YES(?,O(n^2))

Problem:
 a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
 f(a(x),a(y)) -> a(f(x,y))
 f(b(x),b(y)) -> b(f(x,y))

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
             [1 0]     [1]
   [b](x0) = [0 0]x0 + [0],
   
             [1 8]     [2]
   [a](x0) = [0 1]x0 + [2],
   
                           [3]
   [f](x0, x1) = x0 + x1 + [0]
  orientation:
                  [1  16]    [1  16]    [23]    [1 8]    [1 8]    [19]                                       
   a(a(f(x,y))) = [0  1 ]x + [0  1 ]y + [4 ] >= [0 0]x + [0 0]y + [4 ] = f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
   
                  [1 8]    [1 8]    [7]    [1 8]    [1 8]    [5]            
   f(a(x),a(y)) = [0 1]x + [0 1]y + [4] >= [0 1]x + [0 1]y + [2] = a(f(x,y))
   
                  [1 0]    [1 0]    [5]    [1 0]    [1 0]    [4]            
   f(b(x),b(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = b(f(x,y))
  problem:
   
  Qed