YES

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

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

  a_A(x1) = 0
  e_A(x1) = x1 + 1
  d_A(x1) = 0
  b_A(x1) = 0
  c_A(x1) = 0

weights

  w0 = 1
  w(a) = 1
  w(e) = 13
  w(d) = 23
  w(b) = 1
  w(c) = 8

and precedence:

b > d > a > e > c
)