YES

Problem:
 r0(0(x1)) -> 0(r0(x1))
 r0(1(x1)) -> 1(r0(x1))
 r0(m(x1)) -> m(r0(x1))
 r1(0(x1)) -> 0(r1(x1))
 r1(1(x1)) -> 1(r1(x1))
 r1(m(x1)) -> m(r1(x1))
 r0(b(x1)) -> qr(0(b(x1)))
 r1(b(x1)) -> qr(1(b(x1)))
 0(qr(x1)) -> qr(0(x1))
 1(qr(x1)) -> qr(1(x1))
 m(qr(x1)) -> ql(m(x1))
 0(ql(x1)) -> ql(0(x1))
 1(ql(x1)) -> ql(1(x1))
 b(ql(0(x1))) -> 0(b(r0(x1)))
 b(ql(1(x1))) -> 1(b(r1(x1)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
              [1 0 0]  
   [r1](x0) = [0 1 0]x0
              [1 0 0]  ,
   
              [1 1 0]  
   [r0](x0) = [0 1 0]x0
              [1 0 0]  ,
   
             [1 1 0]     [0]
   [m](x0) = [0 1 0]x0 + [1]
             [1 0 0]     [0],
   
             [1 0 0]  
   [b](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 1 0]  
   [0](x0) = [0 1 0]x0
             [0 0 0]  ,
   
              [1 0 0]  
   [ql](x0) = [0 1 0]x0
              [0 0 0]  ,
   
              [1 0 0]  
   [qr](x0) = [0 1 0]x0
              [0 0 0]  ,
   
             [1 0 0]  
   [1](x0) = [0 1 0]x0
             [0 0 0]  
  orientation:
               [1 2 0]      [1 2 0]              
   r0(0(x1)) = [0 1 0]x1 >= [0 1 0]x1 = 0(r0(x1))
               [1 1 0]      [0 0 0]              
   
               [1 1 0]      [1 1 0]              
   r0(1(x1)) = [0 1 0]x1 >= [0 1 0]x1 = 1(r0(x1))
               [1 0 0]      [0 0 0]              
   
               [1 2 0]     [1]    [1 2 0]     [0]            
   r0(m(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = m(r0(x1))
               [1 1 0]     [0]    [1 1 0]     [0]            
   
               [1 1 0]      [1 1 0]              
   r1(0(x1)) = [0 1 0]x1 >= [0 1 0]x1 = 0(r1(x1))
               [1 1 0]      [0 0 0]              
   
               [1 0 0]      [1 0 0]              
   r1(1(x1)) = [0 1 0]x1 >= [0 1 0]x1 = 1(r1(x1))
               [1 0 0]      [0 0 0]              
   
               [1 1 0]     [0]    [1 1 0]     [0]            
   r1(m(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = m(r1(x1))
               [1 1 0]     [0]    [1 0 0]     [0]            
   
               [1 0 0]      [1 0 0]                 
   r0(b(x1)) = [0 0 0]x1 >= [0 0 0]x1 = qr(0(b(x1)))
               [1 0 0]      [0 0 0]                 
   
               [1 0 0]      [1 0 0]                 
   r1(b(x1)) = [0 0 0]x1 >= [0 0 0]x1 = qr(1(b(x1)))
               [1 0 0]      [0 0 0]                 
   
               [1 1 0]      [1 1 0]              
   0(qr(x1)) = [0 1 0]x1 >= [0 1 0]x1 = qr(0(x1))
               [0 0 0]      [0 0 0]              
   
               [1 0 0]      [1 0 0]              
   1(qr(x1)) = [0 1 0]x1 >= [0 1 0]x1 = qr(1(x1))
               [0 0 0]      [0 0 0]              
   
               [1 1 0]     [0]    [1 1 0]     [0]            
   m(qr(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = ql(m(x1))
               [1 0 0]     [0]    [0 0 0]     [0]            
   
