YES

1 decompositions
 #0 -----------
   1: F(c(x)) -> G(x)
   2: G(x) -> F(x)
   3: c(x) -> x

@Strongly Commuting
--- R
   1: F(c(x)) -> G(x)
   2: G(x) -> F(x)
   3: c(x) -> x

--- S
   1: F(c(x)) -> G(x)
   2: G(x) -> F(x)
   3: c(x) -> x