YES
O(n^2)
TRS:
 {
     a(c(d(x))) -> c(x),
  u(b(d(d(x)))) -> b(x),
        v(c(x)) -> b(x),
     v(a(c(x))) -> u(b(d(x))),
     v(a(a(x))) -> u(v(x)),
        w(c(x)) -> b(x),
     w(a(c(x))) -> u(b(d(x))),
     w(a(a(x))) -> u(w(x))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
       a(c(d(x))) -> c(x),
    u(b(d(d(x)))) -> b(x),
          v(c(x)) -> b(x),
       v(a(c(x))) -> u(b(d(x))),
       v(a(a(x))) -> u(v(x)),
          w(c(x)) -> b(x),
       w(a(c(x))) -> u(b(d(x))),
       w(a(a(x))) -> u(w(x))
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [0]
   [w]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [0]
   [v]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 1][X1]   [0]
   [u]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [0]
   [b]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [0]
   [d]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 1][X1]   [0]
   [a]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [1]
   [c]([X0]) = [0 1][X0] + [1]
   
   
   Qed