YES

---- CR(R)
---- Hot decreasingness.
R:
a() -> b()
a() -> c()
a() -> e()
b() -> d()
c() -> a()
d() -> a()
d() -> e()
g(x) -> h(a())
h(x) -> e()

C:
a() -> e()
b() -> d()
c() -> a()
d() -> a()

Label:
[a() -> b()] = 0
[a() -> c()] = 0
[d() -> e()] = 0
[g(x) -> h(a())] = 0
[h(x) -> e()] = 0