YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(x1)) -> c(x1)
  c(a(c(x1))) -> a(c(b(a(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(x1)) -> c#(x1)
    c#(a(c(x1))) -> a#(x1)
    c#(a(c(x1))) -> b#(a(x1))
    c#(a(c(x1))) -> c#(b(a(x1)))
    c#(a(c(x1))) -> a#(c(b(a(x1))))
   TRS:
    a(x1) -> b(x1)
    b(b(x1)) -> c(x1)
    c(a(c(x1))) -> a(c(b(a(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(x1)) -> c#(x1)
     c#(a(c(x1))) -> a#(x1)
     c#(a(c(x1))) -> b#(a(x1))
     c#(a(c(x1))) -> c#(b(a(x1)))
     c#(a(c(x1))) -> a#(c(b(a(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(x1)) -> c(x1)
     c(a(c(x1))) -> a(c(b(a(x1))))
    graph:
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> c#(b(a(x1)))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> b#(a(x1))
     c#(a(c(x1))) -> c#(b(a(x1))) -> c#(a(c(x1))) -> a#(x1)
     c#(a(c(x1))) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1)
     c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1)
     c#(a(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> c#(b(a(x1)))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> b#(a(x1))
     b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [c#](x0) = 2x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = x0,
      
      [c](x0) = 4x0,
      
      [b](x0) = 2x0,
      
      [a](x0) = 2x0
     orientation:
      a#(x1) = x1 >= x1 = b#(x1)
      
      b#(b(x1)) = 2x1 >= 2x1 = c#(x1)
      
      c#(a(c(x1))) = 8x1 >= x1 = a#(x1)
      
      c#(a(c(x1))) = 8x1 >= 2x1 = b#(a(x1))
      
      c#(a(c(x1))) = 8x1 >= 6x1 = c#(b(a(x1)))
      
      c#(a(c(x1))) = 8x1 >= 8x1 = a#(c(b(a(x1))))
      
      a(x1) = 2x1 >= 2x1 = b(x1)
      
      b(b(x1)) = 4x1 >= 4x1 = c(x1)
      
      c(a(c(x1))) = 10x1 >= 10x1 = a(c(b(a(x1))))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(x1)) -> c#(x1)
       c#(a(c(x1))) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(x1)) -> c(x1)
       c(a(c(x1))) -> a(c(b(a(x1))))
     EDG Processor:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(x1)) -> c#(x1)
       c#(a(c(x1))) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(x1)) -> c(x1)
       c(a(c(x1))) -> a(c(b(a(x1))))
      graph:
       c#(a(c(x1))) -> a#(c(b(a(x1)))) -> a#(x1) -> b#(x1)
       b#(b(x1)) -> c#(x1) -> c#(a(c(x1))) -> a#(c(b(a(x1))))
       a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [c#](x0) = [2 2]x0,
        
        [b#](x0) = [0 2]x0,
        
        [a#](x0) = [0 2]x0,
        
                  [1 1]  
        [c](x0) = [0 0]x0,
        
                  [0 1]  
        [b](x0) = [0 0]x0,
        
                  [1 1]  
        [a](x0) = [0 0]x0
       orientation:
        a#(x1) = [0 2]x1 >= [0 2]x1 = b#(x1)
        
        b#(b(x1)) = [2 2]x1 >= [2 2]x1 = c#(x1)
        
        c#(a(c(x1))) = [4 4]x1 >= [3 3]x1 = a#(c(b(a(x1))))
        
                [1 1]      [0 1]          
        a(x1) = [0 0]x1 >= [0 0]x1 = b(x1)
        
                   [1 1]      [1 1]          
        b(b(x1)) = [0 1]x1 >= [0 0]x1 = c(x1)
        
                      [3 3]      [3 3]                   
        c(a(c(x1))) = [2 2]x1 >= [2 2]x1 = a(c(b(a(x1))))
       problem:
        DPs:
         a#(x1) -> b#(x1)
         b#(b(x1)) -> c#(x1)
        TRS:
         a(x1) -> b(x1)
         b(b(x1)) -> c(x1)
         c(a(c(x1))) -> a(c(b(a(x1))))
       EDG Processor:
        DPs:
         a#(x1) -> b#(x1)
         b#(b(x1)) -> c#(x1)
        TRS:
         a(x1) -> b(x1)
         b(b(x1)) -> c(x1)
         c(a(c(x1))) -> a(c(b(a(x1))))
        graph:
         a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
        CDG Processor:
         DPs:
          a#(x1) -> b#(x1)
          b#(b(x1)) -> c#(x1)
         TRS:
          a(x1) -> b(x1)
          b(b(x1)) -> c(x1)
          c(a(c(x1))) -> a(c(b(a(x1))))
         graph:
          
         Qed