YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> b#(b(c(x1)))
   a#(a(x1)) -> a#(b(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(a(x1)) -> a(b(b(c(x1))))
   b(a(x1)) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(a(x1)) -> a(b(b(c(x1))))
    b(a(x1)) -> x1
    c(b(x1)) -> a(c(x1))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(b(c(x1))))
    TRS:
     a(a(x1)) -> a(b(b(c(x1))))
     b(a(x1)) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> a(b(b(c(x1))))
      b(a(x1)) -> x1
      c(b(x1)) -> a(c(x1))
     interpretation:
      [c#](x0) = [0 0]x0 + [3],
      
      [a#](x0) = [-& 0 ]x0 + [0],
      
                [1  0 ]     [3 ]
      [b](x0) = [-& 0 ]x0 + [-&],
      
                [-4 -&]     [0 ]
      [c](x0) = [0  -3]x0 + [-&],
      
                [-4 -3]     [0]
      [a](x0) = [0  1 ]x0 + [3]
     orientation:
      c#(b(x1)) = [1 0]x1 + [3] >= [0 0]x1 + [3] = c#(x1)
      
      c#(b(x1)) = [1 0]x1 + [3] >= [0  -3]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [0 1]x1 + [3] >= [0 0]x1 + [3] = c#(x1)
      
      a#(a(x1)) = [0 1]x1 + [3] >= [0  -3]x1 + [0] = a#(b(b(c(x1))))
      
                 [-3 -2]     [0]    [-3 -6]     [0]                 
      a(a(x1)) = [1  2 ]x1 + [4] >= [1  -2]x1 + [4] = a(b(b(c(x1))))
      
                 [0 1]     [3]           
      b(a(x1)) = [0 1]x1 + [3] >= x1 = x1
      
                 [-3 -4]     [0]    [-3 -6]     [0]           
      c(b(x1)) = [1  0 ]x1 + [3] >= [1  -2]x1 + [3] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(a(x1)) -> x1
       c(b(x1)) -> a(c(x1))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(x1)
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(a(x1)) -> x1
       c(b(x1)) -> a(c(x1))
      EDG Processor:
       DPs:
        c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> a#(b(b(c(x1))))
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        b(a(x1)) -> x1
        c(b(x1)) -> a(c(x1))
       graph:
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
       CDG Processor:
        DPs:
         c#(b(x1)) -> c#(x1)
         a#(a(x1)) -> c#(x1)
         a#(a(x1)) -> a#(b(b(c(x1))))
        TRS:
         a(a(x1)) -> a(b(b(c(x1))))
         b(a(x1)) -> x1
         c(b(x1)) -> a(c(x1))
        graph:
         a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
         a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1)
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/9
         DPs:
          a#(a(x1)) -> a#(b(b(c(x1))))
         TRS:
          a(a(x1)) -> a(b(b(c(x1))))
          b(a(x1)) -> x1
          c(b(x1)) -> a(c(x1))
         Arctic Interpretation Processor:
          dimension: 3
          usable rules:
           a(a(x1)) -> a(b(b(c(x1))))
           b(a(x1)) -> x1
           c(b(x1)) -> a(c(x1))
          interpretation:
           [a#](x0) = [0 1 0]x0,
           
                     [0  -& 1 ]  
           [b](x0) = [0  -& 0 ]x0
                     [0  -& 1 ]  ,
           
                     [0  -& -&]  
           [c](x0) = [0  -& 1 ]x0
                     [-& -& -&]  ,
           
                     [0  0  0 ]  
           [a](x0) = [1  1  0 ]x0
                     [-& -& -&]  
          orientation:
           a#(a(x1)) = [2 2 1]x1 >= [1  -& -&]x1 = a#(b(b(c(x1))))
           
                      [1  1  0 ]      [1  -& -&]                   
           a(a(x1)) = [2  2  1 ]x1 >= [2  -& -&]x1 = a(b(b(c(x1))))
                      [-& -& -&]      [-& -& -&]                   
           
                      [0 0 0]             
           b(a(x1)) = [0 0 0]x1 >= x1 = x1
                      [0 0 0]             
           
                      [0  -& 1 ]      [0  -& 1 ]             
           c(b(x1)) = [1  -& 2 ]x1 >= [1  -& 2 ]x1 = a(c(x1))
                      [-& -& -&]      [-& -& -&]             
          problem:
           DPs:
            
           TRS:
            a(a(x1)) -> a(b(b(c(x1))))
            b(a(x1)) -> x1
            c(b(x1)) -> a(c(x1))
          Qed