YES

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

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