'''))))) (λf x.(f (f x))))
β> ((((λn'.((n' (λz' x'''' y'.y')) (λx'''' y'.x''''))) (λf x.(f (f x)))) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> (((((λf x.(f (f x))) (λz' x'''' y'.y')) (λx'''' y'.x'''')) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> ((((λx.((λz' x'''' y'.y') ((λz' x'''' y'.y') x))) (λx'''' y'.x'''')) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
α> ((((λx.((λz' x''''' y''.y'') ((λz' x''''' y''.y'') x))) (λx'''' y'.x'''')) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> ((((λz' x''''' y''.y'') ((λz' x''''' y''.y'') (λx'''' y'.x''''))) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
α> ((((λz' x'''''' y'''.y''') ((λz' x''''' y''.y'') (λx'''' y'.x''''))) (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> (((λx'''''' y'''.y''') (λf''' x''''.(f''' x''''))) (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> ((λy'''.y''') (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))
β> (((λx'''' y' z'.(x'''' (y' z'))) (λf x.(f (f x)))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))
β> ((λy' z'.((λf x.(f (f x))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))
α> ((λy' z'.((λf'''' x'''.(f'''' (f'''' x'''))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))
β> (λz'.((λf'''' x'''.(f'''' (f'''' x'''))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z')))
β> (λz' x'''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.(((((λx''.((λf''' x''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (f''' ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((λf''' x''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (f''' ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) ((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((λx''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((((λx''''''.((((λn''.((n'' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) x''''''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λn''.((n'' (λz' x''' y'.y')) (λx''' y'.x'''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))) (λz' x''' y'.y')) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((((λf''' x''''.((((λf x.(f (f x))) (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λz' x''' y'.y')) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λx''''.((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''' y'.y'))))) (λu'.x'''')) (λu'.u'))) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((((((λx''''.((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''''' y''.y''))))) (λu'.x'''')) (λu'.u'))) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''''' y''.y''))))) (λu' x''' y'.x''')) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((((λx.((λg' h'.(h' (g' (λz' x''''' y''.y'')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) x))) (λu' x''' y'.x''')) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((((λg' h'.(h' (g' (λz' x''''' y''.y'')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x'''))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.(((((((λg' h''.(h'' (g' (λz'' x'''''' y'''.y''')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x'''))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λh''.(h'' (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x''')) (λz'' x'''''' y'''.y''')))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((((((λh''.(h'' (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y''')))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λu'.u') (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y'''))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λh'.(h' ((λu'' x''' y'.x''') (λz' x''''' y''.y'')))) (λz'' x'''''' y'''.y''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((((λz'' x'''''' y'''.y''') ((λu'' x''' y'.x''') (λz' x''''' y''.y''))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((λx'''''' y'''.y''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((λy'''.y''') (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((λy' z'.(((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((((λy' z'.(((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((λz'.(((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))) z') (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((((λn''' f'''''' x'''''''.(((n''' (λg''' h'''.(h''' (g''' f'''''')))) (λu'''.x''''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(((λf'''''' x'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' f'''''')))) (λu'''.x''''''')) (λu'''.u'''))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((λx'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))))) (λu'''.x''''''')) (λu'''.u'''))) (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.((λx'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))) (λu'''.x''''''')) (λu'''.u'''))) (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))) (λu'''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x'''))) (λu'''.u''')))
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β> (λz' x'''.(((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) ((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu'''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))) (λu'''.u''')))
α> (λz' x'''.(((λg''' h'''''.(h''''' (g''' ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z')))) ((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu'''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))) (λu'''.u''')))
