YES
O(n^5)
TRS:
 {g(a(), x) -> f(b(), x),
  f(a(), x) -> g(a(), x),
  f(a(), x) -> f(b(), x)}
 DUP: We consider a non-duplicating system.
  Trs:
   {g(a(), x) -> f(b(), x),
    f(a(), x) -> g(a(), x),
    f(a(), x) -> f(b(), x)}
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
         [0]
   [b] = [0]
         [0]
         [0]
   
       [X9]  [X4]    [1 0 0 1 1][X9]   [1 0 0 0 0][X4]   [0]
       [X8]  [X3]    [0 0 0 0 0][X8]   [0 0 0 0 0][X3]   [0]
   [f]([X7], [X2]) = [0 0 0 1 0][X7] + [0 0 0 0 0][X2] + [0]
       [X6]  [X1]    [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
       [X5]  [X0]    [0 0 0 0 0][X5]   [0 0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [a] = [0]
         [1]
         [1]
   
       [X9]  [X4]    [1 0 0 0 1][X9]   [1 0 0 0 0][X4]   [0]
       [X8]  [X3]    [0 0 0 0 0][X8]   [0 0 0 0 0][X3]   [0]
   [g]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0]
       [X6]  [X1]    [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
       [X5]  [X0]    [0 0 0 0 0][X5]   [0 0 0 0 0][X0]   [0]
   
   
   Qed