YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> c#(c(x1))
   a#(a(x1)) -> a#(c(c(x1)))
   a#(a(x1)) -> a#(b(a(c(c(x1)))))
   c#(b(x1)) -> a#(x1)
  TRS:
   a(a(x1)) -> a(b(a(c(c(x1)))))
   c(a(x1)) -> x1
   c(b(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(b(a(c(c(x1)))))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(a(x1)) -> a(b(a(c(c(x1)))))
    c(a(x1)) -> x1
    c(b(x1)) -> a(x1)
   graph:
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1)))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(a(c(c(x1))))) ->
    a#(a(x1)) -> a#(b(a(c(c(x1)))))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1)))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1))
    a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> c#(c(x1))
     a#(a(x1)) -> a#(c(c(x1)))
     a#(a(x1)) -> a#(b(a(c(c(x1)))))
     c#(b(x1)) -> a#(x1)
    TRS:
     a(a(x1)) -> a(b(a(c(c(x1)))))
     c(a(x1)) -> x1
     c(b(x1)) -> a(x1)
    graph:
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1)))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
     a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1))
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1)))
     a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1)))))
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/25
     DPs:
      c#(b(x1)) -> a#(x1)
      a#(a(x1)) -> a#(c(c(x1)))
      a#(a(x1)) -> c#(c(x1))
      a#(a(x1)) -> c#(x1)
     TRS:
      a(a(x1)) -> a(b(a(c(c(x1)))))
      c(a(x1)) -> x1
      c(b(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [2 0]x0 + [3],
       
       [a#](x0) = [2 2]x0 + [0],
       
                 [0 1]     [3]
       [b](x0) = [0 0]x0 + [1],
       
                 [-& 0 ]     [0]
       [c](x0) = [0  -&]x0 + [2],
       
                 [-& 0 ]     [0]
       [a](x0) = [0  1 ]x0 + [3]
      orientation:
       c#(b(x1)) = [2 3]x1 + [5] >= [2 2]x1 + [0] = a#(x1)
       
       a#(a(x1)) = [2 3]x1 + [5] >= [2 2]x1 + [4] = a#(c(c(x1)))
       
       a#(a(x1)) = [2 3]x1 + [5] >= [0 2]x1 + [3] = c#(c(x1))
       
       a#(a(x1)) = [2 3]x1 + [5] >= [2 0]x1 + [3] = c#(x1)
       
                  [0 1]     [3]    [0 1]     [3]                    
       a(a(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = a(b(a(c(c(x1)))))
       
                  [0  1 ]     [3]           
       c(a(x1)) = [-& 0 ]x1 + [2] >= x1 = x1
       
                  [0 0]     [1]    [-& 0 ]     [0]        
       c(b(x1)) = [0 1]x1 + [3] >= [0  1 ]x1 + [3] = a(x1)
      problem:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(x1)) -> a#(c(c(x1)))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> a(b(a(c(c(x1)))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(x1)
      EDG Processor:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(x1)) -> a#(c(c(x1)))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(a(x1)) -> a(b(a(c(c(x1)))))
        c(a(x1)) -> x1
        c(b(x1)) -> a(x1)
       graph:
        c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1)))
        c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
        a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1)))
        a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1)
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [c#](x0) = [0 0]x0,
         
         [a#](x0) = [0  -&]x0,
         
                   [0 1]     [0]
         [b](x0) = [1 2]x0 + [2],
         
                   [-& 0 ]     [0]
         [c](x0) = [0  -&]x0 + [0],
         
                   [1  0 ]     [1]
         [a](x0) = [0  -&]x0 + [0]
        orientation:
         c#(b(x1)) = [1 2]x1 + [2] >= [0  -&]x1 = a#(x1)
         
         a#(a(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = a#(c(c(x1)))
         
         a#(a(x1)) = [1 0]x1 + [1] >= [0 0]x1 = c#(x1)
         
                    [2 1]     [2]    [2 1]     [2]                    
         a(a(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(b(a(c(c(x1)))))
         
                    [0  -&]     [0]           
         c(a(x1)) = [1  0 ]x1 + [1] >= x1 = x1
         
                    [1 2]     [2]    [1  0 ]     [1]        
         c(b(x1)) = [0 1]x1 + [0] >= [0  -&]x1 + [0] = a(x1)
        problem:
         DPs:
          a#(a(x1)) -> c#(x1)
         TRS:
          a(a(x1)) -> a(b(a(c(c(x1)))))
          c(a(x1)) -> x1
          c(b(x1)) -> a(x1)
        EDG Processor:
         DPs:
          a#(a(x1)) -> c#(x1)
         TRS:
          a(a(x1)) -> a(b(a(c(c(x1)))))
          c(a(x1)) -> x1
          c(b(x1)) -> a(x1)
         graph:
          
         Qed