               [1 1 0]      [1 1 0]              
   0(ql(x1)) = [0 1 0]x1 >= [0 1 0]x1 = ql(0(x1))
               [0 0 0]      [0 0 0]              
   
               [1 0 0]      [1 0 0]              
   1(ql(x1)) = [0 1 0]x1 >= [0 1 0]x1 = ql(1(x1))
               [0 0 0]      [0 0 0]              
   
                  [1 1 0]      [1 1 0]                 
   b(ql(0(x1))) = [0 0 0]x1 >= [0 0 0]x1 = 0(b(r0(x1)))
                  [0 0 0]      [0 0 0]                 
   
                  [1 0 0]      [1 0 0]                 
   b(ql(1(x1))) = [0 0 0]x1 >= [0 0 0]x1 = 1(b(r1(x1)))
                  [0 0 0]      [0 0 0]                 
  problem:
   r0(0(x1)) -> 0(r0(x1))
   r0(1(x1)) -> 1(r0(x1))
   r1(0(x1)) -> 0(r1(x1))
   r1(1(x1)) -> 1(r1(x1))
   r1(m(x1)) -> m(r1(x1))
   r0(b(x1)) -> qr(0(b(x1)))
   r1(b(x1)) -> qr(1(b(x1)))
   0(qr(x1)) -> qr(0(x1))
   1(qr(x1)) -> qr(1(x1))
   m(qr(x1)) -> ql(m(x1))
   0(ql(x1)) -> ql(0(x1))
   1(ql(x1)) -> ql(1(x1))
   b(ql(0(x1))) -> 0(b(r0(x1)))
   b(ql(1(x1))) -> 1(b(r1(x1)))
  String Reversal Processor:
   0(r0(x1)) -> r0(0(x1))
   1(r0(x1)) -> r0(1(x1))
   0(r1(x1)) -> r1(0(x1))
   1(r1(x1)) -> r1(1(x1))
   m(r1(x1)) -> r1(m(x1))
   b(r0(x1)) -> b(0(qr(x1)))
   b(r1(x1)) -> b(1(qr(x1)))
   qr(0(x1)) -> 0(qr(x1))
   qr(1(x1)) -> 1(qr(x1))
   qr(m(x1)) -> m(ql(x1))
   ql(0(x1)) -> 0(ql(x1))
   ql(1(x1)) -> 1(ql(x1))
   0(ql(b(x1))) -> r0(b(0(x1)))
   1(ql(b(x1))) -> r1(b(1(x1)))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                [1 0]  
     [r1](x0) = [2 0]x0,
     
                [1 0]     [0]
     [r0](x0) = [2 2]x0 + [2],
     
               [1 0]  
     [m](x0) = [2 0]x0,
     
               [1 2]     [0]
     [b](x0) = [1 1]x0 + [1],
     
                 
     [0](x0) = x0,
     
                [1 0]     [0]
     [ql](x0) = [3 1]x0 + [3],
     
                [1 0]  
     [qr](x0) = [2 0]x0,
     
                 
     [1](x0) = x0
    orientation:
                 [1 0]     [0]    [1 0]     [0]            
     0(r0(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = r0(0(x1))
     
                 [1 0]     [0]    [1 0]     [0]            
     1(r0(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = r0(1(x1))
     
                 [1 0]      [1 0]              
     0(r1(x1)) = [2 0]x1 >= [2 0]x1 = r1(0(x1))
     
                 [1 0]      [1 0]              
     1(r1(x1)) = [2 0]x1 >= [2 0]x1 = r1(1(x1))
     
                 [1 0]      [1 0]              
     m(r1(x1)) = [2 0]x1 >= [2 0]x1 = r1(m(x1))
     
                 [5 4]     [4]    [5 0]     [0]               
     b(r0(x1)) = [3 2]x1 + [3] >= [3 0]x1 + [1] = b(0(qr(x1)))
     
                 [5 0]     [0]    [5 0]     [0]               
     b(r1(x1)) = [3 0]x1 + [1] >= [3 0]x1 + [1] = b(1(qr(x1)))
     
