For the string $((AAx)((AAz)((p-=z)z=x))),$ choose ALL statements that apply.

a$.$ The complexity is $4$

b$.$ This is not a first$-$order formula because it contains terms that are not included in atomic formulae

c$.$ This is a Boolean formula, but not a first$-$order formula

d$.$ This is a first$-$order formula with valid formula calculation:

$z=x,p,z,(p-=z),((AAz)p-=z),(((AAz)(p-=z)z=x)),$

$((AAx)((AAz)((p-=z)z=x)))$