YES

3 decompositions
 #0 -----------
   1: F(x,y) -> c(y)

 #1 -----------
   2: G(x) -> x

 #2 -----------
   3: f(x) -> g(x)
   4: g(x) -> c(x)

@Mutually Orthogonal
--- R
   1: F(x,y) -> c(y)

--- S
   1: F(x,y) -> c(y)


@Mutually Orthogonal
--- R
   2: G(x) -> x

--- S
   2: G(x) -> x


@Mutually Orthogonal
--- R
   3: f(x) -> g(x)
   4: g(x) -> c(x)

--- S
   3: f(x) -> g(x)
   4: g(x) -> c(x)