YES

Problem:
 strict:
  a(a(b(b(x1)))) -> x1
 weak:
  b(a(x1)) -> a(b(a(b(x1))))

Proof:
 String Reversal Processor:
  strict:
   b(b(a(a(x1)))) -> x1
  weak:
   a(b(x1)) -> b(a(b(a(x1))))
  Matrix Interpretation Processor: dim=4
   
   interpretation:
              [1 0 0 0]     [0]
              [0 0 0 0]     [0]
    [a](x0) = [0 2 1 1]x0 + [1]
              [0 0 1 0]     [0],
    
              [1 1 0 0]  
              [0 0 0 1]  
    [b](x0) = [0 1 0 0]x0
              [0 0 0 1]  
   orientation:
                     [1 2 1 1]     [1]           
                     [0 2 1 1]     [1]           
    b(b(a(a(x1)))) = [0 2 1 1]x1 + [1] >= x1 = x1
                     [0 2 1 1]     [1]           
    
               [1 1 0 0]     [0]    [1 0 0 0]                   
               [0 0 0 0]     [0]    [0 0 0 0]                   
    a(b(x1)) = [0 1 0 3]x1 + [1] >= [0 0 0 0]x1 = b(a(b(a(x1))))
               [0 1 0 0]     [0]    [0 0 0 0]                   
   problem:
    strict:
     
    weak:
     a(b(x1)) -> b(a(b(a(x1))))
   Qed