YES

1 decompositions
 #0 -----------
   1: a() -> b()
   2: a() -> c()
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()
   7: d() -> e()
   8: g(x) -> h(a())
   9: h(x) -> e()

@--testing feature--
--- R
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()

--- S
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()