YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [g](x0) = 10x0,
   
   [f](x0) = 3x0,
   
   [d](x0) = 2x0,
   
   [b](x0) = x0,
   
   [c](x0) = 6x0,
   
   [a](x0) = 4x0
  orientation:
   a(b(c(a(x1)))) = 14x1 >= 14x1 = b(a(c(b(a(b(x1))))))
   
   a(d(x1)) = 6x1 >= 6x1 = c(x1)
   
   a(f(f(x1))) = 10x1 >= 10x1 = g(x1)
   
   b(g(x1)) = 10x1 >= 10x1 = g(b(x1))
   
   c(x1) = 6x1 >= 6x1 = f(f(x1))
   
   c(a(c(x1))) = 16x1 >= 16x1 = b(c(a(b(c(x1)))))
   
   c(d(x1)) = 8x1 >= 8x1 = a(a(x1))
   
   g(x1) = 10x1 >= 10x1 = c(a(x1))
   
   g(x1) = 10x1 >= 8x1 = d(d(d(d(x1))))
  problem:
   a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
   a(d(x1)) -> c(x1)
   a(f(f(x1))) -> g(x1)
   b(g(x1)) -> g(b(x1))
   c(x1) -> f(f(x1))
   c(a(c(x1))) -> b(c(a(b(c(x1)))))
   c(d(x1)) -> a(a(x1))
   g(x1) -> c(a(x1))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [g](x0) = x0,
    
    [f](x0) = x0,
    
    [d](x0) = 5x0,
    
    [b](x0) = x0,
    
    [c](x0) = x0,
    
    [a](x0) = x0
   orientation:
    a(b(c(a(x1)))) = x1 >= x1 = b(a(c(b(a(b(x1))))))
    
    a(d(x1)) = 5x1 >= x1 = c(x1)
    
    a(f(f(x1))) = x1 >= x1 = g(x1)
    
    b(g(x1)) = x1 >= x1 = g(b(x1))
    
    c(x1) = x1 >= x1 = f(f(x1))
    
    c(a(c(x1))) = x1 >= x1 = b(c(a(b(c(x1)))))
    
    c(d(x1)) = 5x1 >= x1 = a(a(x1))
    
    g(x1) = x1 >= x1 = c(a(x1))
   problem:
    a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
    a(f(f(x1))) -> g(x1)
    b(g(x1)) -> g(b(x1))
    c(x1) -> f(f(x1))
    c(a(c(x1))) -> b(c(a(b(c(x1)))))
    g(x1) -> c(a(x1))
   String Reversal Processor:
    a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
    f(f(a(x1))) -> g(x1)
    g(b(x1)) -> b(g(x1))
    c(x1) -> f(f(x1))
    c(a(c(x1))) -> c(b(a(c(b(x1)))))
    g(x1) -> a(c(x1))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [g](x0) = 4x0 + 8,
      
      [f](x0) = 2x0,
      
      [b](x0) = x0,
      
      [c](x0) = 4x0,
      
      [a](x0) = x0 + 4
     orientation:
      a(c(b(a(x1)))) = 4x1 + 20 >= 4x1 + 20 = b(a(b(c(a(b(x1))))))
      
      f(f(a(x1))) = 4x1 + 16 >= 4x1 + 8 = g(x1)
      
      g(b(x1)) = 4x1 + 8 >= 4x1 + 8 = b(g(x1))
      
      c(x1) = 4x1 >= 4x1 = f(f(x1))
      
      c(a(c(x1))) = 16x1 + 16 >= 16x1 + 16 = c(b(a(c(b(x1)))))
      
      g(x1) = 4x1 + 8 >= 4x1 + 4 = a(c(x1))
     problem:
      a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
      g(b(x1)) -> b(g(x1))
      c(x1) -> f(f(x1))
      c(a(c(x1))) -> c(b(a(c(b(x1)))))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [g](x0) = 3x0,
       
       [f](x0) = x0,
       
       [b](x0) = x0,
       
       [c](x0) = 2x0,
       
       [a](x0) = 6x0
      orientation:
       a(c(b(a(x1)))) = 14x1 >= 14x1 = b(a(b(c(a(b(x1))))))
       
       g(b(x1)) = 3x1 >= 3x1 = b(g(x1))
       
       c(x1) = 2x1 >= x1 = f(f(x1))
       
       c(a(c(x1))) = 10x1 >= 10x1 = c(b(a(c(b(x1)))))
      problem:
       a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
       g(b(x1)) -> b(g(x1))
       c(a(c(x1))) -> c(b(a(c(b(x1)))))
      String Reversal Processor:
       a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
       b(g(x1)) -> g(b(x1))
       c(a(c(x1))) -> b(c(a(b(c(x1)))))
       Matrix Interpretation Processor: dim=3
        
        interpretation:
                   [1 0 0]  
         [g](x0) = [0 0 0]x0
                   [0 0 0]  ,
         
                   [1 0 0]  
         [b](x0) = [0 0 1]x0
                   [0 0 0]  ,
         
                   [1 1 0]     [0]
         [c](x0) = [0 1 1]x0 + [1]
                   [1 0 0]     [0],
         
                   [1 1 1]     [0]
         [a](x0) = [0 1 1]x0 + [1]
                   [0 0 1]     [0]
        orientation:
                          [2 3 3]     [1]    [2 0 2]     [1]                       
         a(b(c(a(x1)))) = [1 1 1]x1 + [1] >= [1 0 1]x1 + [0] = b(a(c(b(a(b(x1))))))
                          [0 0 0]     [0]    [0 0 0]     [0]                       
         
                    [1 0 0]      [1 0 0]             
         b(g(x1)) = [0 0 0]x1 >= [0 0 0]x1 = g(b(x1))
                    [0 0 0]      [0 0 0]             
         
                       [3 3 2]     [3]    [3 1 0]     [1]                    
         c(a(c(x1))) = [2 1 1]x1 + [3] >= [2 1 0]x1 + [0] = b(c(a(b(c(x1)))))
                       [2 2 1]     [1]    [0 0 0]     [0]                    
        problem:
         a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
         b(g(x1)) -> g(b(x1))
        Arctic Interpretation Processor:
         dimension: 2
         interpretation:
                    [0  0 ]  
          [g](x0) = [-& 2 ]x0,
          
                    [0  -&]  
          [b](x0) = [-& -&]x0,
          
                    [0  3 ]  
          [c](x0) = [-& 0 ]x0,
          
                    [0 0]  
          [a](x0) = [0 0]x0
         orientation:
                           [3 3]      [0  -&]                         
          a(b(c(a(x1)))) = [3 3]x1 >= [-& -&]x1 = b(a(c(b(a(b(x1))))))
          
                     [0  0 ]      [0  -&]             
          b(g(x1)) = [-& -&]x1 >= [-& -&]x1 = g(b(x1))
         problem:
          b(g(x1)) -> g(b(x1))
         KBO Processor:
          weight function:
           w0 = 1
           w(g) = w(b) = 1
          precedence:
           b > g
          problem:
           
          Qed