YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [a](x0) = 4x0,
   
   [c](x0) = 4x0,
   
   [d](x0) = x0,
   
   [b](x0) = 4x0
  orientation:
   b(d(b(x1))) = 8x1 >= 8x1 = c(d(b(x1)))
   
   b(a(c(x1))) = 12x1 >= 8x1 = b(c(x1))
   
   a(d(x1)) = 4x1 >= 4x1 = d(c(x1))
   
   b(b(b(x1))) = 12x1 >= 12x1 = a(b(c(x1)))
   
   d(c(x1)) = 4x1 >= 4x1 = b(d(x1))
   
   d(c(x1)) = 4x1 >= 4x1 = d(b(d(x1)))
   
   d(a(c(x1))) = 8x1 >= 8x1 = b(b(x1))
  problem:
   b(d(b(x1))) -> c(d(b(x1)))
   a(d(x1)) -> d(c(x1))
   b(b(b(x1))) -> a(b(c(x1)))
   d(c(x1)) -> b(d(x1))
   d(c(x1)) -> d(b(d(x1)))
   d(a(c(x1))) -> b(b(x1))
  String Reversal Processor:
   b(d(b(x1))) -> b(d(c(x1)))
   d(a(x1)) -> c(d(x1))
   b(b(b(x1))) -> c(b(a(x1)))
   c(d(x1)) -> d(b(x1))
   c(d(x1)) -> d(b(d(x1)))
   c(a(d(x1))) -> b(b(x1))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [1]
     [a](x0) = [1 1 0]x0 + [0]
               [0 0 1]     [1],
     
               [1 0 0]     [1]
     [c](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0],
     
               [1 0 1]  
     [d](x0) = [0 1 0]x0
               [0 0 0]  ,
     
               [1 0 0]     [1]
     [b](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0]
    orientation:
                   [1 0 0]     [2]    [1 0 0]     [2]              
     b(d(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(d(c(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
     
                [1 0 1]     [2]    [1 0 1]     [1]           
     d(a(x1)) = [1 1 0]x1 + [0] >= [0 0 0]x1 + [0] = c(d(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                   [1 0 0]     [3]    [1 0 0]     [3]              
     b(b(b(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(b(a(x1)))
                   [0 0 0]     [0]    [0 0 0]     [0]              
     
                [1 0 1]     [1]    [1 0 0]     [1]           
     c(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(b(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
     
                [1 0 1]     [1]    [1 0 1]     [1]              
     c(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(b(d(x1)))
                [0 0 0]     [0]    [0 0 0]     [0]              
     
                   [1 0 1]     [2]    [1 0 0]     [2]           
     c(a(d(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(b(x1))
                   [0 0 0]     [0]    [0 0 0]     [0]           
    problem:
     b(d(b(x1))) -> b(d(c(x1)))
     b(b(b(x1))) -> c(b(a(x1)))
     c(d(x1)) -> d(b(x1))
     c(d(x1)) -> d(b(d(x1)))
     c(a(d(x1))) -> b(b(x1))
    String Reversal Processor:
     b(d(b(x1))) -> c(d(b(x1)))
     b(b(b(x1))) -> a(b(c(x1)))
     d(c(x1)) -> b(d(x1))
     d(c(x1)) -> d(b(d(x1)))
     d(a(c(x1))) -> b(b(x1))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                 [1 1 0]  
       [a](x0) = [0 0 0]x0
                 [0 0 0]  ,
       
                 [1 0 0]     [0]
       [c](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
       
                 [1 0 0]     [0]
       [d](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [1],
       
                 [1 0 0]  
       [b](x0) = [0 0 1]x0
                 [0 0 0]  
      orientation:
                     [1 0 0]     [0]    [1 0 0]     [0]              
       b(d(b(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(d(b(x1)))
                     [0 0 0]     [0]    [0 0 0]     [0]              
       
                     [1 0 0]      [1 0 0]                
       b(b(b(x1))) = [0 0 0]x1 >= [0 0 0]x1 = a(b(c(x1)))
                     [0 0 0]      [0 0 0]                
       
