YES

---- CR(R)
---- [Knuth and Bendix, 1970]
R:
f(a()) -> b()
f(a()) -> f(c())
a() -> d()
f(d()) -> b()
f(c()) -> b()
d() -> c()
CP(R):
b() -> f(c())
f(c()) -> b()
f(d()) -> b()
f(d()) -> f(c())
f(c()) -> b()