YES

---- CR(R)
---- [Knuth and Bendix, 1970]
R:
b(c(x)) -> a(x)
b(b(x)) -> a(c(x))
a(x) -> c(b(x))
c(c(c(x))) -> b(x)
CP(R):
b(a(___y3)) -> a(c(c(___y3)))
b(a(c(___y11))) -> a(c(b(___y11)))
b(b(___y25)) -> a(c(c(___y25)))
c(b(___y31)) -> b(c(___y31))
c(c(b(___y31))) -> b(c(c(___y31)))