YES

Problem:
 a(a(b(b(b(b(a(a(x1)))))))) -> a(a(c(c(a(a(b(b(x1))))))))
 a(a(c(c(x1)))) -> c(c(c(c(a(a(x1))))))
 c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1))))))

Proof:
 String Reversal Processor:
  a(a(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(c(c(a(a(x1))))))))
  c(c(a(a(x1)))) -> a(a(c(c(c(c(x1))))))
  c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1))))))
  Matrix Interpretation Processor: dim=4
   
   interpretation:
              [1 0 0 0]  
              [0 0 0 0]  
    [c](x0) = [0 0 1 0]x0
              [0 0 0 0]  ,
    
              [1 0 0 0]  
              [0 1 1 0]  
    [b](x0) = [0 0 0 0]x0
              [0 0 0 0]  ,
    
              [1 0 0 1]     [0]
              [0 1 0 0]     [0]
    [a](x0) = [1 0 0 0]x0 + [1]
              [0 1 0 0]     [0]
   orientation:
                                 [2 2 0 2]     [1]    [1 1 0 1]     [0]                             
                                 [1 1 0 1]     [1]    [1 1 0 1]     [1]                             
    a(a(b(b(b(b(a(a(x1)))))))) = [1 1 0 1]x1 + [1] >= [0 0 0 0]x1 + [0] = b(b(a(a(c(c(a(a(x1))))))))
                                 [1 1 0 1]     [1]    [0 0 0 0]     [0]                             
    
                     [1 1 0 1]     [0]    [1 0 0 0]     [0]                       
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]                       
    c(c(a(a(x1)))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 + [1] = a(a(c(c(c(c(x1))))))
                     [0 0 0 0]     [0]    [0 0 0 0]     [0]                       
    
                           [1 0 0 0]      [1 0 0 0]                         
                           [0 0 0 0]      [0 0 0 0]                         
    c(c(c(c(c(c(x1)))))) = [0 0 1 0]x1 >= [0 0 0 0]x1 = b(b(c(c(b(b(x1))))))
                           [0 0 0 0]      [0 0 0 0]                         
   problem:
    c(c(a(a(x1)))) -> a(a(c(c(c(c(x1))))))
    c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1))))))
   String Reversal Processor:
    a(a(c(c(x1)))) -> c(c(c(c(a(a(x1))))))
    c(c(c(c(c(c(x1)))))) -> b(b(c(c(b(b(x1))))))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [c](x0) = x0 + 1,
      
      [b](x0) = x0,
      
      [a](x0) = 2x0 + 1
     orientation:
      a(a(c(c(x1)))) = 4x1 + 11 >= 4x1 + 7 = c(c(c(c(a(a(x1))))))
      
      c(c(c(c(c(c(x1)))))) = x1 + 6 >= x1 + 2 = b(b(c(c(b(b(x1))))))
     problem:
      
     Qed