YES

---- CR(R)
---- Hot decreasingness.
R:
b(c(x)) -> a(x)
b(b(x)) -> a(c(x))
a(x) -> c(b(x))
c(c(c(x))) -> b(x)

C:
b(c(x)) -> a(x)
b(b(x)) -> a(c(x))
a(x) -> c(b(x))
c(c(c(x))) -> b(x)

Label: