YES

---- CR(R)
---- [Knuth and Bendix, 1970]
R:
a(s(x)) -> s(a(x))
b(a(b(s(x)))) -> a(b(s(a(x))))
b(a(b(b(x)))) -> c(s(x))
c(s(x)) -> a(b(a(b(x))))
a(b(a(a(x)))) -> b(a(b(a(x))))
CP(R):
a(b(a(s(a(___y9))))) -> b(a(b(a(s(___y9)))))
b(a(b(a(b(s(a(___y15))))))) -> c(s(a(b(s(___y15)))))
b(a(b(c(s(___y25))))) -> c(s(a(b(b(___y25)))))
a(b(a(b(a(b(a(___y49))))))) -> b(a(b(a(b(a(a(___y49)))))))