Let $L=\{f,g,R,S,c,d\}$ where $f$ is a unary function symbol, $g$ is a binary function symbol, $R$ is a binary relation symbol, $S$ is a ternary relation symbol, and $c$ and $d$ are constants. State whether or not each of the following are terms of $L.$ For those that are, prove it$-$ i$.$e$.,$ show how they are built up from the constants and variables. $($When citing the definition of a term, please be consistent with the way the clauses are numbered in the notes.$)$

$($a$)g(f(x_1),d)$

$($b$)g(f(x_1,d))$

$($c$)R(g(c,d),x_3)$

$($d$)d$