YES

Problem:
 r(e(x1)) -> w(r(x1))
 i(t(x1)) -> e(r(x1))
 e(w(x1)) -> r(i(x1))
 t(e(x1)) -> r(e(x1))
 w(r(x1)) -> i(t(x1))
 e(r(x1)) -> e(w(x1))
 r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [i](x0) = x0,
   
   [t](x0) = 3x0,
   
   [w](x0) = 1x0,
   
   [r](x0) = 2x0,
   
   [e](x0) = 1x0
  orientation:
   r(e(x1)) = 3x1 >= 3x1 = w(r(x1))
   
   i(t(x1)) = 3x1 >= 3x1 = e(r(x1))
   
   e(w(x1)) = 2x1 >= 2x1 = r(i(x1))
   
   t(e(x1)) = 4x1 >= 3x1 = r(e(x1))
   
   w(r(x1)) = 3x1 >= 3x1 = i(t(x1))
   
   e(r(x1)) = 3x1 >= 2x1 = e(w(x1))
   
   r(i(t(e(r(x1))))) = 8x1 >= 8x1 = e(w(r(i(t(e(x1))))))
  problem:
   r(e(x1)) -> w(r(x1))
   i(t(x1)) -> e(r(x1))
   e(w(x1)) -> r(i(x1))
   w(r(x1)) -> i(t(x1))
   r(i(t(e(r(x1))))) -> e(w(r(i(t(e(x1))))))
  String Reversal Processor:
   e(r(x1)) -> r(w(x1))
   t(i(x1)) -> r(e(x1))
   w(e(x1)) -> i(r(x1))
   r(w(x1)) -> t(i(x1))
   r(e(t(i(r(x1))))) -> e(t(i(r(w(e(x1))))))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]  
     [i](x0) = [0 0 0]x0
               [0 1 0]  ,
     
               [1 0 1]     [0]
     [t](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 1 0]     [0]
     [w](x0) = [0 0 0]x0 + [0]
               [1 0 0]     [1],
     
               [1 1 0]     [0]
     [r](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 0]  
     [e](x0) = [0 1 0]x0
               [0 0 0]  
    orientation:
                [1 1 0]     [0]    [1 1 0]     [0]           
     e(r(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = r(w(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                [1 1 0]     [0]    [1 1 0]     [0]           
     t(i(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = r(e(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                [1 1 0]     [0]    [1 1 0]     [0]           
     w(e(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = i(r(x1))
                [1 0 0]     [1]    [0 0 0]     [1]           
     
                [1 1 0]     [0]    [1 1 0]     [0]           
     r(w(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = t(i(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                         [1 1 0]     [2]    [1 1 0]     [1]                       
     r(e(t(i(r(x1))))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = e(t(i(r(w(e(x1))))))
                         [0 0 0]     [0]    [0 0 0]     [0]                       
    problem:
     e(r(x1)) -> r(w(x1))
     t(i(x1)) -> r(e(x1))
     w(e(x1)) -> i(r(x1))
     r(w(x1)) -> t(i(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
                [0  -&]  
      [i](x0) = [-& 1 ]x0,
      
                [0 1]  
      [t](x0) = [2 2]x0,
      
                [1  -&]  
      [w](x0) = [1  2 ]x0,
      
                [0 0]  
      [r](x0) = [0 1]x0,
      
                [0 1]  
      [e](x0) = [0 2]x0
     orientation:
                 [1 2]      [1 2]             
      e(r(x1)) = [2 3]x1 >= [2 3]x1 = r(w(x1))
      
                 [0 2]      [0 2]             
      t(i(x1)) = [2 3]x1 >= [1 3]x1 = r(e(x1))
      
                 [1 2]      [0 0]             
      w(e(x1)) = [2 4]x1 >= [1 2]x1 = i(r(x1))
      
                 [1 2]      [0 2]             
      r(w(x1)) = [2 3]x1 >= [2 3]x1 = t(i(x1))
     problem:
      e(r(x1)) -> r(w(x1))
      t(i(x1)) -> r(e(x1))
      r(w(x1)) -> t(i(x1))
     String Reversal Processor:
      r(e(x1)) -> w(r(x1))
      i(t(x1)) -> e(r(x1))
      w(r(x1)) -> i(t(x1))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                  [1 1 1]     [0]
        [i](x0) = [0 0 1]x0 + [0]
                  [1 1 1]     [1],
        
                  [1 0 0]  
        [t](x0) = [0 0 1]x0
                  [1 0 1]  ,
        
                  [1 0 1]     [1]
        [w](x0) = [1 0 0]x0 + [0]
                  [1 0 1]     [1],
        
                  [1 0 1]  
        [r](x0) = [1 0 0]x0
                  [1 0 1]  ,
        
                  [1 0 1]     [0]
        [e](x0) = [0 0 1]x0 + [0]
                  [1 0 1]     [1]
       orientation:
                   [2 0 2]     [1]    [2 0 2]     [1]           
        r(e(x1)) = [1 0 1]x1 + [0] >= [1 0 1]x1 + [0] = w(r(x1))
                   [2 0 2]     [1]    [2 0 2]     [1]           
        
                   [2 0 2]     [0]    [2 0 2]     [0]           
        i(t(x1)) = [1 0 1]x1 + [0] >= [1 0 1]x1 + [0] = e(r(x1))
                   [2 0 2]     [1]    [2 0 2]     [1]           
        
                   [2 0 2]     [1]    [2 0 2]     [0]           
        w(r(x1)) = [1 0 1]x1 + [0] >= [1 0 1]x1 + [0] = i(t(x1))
                   [2 0 2]     [1]    [2 0 2]     [1]           
       problem:
        r(e(x1)) -> w(r(x1))
        i(t(x1)) -> e(r(x1))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
                   [2  1 ]  
         [i](x0) = [-& 3 ]x0,
         
                   [2 2]  
         [t](x0) = [1 0]x0,
         
                     
         [w](x0) = x0,
         
                   [0  -&]  
         [r](x0) = [0  0 ]x0,
         
                   [0  -&]  
         [e](x0) = [2  2 ]x0
        orientation:
                    [0  -&]      [0  -&]             
         r(e(x1)) = [2  2 ]x1 >= [0  0 ]x1 = w(r(x1))
         
                    [4 4]      [0  -&]             
         i(t(x1)) = [4 3]x1 >= [2  2 ]x1 = e(r(x1))
        problem:
         r(e(x1)) -> w(r(x1))
        Arctic Interpretation Processor:
         dimension: 3
         interpretation:
                    [0  0  -&]  
          [w](x0) = [0  2  1 ]x0
                    [0  -& 0 ]  ,
          
                    [1  0  0 ]  
          [r](x0) = [0  -& 0 ]x0
                    [-& 0  0 ]  ,
          
                    [2 0 2]  
          [e](x0) = [1 2 0]x0
                    [3 3 3]  
         orientation:
                     [3 3 3]      [1 0 0]             
          r(e(x1)) = [3 3 3]x1 >= [2 1 2]x1 = w(r(x1))
                     [3 3 3]      [1 0 0]             
         problem:
          
         Qed