YES

Problem:
 a(b(x)) -> b(b(a(x)))

Proof:
 String Reversal Processor:
  b(a(x)) -> a(b(b(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [a](x0) = [0 1 1]x0 + [1]
              [0 1 1]     [1],
    
              [1 1 1]     [1]
    [b](x0) = [0 1 0]x0 + [0]
              [0 0 1]     [0]
   orientation:
              [1 2 2]    [3]    [1 2 2]    [2]             
    b(a(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = a(b(b(x)))
              [0 1 1]    [1]    [0 1 1]    [1]             
   problem:
    
   Qed