YES

(VAR x)
(RULES
  a(a(a(x))) -> a(a(x))
  b(x) -> a(x)
  c(x) -> a(x)
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  a_A(x1) = x1 + 1
  b_A(x1) = x1 + 2
  c_A(x1) = x1 + 2

weights

  w0 = 1
  w(a) = 1
  w(b) = 1
  w(c) = 2

and precedence:

b > c > a
)