β> (λz' x'''.((λh'''''.(h''''' (((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu'''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x'''))) ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z')))) (λu'''.u''')))
α> (λz' x'''.((λh'''''.(h''''' (((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x'''))) ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z')))) (λu'''.u''')))
β> (λz' x'''.((λu'''.u''') (((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x'''))) ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z'))))
β> (λz' x'''.(((λg''' h'''.(h''' (g''' ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) (λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x'''))) ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z')))
β> (λz' x'''.((λh'''.(h''' ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z')))) ((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z')))
β> (λz' x'''.(((((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
α> (λz' x'''.(((((λx'''''''''''.((λf'''''''''' x''''''''''''''.((((λn'''''.((n''''' (λz'''' x''''''''''''''' y'''.y''')) (λx''''''''''''''' y'''.x'''''''''''''''))) x'''''''''''''') (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) x'''''''''''''') (f'''''''''' ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) x''''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.(((((λf'''''''''' x''''''''''''''.((((λn'''''.((n''''' (λz'''' x''''''''''''''' y'''.y''')) (λx''''''''''''''' y'''.x'''''''''''''''))) x'''''''''''''') (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) x'''''''''''''') (f'''''''''' ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) x''''''''''''''))))) ((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.((((λx''''''''''''''.((((λn'''''.((n''''' (λz'''' x''''''''''''''' y'''.y''')) (λx''''''''''''''' y'''.x'''''''''''''''))) x'''''''''''''') (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) x'''''''''''''') (((λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf'''''''' x''''''''''''.((((λn''''.((n'''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''' ((λn'''' f''''''''' x'''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x''''''''''''')) (λu'''''.u'''''))) x''''''''''''))))) (x''''''''''' x''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) x''''''''''''''))))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
α> (λz' x'''.((((λx''''''''''''''.((((λn'''''.((n''''' (λz'''' x''''''''''''''' y'''.y''')) (λx''''''''''''''' y'''.x'''''''''''''''))) x'''''''''''''') (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) x'''''''''''''') (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) x''''''''''''''))))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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α> (λz' x'''.(((((((((λn'''' f''''''''' x''''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''''''')))) (λu'''''.x'''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))) (λg'''''' h'''''''.(h''''''' (g'''''' (λz'''' x'''''''''''''''' y''''.y''''))))) (λu'''''' x''''''''''''''' y'''.x''''''''''''''')) (λu''''''.u'''''')) (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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β> (λz' x'''.((((((((λg''''' h''''''.(h'''''' (g''''' (λg'''''' h'''''''.(h''''''' (g'''''' (λz'''' x'''''''''''''''' y''''.y''''))))))) (λu''''''' u'''''' x''''''''''''''' y'''.x''''''''''''''')) (λg''''''' h'''''''''.(h''''''''' (g''''''' (λz''''' x''''''''''''''''' y'''''.y'''''))))) (λu''''''.u'''''')) (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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β> (λz' x'''.(((((((λg''''''' h'''''''''.(h''''''''' (g''''''' (λz''''' x''''''''''''''''' y'''''.y''''')))) ((λu''''''' u'''''' x''''''''''''''' y'''.x''''''''''''''') (λg'''''' h'''''''.(h''''''' (g'''''' (λz'''' x'''''''''''''''' y''''.y'''')))))) (λu''''''.u'''''')) (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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α> (λz' x'''.((((((λh'''''''''.(h''''''''' (((λu''''''' u'''''''' x''''''''''''''' y'''.x''''''''''''''') (λg'''''' h'''''''.(h''''''' (g'''''' (λz'''' x'''''''''''''''' y''''.y''''))))) (λz''''' x''''''''''''''''' y'''''.y''''')))) (λu''''''.u'''''')) (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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β> (λz' x'''.(((((((λu''''''' u'''''''' x''''''''''''''' y'''.x''''''''''''''') (λg'''''' h'''''''.(h''''''' (g'''''' (λz'''' x'''''''''''''''' y''''.y''''))))) (λz''''' x''''''''''''''''' y'''''.y''''')) (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
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β> (λz' x'''.(((((λx''''''''''''''' y'''.x''''''''''''''') (λf''''''''''' x'''''''''''''''.(f''''''''''' x'''''''''''''''))) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.((((λy''' f''''''''''' x'''''''''''''''.(f''''''''''' x''''''''''''''')) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
