YES

---- CR(R)
---- Hot decreasingness.
R:
f(f(f(x))) -> a()
f(f(a())) -> a()
f(a()) -> a()
f(f(g(g(x)))) -> f(a())
g(f(a())) -> a()
g(a()) -> a()

C:
f(f(f(x))) -> a()
f(f(a())) -> a()
f(a()) -> a()
f(f(g(g(x)))) -> f(a())
g(f(a())) -> a()
g(a()) -> a()

Label: