YES

1 decompositions
 #0 -----------
   1: a() -> c()
   2: b() -> c()
   3: f(a(),b()) -> d()
   4: f(x,c()) -> f(c(),c())
   5: f(c(),x) -> f(c(),c())
   6: d() -> f(a(),c())
   7: d() -> f(c(),b())

@Strongly Commuting
--- R
   1: a() -> c()
   2: b() -> c()
   3: f(a(),b()) -> d()
   4: f(x,c()) -> f(c(),c())
   5: f(c(),x) -> f(c(),c())
   6: d() -> f(a(),c())
   7: d() -> f(c(),b())

--- S
   1: a() -> c()
   2: b() -> c()
   3: f(a(),b()) -> d()
   4: f(x,c()) -> f(c(),c())
   5: f(c(),x) -> f(c(),c())
   6: d() -> f(a(),c())
   7: d() -> f(c(),b())