α> (λz' x'''.((((λy''' f'''''''''''' x'''''''''''''''''.(f'''''''''''' x''''''''''''''''')) (((λx''''''''''''''' y''' z''''.(x''''''''''''''' (y''' z''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x''''''''''')))))) (((λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x''''''''''''''''))) (λx''''''''''''''''.((λf'''''''''' x''''''''''''.((((λn''''''.((n'''''' (λz''' x''''''''''''' y''.y'')) (λx''''''''''''' y''.x'''''''''''''))) x'''''''''''') (λf''''''''' x'''''''''''''.(f''''''''' x'''''''''''''))) (((λx''''''''''''' y'' z'''.(x''''''''''''' (y'' z'''))) x'''''''''''') (f'''''''''' ((λn'''''' f''''''''' x'''''''''''''.(((n'''''' (λg''''''' h''''''''.(h'''''''' (g''''''' f''''''''')))) (λu'''''''.x''''''''''''')) (λu'''''''.u'''''''))) x''''''''''''))))) (x'''''''''''''''' x'''''''''''''''')))) ((λn''''' f''''''''''' x'''''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f''''''''''')))) (λu''''''.x''''''''''''''')) (λu''''''.u''''''))) ((λn'''' f''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) ((λn'''' f'''''''' x'''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x''''''''''')) (λu'''''.u'''''))) (λf'''''''' x'''''''''''.(f'''''''' (f'''''''' x'''''''''''))))))))) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.(((λf'''''''''''' x'''''''''''''''''.(f'''''''''''' x''''''''''''''''')) z') ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.((λx'''''''''''''''''.(z' x''''''''''''''''')) ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.(z' ((λu''''''.(((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')) ((((λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x''''''''))) (λx''''''''.((λf'''''' x'''''''''.((((λn'''.((n''' (λz'' x'''''''''' y'.y')) (λx'''''''''' y'.x''''''''''))) x''''''''') (λf''''''' x''''''''''.(f''''''' x''''''''''))) (((λx'''''''''' y' z''.(x'''''''''' (y' z''))) x''''''''') (f'''''' ((λn''' f''''''' x''''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f''''''')))) (λu''''.x'''''''''')) (λu''''.u''''))) x'''''''''))))) (x'''''''' x'''''''')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn''' f'''''' x''''''''.(((n''' (λg'''' h''''.(h'''' (g'''' f'''''')))) (λu''''.x'''''''')) (λu''''.u''''))) (λf'''''' x''''''''.(f'''''' (f'''''' x'''''''')))))) z'))))
β> (λz' x'''.(z' (((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.(z' (((((λx''.((λf''' x''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (f''' ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(z' (((((λf''' x''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (f''' ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) ((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(z' ((((λx''''''.((((λn'.((n' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn' f'''' x'''.(((n' (λg' h'.(h' (g' f'''')))) (λu'.x''')) (λu'.u'))) x''''''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
α> (λz' x'''.(z' ((((λx''''''.((((λn''.((n'' (λz' x''' y'.y')) (λx''' y'.x'''))) x'''''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) x'''''') (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) x''''''))))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) z') x''')))
β> (λz' x'''.(z' ((((((λn''.((n'' (λz' x''' y'.y')) (λx''' y'.x'''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))) (λz' x''' y'.y')) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((((λf''' x''''.((((λf x.(f (f x))) (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λz' x''' y'.y')) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((λx''''.((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''' y'.y'))))) (λu'.x'''')) (λu'.u'))) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
α> (λz' x'''.(z' ((((((λx''''.((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''''' y''.y''))))) (λu'.x'''')) (λu'.u'))) (λx''' y'.x''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((((λf x.(f (f x))) (λg' h'.(h' (g' (λz' x''''' y''.y''))))) (λu' x''' y'.x''')) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((((λx.((λg' h'.(h' (g' (λz' x''''' y''.y'')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) x))) (λu' x''' y'.x''')) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((((λg' h'.(h' (g' (λz' x''''' y''.y'')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x'''))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
α> (λz' x'''.(z' (((((((λg' h''.(h'' (g' (λz'' x'''''' y'''.y''')))) ((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x'''))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((λh''.(h'' (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu' x''' y'.x''')) (λz'' x'''''' y'''.y''')))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
α> (λz' x'''.(z' ((((((λh''.(h'' (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y''')))) (λu'.u')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((λu'.u') (((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y'''))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((((λg' h'.(h' (g' (λz' x''''' y''.y'')))) (λu'' x''' y'.x''')) (λz'' x'''''' y'''.y''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((λh'.(h' ((λu'' x''' y'.x''') (λz' x''''' y''.y'')))) (λz'' x'''''' y'''.y''')) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((((λz'' x'''''' y'''.y''') ((λu'' x''' y'.x''') (λz' x''''' y''.y''))) (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((λx'''''' y'''.y''') (λf'''' x'''.(f'''' x'''))) (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' ((((λy'''.y''') (((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))))) z') x''')))
β> (λz' x'''.(z' (((((λx''' y' z'.(x''' (y' z'))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') x''')))
β> (λz' x'''.(z' ((((λy' z'.(((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') x''')))
α> (λz' x'''.(z' ((((λy' z'.(((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (y' z'))) (((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x))))))) z') x''')))