                 [1 0]      [1 0]              
     qr(0(x1)) = [2 0]x1 >= [2 0]x1 = 0(qr(x1))
     
                 [1 0]      [1 0]              
     qr(1(x1)) = [2 0]x1 >= [2 0]x1 = 1(qr(x1))
     
                 [1 0]      [1 0]              
     qr(m(x1)) = [2 0]x1 >= [2 0]x1 = m(ql(x1))
     
                 [1 0]     [0]    [1 0]     [0]            
     ql(0(x1)) = [3 1]x1 + [3] >= [3 1]x1 + [3] = 0(ql(x1))
     
                 [1 0]     [0]    [1 0]     [0]            
     ql(1(x1)) = [3 1]x1 + [3] >= [3 1]x1 + [3] = 1(ql(x1))
     
                    [1 2]     [0]    [1 2]     [0]               
     0(ql(b(x1))) = [4 7]x1 + [4] >= [4 6]x1 + [4] = r0(b(0(x1)))
     
                    [1 2]     [0]    [1 2]                 
     1(ql(b(x1))) = [4 7]x1 + [4] >= [2 4]x1 = r1(b(1(x1)))
    problem:
     0(r0(x1)) -> r0(0(x1))
     1(r0(x1)) -> r0(1(x1))
     0(r1(x1)) -> r1(0(x1))
     1(r1(x1)) -> r1(1(x1))
     m(r1(x1)) -> r1(m(x1))
     b(r1(x1)) -> b(1(qr(x1)))
     qr(0(x1)) -> 0(qr(x1))
     qr(1(x1)) -> 1(qr(x1))
     qr(m(x1)) -> m(ql(x1))
     ql(0(x1)) -> 0(ql(x1))
     ql(1(x1)) -> 1(ql(x1))
     0(ql(b(x1))) -> r0(b(0(x1)))
     1(ql(b(x1))) -> r1(b(1(x1)))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [r1](x0) = 2x0,
      
      [r0](x0) = x0 + 2,
      
      [m](x0) = x0,
      
      [b](x0) = 8x0 + 6,
      
      [0](x0) = x0,
      
      [ql](x0) = 2x0,
      
      [qr](x0) = 2x0,
      
      [1](x0) = x0
     orientation:
      0(r0(x1)) = x1 + 2 >= x1 + 2 = r0(0(x1))
      
      1(r0(x1)) = x1 + 2 >= x1 + 2 = r0(1(x1))
      
      0(r1(x1)) = 2x1 >= 2x1 = r1(0(x1))
      
      1(r1(x1)) = 2x1 >= 2x1 = r1(1(x1))
      
      m(r1(x1)) = 2x1 >= 2x1 = r1(m(x1))
      
      b(r1(x1)) = 16x1 + 6 >= 16x1 + 6 = b(1(qr(x1)))
      
      qr(0(x1)) = 2x1 >= 2x1 = 0(qr(x1))
      
      qr(1(x1)) = 2x1 >= 2x1 = 1(qr(x1))
      
      qr(m(x1)) = 2x1 >= 2x1 = m(ql(x1))
      
      ql(0(x1)) = 2x1 >= 2x1 = 0(ql(x1))
      
      ql(1(x1)) = 2x1 >= 2x1 = 1(ql(x1))
      
      0(ql(b(x1))) = 16x1 + 12 >= 8x1 + 8 = r0(b(0(x1)))
      
