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)))))
       Bounds Processor:
        bound: 0
        enrichment: match
        automaton:
         final states: {9,8,1}
         transitions:
          f60() -> 2*
          b0(10) -> 11*
          b0(7) -> 1*
          b0(2) -> 3*
          b0(4) -> 5*
          b0(13) -> 9*
          a0(11) -> 12*
          a0(6) -> 7*
          a0(3) -> 4*
          c0(5) -> 6*
          c0(12) -> 13*
          c0(2) -> 10*
          g0(3) -> 8*
          1 -> 4,12
          8 -> 3*
          9 -> 10*
        problem:
         
        Qed