β> (λz' x'''.(z' (((λz'.(((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))) z') x''')))
β> (λz' x'''.(z' ((((λn''' f''''' x''''''.(((n''' (λg''' h'''.(h''' (g''' f''''')))) (λu'''.x'''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) x''')))
α> (λz' x'''.(z' ((((λn''' f'''''' x'''''''.(((n''' (λg''' h'''.(h''' (g''' f'''''')))) (λu'''.x''''''')) (λu'''.u'''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) x''')))
β> (λz' x'''.(z' (((λf'''''' x'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' f'''''')))) (λu'''.x''''''')) (λu'''.u'''))) ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')) x''')))
β> (λz' x'''.(z' ((λx'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x'''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))))) (λu'''.x''''''')) (λu'''.u'''))) x''')))
α> (λz' x'''.(z' ((λx'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))))) (λu'''.x''''''')) (λu'''.u'''))) x''')))
β> (λz' x'''.(z' ((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z'))))) (λu'''.x''')) (λu'''.u'''))))
β> (λz' x'''.(z' (((λx''''''.((λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))) ((λg''' h'''.(h''' (g''' ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))) x''''''))) (λu'''.x''')) (λu'''.u'''))))
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β> (λz' x'''.(z' (((((λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x''''''))) (λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x'''''')))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' (((((λx''''''.((λf''''''' x''''''''.((((λn''''.((n'''' (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x''''''''''))) x'''''''') (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) x'''''''') (f''''''' ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) x''''''''))))) (x'''''' x''''''))) (λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x'''''')))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((λf''''''' x''''''''.((((λn''''.((n'''' (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x''''''''''))) x'''''''') (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) x'''''''') (f''''''' ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) x''''''''))))) ((λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x''''''))) (λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x''''''))))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((λx''''''''.((((λn''''.((n'''' (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x''''''''''))) x'''''''') (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) x'''''''') (((λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x''''''))) (λx''''''.((λf''''' x'''''''.((((λn'''.((n''' (λz'' x''''''''' y'.y')) (λx''''''''' y'.x'''''''''))) x''''''') (λf'''''' x'''''''''.(f'''''' x'''''''''))) (((λx''''''''' y' z''.(x''''''''' (y' z''))) x''''''') (f''''' ((λn''' f'''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''''')) (λu''''.u''''))) x'''''''))))) (x'''''' x'''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) x''''''''))))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((λx''''''''.((((λn''''.((n'''' (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x''''''''''))) x'''''''') (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) x'''''''') (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) x''''''''))))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((λn''''.((n'''' (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x''''''''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))) (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x'''''''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((((((λn''' f'''''' x'''''''''.(((n''' (λg''''' h''''''.(h'''''' (g''''' f'''''')))) (λu'''''.x''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))) (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x'''''''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λf'''''' x'''''''''.(((((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (λg''''' h''''''.(h'''''' (g''''' f'''''')))) (λu'''''.x''''''''')) (λu'''''.u'''''))) (λz''' x'''''''''' y''.y'')) (λx'''''''''' y''.x'''''''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((λx'''''''''.(((((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (λg''''' h''''''.(h'''''' (g''''' (λz''' x'''''''''' y''.y''))))) (λu'''''.x''''''''')) (λu'''''.u'''''))) (λx'''''''''' y''.x'''''''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((((λx'''''''''.(((((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λu'''''.x''''''''')) (λu'''''.u'''''))) (λx'''''''''' y''.x'''''''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λu''''' x'''''''''' y''.x'''''''''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' (((((((((λn''' f'''''' x'''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))) (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λu''''' x'''''''''' y''.x'''''''''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((((λf'''''' x'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg'''' h'''''.(h''''' (g'''' f'''''')))) (λu''''.x''''''')) (λu''''.u''''))) (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λu''''' x'''''''''' y''.x'''''''''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λx'''''''.