YES

(VAR x0)
(RULES
  w(a(a(a(a(w(x0)))))) -> a(a(a(w(a(a(a(a(a(a(x0))))))))))
  w(a(a(a(w(x0))))) -> a(a(a(a(a(w(a(a(a(x0)))))))))
  w(w(x0)) -> a(w(a(a(a(a(x0))))))
  w(a(a(a(a(a(w(x0))))))) -> a(a(w(a(x0))))
  w(a(w(x0))) -> a(a(a(a(w(a(a(x0)))))))
  c(x0) -> a(a(w(a(a(x0)))))
  w(a(a(a(a(a(a(w(x0)))))))) -> a(a(a(a(a(a(w(a(a(a(a(a(x0))))))))))))
  a(a(a(a(a(a(a(x0))))))) -> x0
  w(a(a(w(x0)))) -> a(a(a(a(a(x0)))))
  u(x0) -> a(a(a(a(a(a(x0))))))
  v(x0) -> a(a(w(a(a(a(x0))))))
  b(x0) -> w(a(a(a(a(a(a(w(a(a(x0))))))))))
)

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

  a_A(x1) = x1 + 2
  c_A(x1) = x1 + 2339
  b_A(x1) = x1 + 5844
  u_A(x1) = x1 + 15195
  v_A(x1) = x1 + 3506
  w_A(x1) = x1 + 12
  a#_A(x1) = x1
  b#_A(x1) = x1

weights

  w0 = 1
  w(a) = 84
  w(c) = 2421
  w(b) = 7095
  w(u) = 16757
  w(v) = 2507
  w(w) = 2084

and precedence:

u > b > v > w > c > a
)