YES(?,O(n^2))
TRS:
 {
  f(a x, a y) -> a f(x, y),
  f(b x, b y) -> b f(x, y),
  a a f(x, y) -> f(a b a b a x, a b a b a y)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    f(a x, a y) -> a f(x, y),
    f(b x, b y) -> b f(x, y),
    a a f(x, y) -> f(a b a b a x, a b a b a y)
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [1]
   [b]([X0]) = [0 0][X0] + [0]
   
       [X1]    [1 3][X1]   [1]
   [a]([X0]) = [0 1][X0] + [3]
   
       [X3]  [X1]    [1 0][X3]   [1 0][X1]   [2]
   [f]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0]
   
   
   Qed