      1(ql(b(x1))) = 16x1 + 12 >= 16x1 + 12 = r1(b(1(x1)))
     problem:
      0(r0(x1)) -> r0(0(x1))
      1(r0(x1)) -> r0(1(x1))
      0(r1(x1)) -> r1(0(x1))
      1(r1(x1)) -> r1(1(x1))
      m(r1(x1)) -> r1(m(x1))
      b(r1(x1)) -> b(1(qr(x1)))
      qr(0(x1)) -> 0(qr(x1))
      qr(1(x1)) -> 1(qr(x1))
      qr(m(x1)) -> m(ql(x1))
      ql(0(x1)) -> 0(ql(x1))
      ql(1(x1)) -> 1(ql(x1))
      1(ql(b(x1))) -> r1(b(1(x1)))
     String Reversal Processor:
      r0(0(x1)) -> 0(r0(x1))
      r0(1(x1)) -> 1(r0(x1))
      r1(0(x1)) -> 0(r1(x1))
      r1(1(x1)) -> 1(r1(x1))
      r1(m(x1)) -> m(r1(x1))
      r1(b(x1)) -> qr(1(b(x1)))
      0(qr(x1)) -> qr(0(x1))
      1(qr(x1)) -> qr(1(x1))
      m(qr(x1)) -> ql(m(x1))
      0(ql(x1)) -> ql(0(x1))
      1(ql(x1)) -> ql(1(x1))
      b(ql(1(x1))) -> 1(b(r1(x1)))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [r1](x0) = x0 + 2,
        
        [r0](x0) = 2x0 + 1,
        
        [m](x0) = x0,
        
        [b](x0) = x0,
        
        [0](x0) = x0 + 1,
        
        [ql](x0) = x0 + 2,
        
        [qr](x0) = x0 + 2,
        
        [1](x0) = x0
       orientation:
        r0(0(x1)) = 2x1 + 3 >= 2x1 + 2 = 0(r0(x1))
        
        r0(1(x1)) = 2x1 + 1 >= 2x1 + 1 = 1(r0(x1))
        
        r1(0(x1)) = x1 + 3 >= x1 + 3 = 0(r1(x1))
        
        r1(1(x1)) = x1 + 2 >= x1 + 2 = 1(r1(x1))
        
        r1(m(x1)) = x1 + 2 >= x1 + 2 = m(r1(x1))
        
        r1(b(x1)) = x1 + 2 >= x1 + 2 = qr(1(b(x1)))
        
        0(qr(x1)) = x1 + 3 >= x1 + 3 = qr(0(x1))
        
        1(qr(x1)) = x1 + 2 >= x1 + 2 = qr(1(x1))
        
        m(qr(x1)) = x1 + 2 >= x1 + 2 = ql(m(x1))
        
        0(ql(x1)) = x1 + 3 >= x1 + 3 = ql(0(x1))
        
        1(ql(x1)) = x1 + 2 >= x1 + 2 = ql(1(x1))
        
        b(ql(1(x1))) = x1 + 2 >= x1 + 2 = 1(b(r1(x1)))
       problem:
        r0(1(x1)) -> 1(r0(x1))
        r1(0(x1)) -> 0(r1(x1))
        r1(1(x1)) -> 1(r1(x1))
        r1(m(x1)) -> m(r1(x1))
        r1(b(x1)) -> qr(1(b(x1)))
        0(qr(x1)) -> qr(0(x1))
        1(qr(x1)) -> qr(1(x1))
        m(qr(x1)) -> ql(m(x1))
        0(ql(x1)) -> ql(0(x1))
        1(ql(x1)) -> ql(1(x1))
        b(ql(1(x1))) -> 1(b(r1(x1)))
       String Reversal Processor:
        1(r0(x1)) -> r0(1(x1))
        0(r1(x1)) -> r1(0(x1))
        1(r1(x1)) -> r1(1(x1))
        m(r1(x1)) -> r1(m(x1))
        b(r1(x1)) -> b(1(qr(x1)))
        qr(0(x1)) -> 0(qr(x1))
        qr(1(x1)) -> 1(qr(x1))
        qr(m(x1)) -> m(ql(x1))
        ql(0(x1)) -> 0(ql(x1))
        ql(1(x1)) -> 1(ql(x1))
        1(ql(b(x1))) -> r1(b(1(x1)))
        Matrix Interpretation Processor: dim=3
         
         interpretation:
                     [1 0 0]  
          [r1](x0) = [0 0 0]x0
                     [0 0 1]  ,
          
