YES

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

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

  a_A(x1) = x1 + 1
  e_A(x1) = 1
  d_A(x1) = 1
  b_A(x1) = 0
  c_A(x1) = 1
  a#_A(x1) = x1
  b#_A(x1) = x1

and precedence:

a > c > d > e > b
)