YES

TRS:

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

linear polynomial interpretations on N:

  d_A(x1) = 2
  d#_A(x1) = x1 + 4
  e_A(x1) = x1 + 1
  e#_A(x1) = 2
  u_A(x1) = 1
  u#_A(x1) = 3
  c_A(x1) = 0
  c#_A(x1) = 2
  b_A(x1) = 0
  b#_A(x1) = 1
  v_A(x1) = x1
  v#_A(x1) = x1
  a_A(x1) = 0
  a#_A(x1) = 0

precedence:

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