                     [1 0 0]     [1]
          [r0](x0) = [0 0 0]x0 + [0]
                     [0 0 1]     [1],
          
                    [1 0 0]  
          [m](x0) = [0 0 0]x0
                    [0 0 0]  ,
          
                    [1 0 0]  
          [b](x0) = [0 0 0]x0
                    [0 0 1]  ,
          
                    [1 0 0]  
          [0](x0) = [0 0 0]x0
                    [0 0 0]  ,
          
                     [1 0 0]  
          [ql](x0) = [1 0 0]x0
                     [0 0 1]  ,
          
                     [1 0 0]  
          [qr](x0) = [1 0 0]x0
                     [0 0 0]  ,
          
                    [1 0 1]  
          [1](x0) = [0 0 0]x0
                    [0 0 1]  
         orientation:
                      [1 0 1]     [2]    [1 0 1]     [1]            
          1(r0(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = r0(1(x1))
                      [0 0 1]     [1]    [0 0 1]     [1]            
          
                      [1 0 0]      [1 0 0]              
          0(r1(x1)) = [0 0 0]x1 >= [0 0 0]x1 = r1(0(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 1]      [1 0 1]              
          1(r1(x1)) = [0 0 0]x1 >= [0 0 0]x1 = r1(1(x1))
                      [0 0 1]      [0 0 1]              
          
                      [1 0 0]      [1 0 0]              
          m(r1(x1)) = [0 0 0]x1 >= [0 0 0]x1 = r1(m(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 0]      [1 0 0]                 
          b(r1(x1)) = [0 0 0]x1 >= [0 0 0]x1 = b(1(qr(x1)))
                      [0 0 1]      [0 0 0]                 
          
                      [1 0 0]      [1 0 0]              
          qr(0(x1)) = [1 0 0]x1 >= [0 0 0]x1 = 0(qr(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 1]      [1 0 0]              
          qr(1(x1)) = [1 0 1]x1 >= [0 0 0]x1 = 1(qr(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 0]      [1 0 0]              
          qr(m(x1)) = [1 0 0]x1 >= [0 0 0]x1 = m(ql(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 0]      [1 0 0]              
          ql(0(x1)) = [1 0 0]x1 >= [0 0 0]x1 = 0(ql(x1))
                      [0 0 0]      [0 0 0]              
          
                      [1 0 1]      [1 0 1]              
          ql(1(x1)) = [1 0 1]x1 >= [0 0 0]x1 = 1(ql(x1))
                      [0 0 1]      [0 0 1]              
          
                         [1 0 1]      [1 0 1]                 
          1(ql(b(x1))) = [0 0 0]x1 >= [0 0 0]x1 = r1(b(1(x1)))
                         [0 0 1]      [0 0 1]                 
         problem:
          0(r1(x1)) -> r1(0(x1))
          1(r1(x1)) -> r1(1(x1))
          m(r1(x1)) -> r1(m(x1))
          b(r1(x1)) -> b(1(qr(x1)))
          qr(0(x1)) -> 0(qr(x1))
          qr(1(x1)) -> 1(qr(x1))
          qr(m(x1)) -> m(ql(x1))
          ql(0(x1)) -> 0(ql(x1))
          ql(1(x1)) -> 1(ql(x1))
          1(ql(b(x1))) -> r1(b(1(x1)))
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                      [1 0 0]     [0]
           [r1](x0) = [0 0 1]x0 + [1]
                      [0 1 0]     [0],
           
                     [1 1 1]  
           [m](x0) = [1 1 0]x0
                     [1 0 1]  ,
           
                     [1 0 0]     [1]
           [b](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [0],
           
                       
           [0](x0) = x0
                       ,
           
                        
           [ql](x0) = x0
                        ,
           
                        
           [qr](x0) = x0
                        ,
           
                     [1 0 0]     [0]
           [1](x0) = [0 0 1]x0 + [1]
                     [0 1 0]     [0]
          orientation:
                       [1 0 0]     [0]    [1 0 0]     [0]            
           0(r1(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = r1(0(x1))
                       [0 1 0]     [0]    [0 1 0]     [0]            
           
