YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(a(x1))) -> c(x1)
  c(a(x1)) -> a(a(b(c(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(a(x1))) -> c#(x1)
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> b#(c(x1))
    c#(a(x1)) -> a#(b(c(x1)))
    c#(a(x1)) -> a#(a(b(c(x1))))
   TRS:
    a(x1) -> b(x1)
    b(b(a(x1))) -> c(x1)
    c(a(x1)) -> a(a(b(c(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> a#(a(b(c(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(a(x1))) -> c(x1)
     c(a(x1)) -> a(a(b(c(x1))))
    graph:
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1)) -> b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
     c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [0 3]x0,
      
      [b#](x0) = [1 0]x0 + [0],
      
      [a#](x0) = [1 0]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  2 ]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [0],
      
                [0 0]     [0]
      [a](x0) = [0 2]x0 + [3]
     orientation:
      a#(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = b#(x1)
      
      b#(b(a(x1))) = [1 3]x1 + [4] >= [0 3]x1 = c#(x1)
      
      c#(a(x1)) = [3 5]x1 + [6] >= [0 3]x1 = c#(x1)
      
      c#(a(x1)) = [3 5]x1 + [6] >= [0 2]x1 + [1] = b#(c(x1))
      
      c#(a(x1)) = [3 5]x1 + [6] >= [1 3]x1 + [1] = a#(b(c(x1)))
      
      c#(a(x1)) = [3 5]x1 + [6] >= [1 3]x1 + [3] = a#(a(b(c(x1))))
      
              [0 0]     [0]    [-& 0 ]     [0]        
      a(x1) = [0 2]x1 + [3] >= [0  -&]x1 + [0] = b(x1)
      
                    [0 0]     [0]    [-& 0 ]     [0]        
      b(b(a(x1))) = [0 2]x1 + [3] >= [0  2 ]x1 + [0] = c(x1)
      
                 [0 2]     [3]    [0 2]     [3]                 
      c(a(x1)) = [2 4]x1 + [5] >= [2 4]x1 + [5] = a(a(b(c(x1))))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(a(x1))) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
     EDG Processor:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(a(x1))) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
      graph:
       a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
      CDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        b#(b(a(x1))) -> c#(x1)
       TRS:
        a(x1) -> b(x1)
        b(b(a(x1))) -> c(x1)
        c(a(x1)) -> a(a(b(c(x1))))
       graph:
        
       Qed