YES

---- CR(R)
---- Rule Labeling [van Oostrom, RTA 2008].
R:
g(a()) -> f(g(a()))
g(b()) -> c(a())
a() -> b()
f(x) -> h(x)
h(x) -> c(b())

Label:
[g(a()) -> f(g(a()))] = 1
[g(b()) -> c(a())] = 0
[a() -> b()] = 1
[f(x) -> h(x)] = 1
[h(x) -> c(b())] = 0