YES
O(n^4)
TRS:
 {
   f(a(), a()) -> f(a(), b()),
   f(a(), b()) -> f(s(a()), c()),
  f(s(X), c()) -> f(X, c()),
   f(c(), c()) -> f(a(), a())
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
     f(a(), a()) -> f(a(), b()),
     f(a(), b()) -> f(s(a()), c()),
    f(s(X), c()) -> f(X, c()),
     f(c(), c()) -> f(a(), a())
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [3]
         [0]
   [c] = [0]
         [1]
   
       [X3]    [1 0 0 2][X3]   [1]
       [X2]    [0 0 0 0][X2]   [0]
   [s]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
         [3]
         [1]
   [b] = [0]
         [1]
   
         [0]
         [2]
   [a] = [2]
         [0]
   
       [X7]  [X3]    [1 0 0 2][X7]   [1 2 2 1][X3]   [0]
       [X6]  [X2]    [0 0 0 0][X6]   [0 0 0 0][X2]   [0]
   [f]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
   
   Qed