                  [1 0 0]     [0]    [1 0 0]     [0]           
       d(c(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(d(x1))
                  [0 0 0]     [1]    [0 0 0]     [0]           
       
                  [1 0 0]     [0]    [1 0 0]     [0]              
       d(c(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(b(d(x1)))
                  [0 0 0]     [1]    [0 0 0]     [1]              
       
                     [1 0 0]     [1]    [1 0 0]             
       d(a(c(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(b(x1))
                     [0 0 0]     [1]    [0 0 0]             
      problem:
       b(d(b(x1))) -> c(d(b(x1)))
       b(b(b(x1))) -> a(b(c(x1)))
       d(c(x1)) -> b(d(x1))
       d(c(x1)) -> d(b(d(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [a](x0) = 6x0,
        
        [c](x0) = 8x0,
        
        [d](x0) = x0,
        
        [b](x0) = 8x0
       orientation:
        b(d(b(x1))) = 16x1 >= 16x1 = c(d(b(x1)))
        
        b(b(b(x1))) = 24x1 >= 22x1 = a(b(c(x1)))
        
        d(c(x1)) = 8x1 >= 8x1 = b(d(x1))
        
        d(c(x1)) = 8x1 >= 8x1 = d(b(d(x1)))
       problem:
        b(d(b(x1))) -> c(d(b(x1)))
        d(c(x1)) -> b(d(x1))
        d(c(x1)) -> d(b(d(x1)))
       String Reversal Processor:
        b(d(b(x1))) -> b(d(c(x1)))
        c(d(x1)) -> d(b(x1))
        c(d(x1)) -> d(b(d(x1)))
        Matrix Interpretation Processor: dim=3
         
         interpretation:
                    [1 1 1]     [0]
          [c](x0) = [0 0 0]x0 + [0]
                    [0 1 1]     [1],
          
                    [1 0 0]  
          [d](x0) = [0 0 1]x0
                    [0 1 0]  ,
          
                    [1 0 1]     [0]
          [b](x0) = [0 1 1]x0 + [1]
                    [0 0 0]     [0]
         orientation:
                        [1 1 2]     [1]    [1 1 1]     [0]              
          b(d(b(x1))) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [2] = b(d(c(x1)))
                        [0 0 0]     [0]    [0 0 0]     [0]              
          
                     [1 1 1]     [0]    [1 0 1]     [0]           
          c(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(b(x1))
                     [0 1 1]     [1]    [0 1 1]     [1]           
          
                     [1 1 1]     [0]    [1 1 0]     [0]              
          c(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(b(d(x1)))
                     [0 1 1]     [1]    [0 1 1]     [1]              
         problem:
          c(d(x1)) -> d(b(x1))
          c(d(x1)) -> d(b(d(x1)))
         Arctic Interpretation Processor:
          dimension: 2
          interpretation:
                     [1  -&]  
           [c](x0) = [2  3 ]x0,
           
                     [0  0 ]  
           [d](x0) = [1  -&]x0,
           
                     [0  0 ]  
           [b](x0) = [0  -&]x0
          orientation:
                      [1 1]      [0 0]             
           c(d(x1)) = [4 2]x1 >= [1 1]x1 = d(b(x1))
           
                      [1 1]      [1 0]                
           c(d(x1)) = [4 2]x1 >= [2 1]x1 = d(b(d(x1)))
          problem:
           c(d(x1)) -> d(b(d(x1)))
          Arctic Interpretation Processor:
           dimension: 3
           interpretation:
                      [0  1  1 ]  
            [c](x0) = [0  1  -&]x0
                      [-& 1  1 ]  ,
            
                      [0  -& -&]  
            [d](x0) = [1  0  -&]x0
                      [0  0  -&]  ,
            
                      [0  -& -&]  
            [b](x0) = [-& 0  0 ]x0
                      [-& 0  -&]  
           orientation:
                       [2  1  -&]      [0  -& -&]                
            c(d(x1)) = [2  1  -&]x1 >= [1  0  -&]x1 = d(b(d(x1)))
                       [2  1  -&]      [1  0  -&]                
           problem:
            
           Qed