YES

Problem:
 1(0(x1)) -> 0(0(0(1(x1))))
 0(1(x1)) -> 1(x1)
 1(1(x1)) -> 0(0(0(0(x1))))
 0(0(x1)) -> 0(x1)

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