YES

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

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

Label:
[a(b(c(x))) -> c(c(c(b(b(b(a(a(a(x)))))))))] = 0
[c(x) -> x] = 0