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]   [0]
   [f]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0]
   
   
   Qed