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:
 String Reversal Processor:
  a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
  d(a(x1)) -> c(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)))))
  d(c(x1)) -> a(a(x1))
  g(x1) -> a(c(x1))
  g(x1) -> d(d(d(d(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0) = x0 + 3,
    
    [c](x0) = x0 + 6,
    
    [d](x0) = x0 + 2,
    
    [g](x0) = x0 + 10,
    
    [a](x0) = x0 + 4,
    
    [b](x0) = x0
   orientation:
    a(c(b(a(x1)))) = x1 + 14 >= x1 + 14 = b(a(b(c(a(b(x1))))))
    
    d(a(x1)) = x1 + 6 >= x1 + 6 = c(x1)
    
    f(f(a(x1))) = x1 + 10 >= x1 + 10 = g(x1)
    
    g(b(x1)) = x1 + 10 >= x1 + 10 = b(g(x1))
    
    c(x1) = x1 + 6 >= x1 + 6 = f(f(x1))
    
    c(a(c(x1))) = x1 + 16 >= x1 + 16 = c(b(a(c(b(x1)))))
    
    d(c(x1)) = x1 + 8 >= x1 + 8 = a(a(x1))
    
    g(x1) = x1 + 10 >= x1 + 10 = a(c(x1))
    
    g(x1) = x1 + 10 >= x1 + 8 = d(d(d(d(x1))))
   problem:
    a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
    d(a(x1)) -> c(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)))))
    d(c(x1)) -> a(a(x1))
    g(x1) -> a(c(x1))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [f](x0) = x0,
     
     [c](x0) = x0,
     
     [d](x0) = 4x0 + 12,
     
     [g](x0) = 2x0 + 4,
     
     [a](x0) = 2x0 + 4,
     
     [b](x0) = x0
    orientation:
     a(c(b(a(x1)))) = 4x1 + 12 >= 4x1 + 12 = b(a(b(c(a(b(x1))))))
     
     d(a(x1)) = 8x1 + 28 >= x1 = c(x1)
     
     f(f(a(x1))) = 2x1 + 4 >= 2x1 + 4 = g(x1)
     
     g(b(x1)) = 2x1 + 4 >= 2x1 + 4 = b(g(x1))
     
     c(x1) = x1 >= x1 = f(f(x1))
     
     c(a(c(x1))) = 2x1 + 4 >= 2x1 + 4 = c(b(a(c(b(x1)))))
     
     d(c(x1)) = 4x1 + 12 >= 4x1 + 12 = a(a(x1))
     
     g(x1) = 2x1 + 4 >= 2x1 + 4 = a(c(x1))
    problem:
     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)))))
     d(c(x1)) -> a(a(x1))
     g(x1) -> a(c(x1))
    String Reversal Processor:
     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)))))
     c(d(x1)) -> a(a(x1))
     g(x1) -> c(a(x1))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [f](x0) = x0,
       
       [c](x0) = x0,
       
       [d](x0) = 10x0 + 8,
       
       [g](x0) = x0,
       
       [a](x0) = x0,
       
       [b](x0) = x0
      orientation:
       a(b(c(a(x1)))) = x1 >= x1 = b(a(c(b(a(b(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)) = 10x1 + 8 >= 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))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [f](x0) = x0 + 1,
        
        [c](x0) = x0 + 4,
        
        [g](x0) = 4x0 + 9,
        
        [a](x0) = 4x0 + 1,
        
        [b](x0) = x0
       orientation:
        a(b(c(a(x1)))) = 16x1 + 21 >= 16x1 + 21 = b(a(c(b(a(b(x1))))))
        
        a(f(f(x1))) = 4x1 + 9 >= 4x1 + 9 = g(x1)
        
        b(g(x1)) = 4x1 + 9 >= 4x1 + 9 = g(b(x1))
        
        c(x1) = x1 + 4 >= x1 + 2 = f(f(x1))
        
        c(a(c(x1))) = 4x1 + 21 >= 4x1 + 21 = b(c(a(b(c(x1)))))
        
        g(x1) = 4x1 + 9 >= 4x1 + 5 = 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(a(c(x1))) -> b(c(a(b(c(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(a(c(x1))) -> c(b(a(c(b(x1)))))
        Bounds Processor:
         bound: 0
         enrichment: match
         automaton:
          final states: {10,9,8,1}
          transitions:
           b0(5) -> 6*
           b0(12) -> 13*
           b0(7) -> 1*
           b0(8) -> 9*
           b0(2) -> 3*
           g0(2) -> 8*
           c0(4) -> 5*
           c0(13) -> 10*
           c0(3) -> 11*
           a0(3) -> 4*
           a0(6) -> 7*
           a0(11) -> 12*
           f60() -> 2*
           1 -> 12*
           9 -> 8*
         problem:
          
         Qed