YES
O(n^4)
TRS:
 {a(b(x)) -> b(a(x)),
  a(c(x)) -> x}
 DUP: We consider a non-duplicating system.
  Trs:
   {a(b(x)) -> b(a(x)),
    a(c(x)) -> x}
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [0]
   [c]([X1]) = [0 0 1 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 0 1][X3]   [1]
       [X2]    [0 1 0 0][X2]   [0]
   [a]([X1]) = [0 0 1 0][X1] + [0]
       [X0]    [0 0 0 1][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 1][X0]   [1]
   
   
   Qed