Reduce the following lambda expressions to $-$normal form. Show the individual reduction steps. Make sure to rename bound variables when necessary to avoid the capture of free variables.

$($a$)(z.z)(y.yy)(x.xa)$

$($b$)(xy.xyy)(a.a)b$

$($c$)(xy*xy)yz$

$($d$)(xz.xy)(xz.xyz)(x.z)$