YES

TRS:

  a(c(d(x))) -> c(x)
  u(b(d(d(x)))) -> b(x)
  v(a(a(x))) -> u(v(x))
  v(a(c(x))) -> u(b(d(x)))
  v(c(x)) -> b(x)
  w(a(a(x))) -> u(w(x))
  w(a(c(x))) -> u(b(d(x)))
  w(c(x)) -> b(x)

linear polynomial interpretations on N:

  a_A(x1) = x1 + 1
  a#_A(x1) = x1 + 1
  c_A(x1) = x1 + 1
  c#_A(x1) = x1 + 1
  d_A(x1) = x1
  d#_A(x1) = x1
  u_A(x1) = x1
  u#_A(x1) = x1
  b_A(x1) = x1 + 1
  b#_A(x1) = x1 + 1
  v_A(x1) = x1
  v#_A(x1) = x1
  w_A(x1) = x1
  w#_A(x1) = x1

precedence:

  a > c = b > v = w > d = u