YES
O(n^4)
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
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [w]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [v]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [u]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [b]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 1 0 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [1]
   [d]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 1 0 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [1]
   [a]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [1]
       [X2]    [0 1 0 0][X2]   [0]
   [c]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
   
   Qed