YES

   1: a() -> b()
   2: a() -> c()
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()
   7: d() -> e()
   8: g(x1) -> h(a())
   9: h(x1) -> e()

@Rule Labeling
--- R
   1: a() -> b()
   2: a() -> c()
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()
   7: d() -> e()
   8: g(x1) -> h(a())
   9: h(x1) -> e()

--- S
   1: a() -> b()
   2: a() -> c()
   3: a() -> e()
   4: b() -> d()
   5: c() -> a()
   6: d() -> a()
   7: d() -> e()
   8: g(x1) -> h(a())
   9: h(x1) -> e()