                            [0]         [0]            
           1(r1(x1)) = x1 + [1] >= x1 + [1] = r1(1(x1))
                            [1]         [1]            
           
                       [1 1 1]     [1]    [1 1 1]     [0]            
           m(r1(x1)) = [1 0 1]x1 + [1] >= [1 0 1]x1 + [1] = r1(m(x1))
                       [1 1 0]     [0]    [1 1 0]     [0]            
           
                       [1 0 0]     [1]    [1 0 0]     [1]               
           b(r1(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(1(qr(x1)))
                       [0 0 0]     [0]    [0 0 0]     [0]               
           
                                           
           qr(0(x1)) = x1 >= x1 = 0(qr(x1))
                                           
           
                       [1 0 0]     [0]    [1 0 0]     [0]            
           qr(1(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = 1(qr(x1))
                       [0 1 0]     [0]    [0 1 0]     [0]            
           
                       [1 1 1]      [1 1 1]              
           qr(m(x1)) = [1 1 0]x1 >= [1 1 0]x1 = m(ql(x1))
                       [1 0 1]      [1 0 1]              
           
                                           
           ql(0(x1)) = x1 >= x1 = 0(ql(x1))
                                           
           
                       [1 0 0]     [0]    [1 0 0]     [0]            
           ql(1(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = 1(ql(x1))
                       [0 1 0]     [0]    [0 1 0]     [0]            
           
                          [1 0 0]     [1]    [1 0 0]     [1]               
           1(ql(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = r1(b(1(x1)))
                          [0 0 0]     [0]    [0 0 0]     [0]               
          problem:
           0(r1(x1)) -> r1(0(x1))
           1(r1(x1)) -> r1(1(x1))
           b(r1(x1)) -> b(1(qr(x1)))
           qr(0(x1)) -> 0(qr(x1))
           qr(1(x1)) -> 1(qr(x1))
           qr(m(x1)) -> m(ql(x1))
           ql(0(x1)) -> 0(ql(x1))
           ql(1(x1)) -> 1(ql(x1))
           1(ql(b(x1))) -> r1(b(1(x1)))
          String Reversal Processor:
           r1(0(x1)) -> 0(r1(x1))
           r1(1(x1)) -> 1(r1(x1))
           r1(b(x1)) -> qr(1(b(x1)))
           0(qr(x1)) -> qr(0(x1))
           1(qr(x1)) -> qr(1(x1))
           m(qr(x1)) -> ql(m(x1))
           0(ql(x1)) -> ql(0(x1))
           1(ql(x1)) -> ql(1(x1))
           b(ql(1(x1))) -> 1(b(r1(x1)))
           Bounds Processor:
            bound: 1
            enrichment: match
            automaton:
             final states: {16,15,14,12,10,8,5,4,1}
             transitions:
              b0(2) -> 6*
              b0(3) -> 17*
              m0(2) -> 13*
              qr0(11) -> 10*
              qr0(9) -> 8*
              qr0(7) -> 5*
              10(2) -> 11*
              10(3) -> 4*
              10(6) -> 7*
              10(17) -> 16*
              f80() -> 2*
              r10(2) -> 3*
              00(2) -> 9*
              00(3) -> 1*
              qr1(22) -> 23*
              11(26) -> 27*
              11(32) -> 33*
              01(21) -> 22*
              01(30) -> 31*
              ql0(11) -> 15*
              ql0(13) -> 12*
              ql0(9) -> 14*
              27 -> 22*
              7 -> 26,21
              12 -> 13*
              14 -> 9*
              16 -> 6*
              4 -> 3*
              22 -> 32,30
              8 -> 9*
              1 -> 3*
              31 -> 22*
              5 -> 3*
              15 -> 11*
              10 -> 11*
              23 -> 4,1,3
              33 -> 22*
            problem:
             
            Qed