Problem $2($reducible expressions$).$ In this problem you are asked to determine the reducible

expressions in each of the following lambda expressions. The format of the answer is shown in the

examples below

Examples to show the format of the answer

Example $1$: for the expressions

$!$x$.$ x x $(!$x$.$ x $)$ x $!$x$.$ x x

Your answer should be that there are no reducible expressions.

Example $2$: for the expression

$(!$x$.(!$x$.$ x $)$ x $)!$x$.$ x x

Your answer should be

$(!$x$.(!$x$.$ x $)$ x $)!$x$.$ x x

$(!$x$.$ t $)$ t$$

$(!$x$.(!$x$.$ x $)$ x $)!$x$.$ x x

$(!$x$.$ t $)$ t$$

a$.$ x $!$x$.(!$x$.!$x$.$ x x $)$ x

b$.!$x$.$ x $!$x$.$ x x

c$.!$x$.(!$y$.$ x $)!$x$.$ x x

d$.!$x$.!$x$.$ x x x

e$.(!$x$.$ x x $)(!$x$.$ x $)$ x

f$.(!$x$.(!$x$.(!$x$.$ x $)$ x $(!$x$.$ x $)$ x $)(!$x$.$ x x $)(!$x$.$ x $))$ x