((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y''')))))))) (λu''''.x''''''')) (λu''''.u''''))) (λu''''' x'''''''''' y''.x'''''''''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((((λf''''' x''''''.(f''''' (f''''' x''''''))) (λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y''')))))))) (λu'''' u''''' x'''''''''' y''.x'''''''''')) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((((λx''''''.((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) ((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) x''''''))) (λu'''' u''''' x'''''''''' y''.x'''''''''')) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) ((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''' u''''' x'''''''''' y''.x''''''''''))) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((((((λg'''' h'''''''.(h''''''' (g'''' (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y''''))))))) ((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''' u''''' x'''''''''' y''.x''''''''''))) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λh'''''''.(h''''''' (((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''' u''''' x'''''''''' y''.x'''''''''')) (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y''''))))))) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' (((((((λh'''''''.(h''''''' (((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''''' u''''' x'''''''''' y''.x'''''''''')) (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y''''))))))) (λu''''.u'''')) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λu''''.u'''') (((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''''' u''''' x'''''''''' y''.x'''''''''')) (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y'''')))))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((((λg'''' h'''''.(h''''' (g'''' (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λu'''''' u''''' x'''''''''' y''.x'''''''''')) (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y''''))))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λh'''''.(h''''' ((λu'''''' u''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))))) (λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y''''))))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λg'''''' h''''''''.(h'''''''' (g'''''' (λz'''' x'''''''''''' y''''.y'''')))) ((λu'''''' u''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y''')))))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((λh''''''''.(h'''''''' (((λu'''''' u''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λz'''' x'''''''''''' y''''.y'''')))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((((λh''''''''.(h'''''''' (((λu'''''' u''''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λz'''' x'''''''''''' y''''.y'''')))) (λu'''''.u''''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((λu'''''.u''''') (((λu'''''' u''''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λz'''' x'''''''''''' y''''.y''''))) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((((λu'''''' u''''''' x'''''''''' y''.x'''''''''') (λg''''' h''''''.(h'''''' (g''''' (λz''' x''''''''''' y'''.y'''))))) (λz'''' x'''''''''''' y''''.y'''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((((λu''''''' x'''''''''' y''.x'''''''''') (λz'''' x'''''''''''' y''''.y'''')) (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((((λx'''''''''' y''.x'''''''''') (λf'''''''' x''''''''''.(f'''''''' x''''''''''))) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((((λy'' f'''''''' x''''''''''.(f'''''''' x'''''''''')) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
α> (λz' x'''.(z' ((((λy'' f''''''''' x'''''''''''''.(f''''''''' x''''''''''''')) (((λx'''''''''' y'' z'''.(x'''''''''' (y'' z'''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x'''''')))))) (((λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x'''''''''''))) (λx'''''''''''.((λf''''''' x'''''''.((((λn'''''.((n''''' (λz'' x'''''''''''' y'.y')) (λx'''''''''''' y'.x''''''''''''))) x''''''') (λf'''''' x''''''''''''.(f'''''' x''''''''''''))) (((λx'''''''''''' y' z''.(x'''''''''''' (y' z''))) x''''''') (f''''''' ((λn''''' f'''''' x''''''''''''.(((n''''' (λg'''''' h'''''''.(h''''''' (g'''''' f'''''')))) (λu''''''.x'''''''''''')) (λu''''''.u''''''))) x'''''''))))) (x''''''''''' x''''''''''')))) ((λn'''' f'''''''' x''''''''''.(((n'''' (λg''''' h''''''.(h'''''' (g''''' f'''''''')))) (λu'''''.x'''''''''')) (λu'''''.u'''''))) ((λn''' f''''' x'''''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x''''''''')) (λu''''.u''''))) ((λn''' f''''' x''''''.(((n''' (λg'''' h'''''.(h''''' (g'''' f''''')))) (λu''''.x'''''')) (λu''''.u''''))) (λf''''' x''''''.(f''''' (f''''' x''''''))))))))) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (((λf''''''''' x'''''''''''''.(f''''''''' x''''''''''''')) z') ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' ((λx'''''''''''''.(z' x''''''''''''')) ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (z' ((λu'''''.x''') ((((λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x''))) (λx''.((λf'' x'''''.((((λn.((n (λz x' y.y)) (λx' y.x'))) x''''') (λf' x'.(f' x'))) (((λx' y z.(x' (y z))) x''''') (f'' ((λn f' x'.(((n (λg h.(h (g f')))) (λu.x')) (λu.u))) x'''''))))) (x'' x'')))) ((λn'' f'''' x''''''''.(((n'' (λg'' h''.(h'' (g'' f'''')))) (λu''.x'''''''')) (λu''.u''))) ((λn' f''' x''''.(((n' (λg' h'.(h' (g' f''')))) (λu'.x'''')) (λu'.u'))) (λf x.(f (f x)))))) z')))))
β> (λz' x'''.(z' (z' x''')))
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