YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> b#(c(x1))
   b#(b(x1)) -> a#(b(c(x1)))
   c#(c(x1)) -> b#(x1)
   c#(c(x1)) -> b#(b(x1))
   c#(c(x1)) -> b#(b(b(x1)))
  TRS:
   a(a(x1)) -> x1
   b(b(x1)) -> a(b(c(x1)))
   c(c(x1)) -> b(b(b(x1)))
  TDG Processor:
   DPs:
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> b#(b(x1))
    c#(c(x1)) -> b#(b(b(x1)))
   TRS:
    a(a(x1)) -> x1
    b(b(x1)) -> a(b(c(x1)))
    c(c(x1)) -> b(b(b(x1)))
   graph:
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1)
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1)
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(b(b(x1)))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(b(x1))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 15/36
    DPs:
     c#(c(x1)) -> b#(b(b(x1)))
     b#(b(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1)
     b#(b(x1)) -> b#(c(x1))
     c#(c(x1)) -> b#(b(x1))
    TRS:
     a(a(x1)) -> x1
     b(b(x1)) -> a(b(c(x1)))
     c(c(x1)) -> b(b(b(x1)))
    Matrix Interpretation Processor: dim=5
     
     interpretation:
      [c#](x0) = [0 0 0 1 1]x0,
      
      [b#](x0) = [0 0 0 1 0]x0 + [1],
      
                [0 1 0 0 0]     [1]
                [0 0 0 1 1]     [0]
      [c](x0) = [0 1 0 0 1]x0 + [1]
                [0 0 0 1 1]     [0]
                [0 0 0 0 0]     [1],
      
                [0 1 0 0 0]     [0]
                [0 0 0 1 1]     [1]
      [b](x0) = [0 1 0 0 0]x0 + [1]
                [0 0 0 1 1]     [0]
                [0 0 0 0 0]     [0],
      
                [0 0 0 1 0]  
                [0 0 1 0 0]  
      [a](x0) = [0 1 0 0 0]x0
                [1 0 0 0 0]  
                [0 0 0 0 1]  
     orientation:
      c#(c(x1)) = [0 0 0 1 1]x1 + [1] >= [0 0 0 1 1]x1 + [1] = b#(b(b(x1)))
      
      b#(b(x1)) = [0 0 0 1 1]x1 + [1] >= [0 0 0 1 1]x1 = c#(x1)
      
      c#(c(x1)) = [0 0 0 1 1]x1 + [1] >= [0 0 0 1 0]x1 + [1] = b#(x1)
      
      b#(b(x1)) = [0 0 0 1 1]x1 + [1] >= [0 0 0 1 1]x1 + [1] = b#(c(x1))
      
      c#(c(x1)) = [0 0 0 1 1]x1 + [1] >= [0 0 0 1 1]x1 + [1] = b#(b(x1))
      
                              
                              
      a(a(x1)) = x1 >= x1 = x1
                              
                              
      
                 [0 0 0 1 1]     [1]    [0 0 0 1 1]     [1]              
                 [0 0 0 1 1]     [1]    [0 0 0 1 1]     [1]              
      b(b(x1)) = [0 0 0 1 1]x1 + [2] >= [0 0 0 1 1]x1 + [2] = a(b(c(x1)))
                 [0 0 0 1 1]     [0]    [0 0 0 1 1]     [0]              
                 [0 0 0 0 0]     [0]    [0 0 0 0 0]     [0]              
      
                 [0 0 0 1 1]     [1]    [0 0 0 1 1]     [1]              
                 [0 0 0 1 1]     [1]    [0 0 0 1 1]     [1]              
      c(c(x1)) = [0 0 0 1 1]x1 + [2] >= [0 0 0 1 1]x1 + [2] = b(b(b(x1)))
                 [0 0 0 1 1]     [1]    [0 0 0 1 1]     [0]              
                 [0 0 0 0 0]     [1]    [0 0 0 0 0]     [0]              
     problem:
      DPs:
       c#(c(x1)) -> b#(b(b(x1)))
       c#(c(x1)) -> b#(x1)
       b#(b(x1)) -> b#(c(x1))
       c#(c(x1)) -> b#(b(x1))
      TRS:
       a(a(x1)) -> x1
       b(b(x1)) -> a(b(c(x1)))
       c(c(x1)) -> b(b(b(x1)))
     EDG Processor:
      DPs:
       c#(c(x1)) -> b#(b(b(x1)))
       c#(c(x1)) -> b#(x1)
       b#(b(x1)) -> b#(c(x1))
       c#(c(x1)) -> b#(b(x1))
      TRS:
       a(a(x1)) -> x1
       b(b(x1)) -> a(b(c(x1)))
       c(c(x1)) -> b(b(b(x1)))
      graph:
       c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> b#(c(x1))
       c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> b#(c(x1))
       c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
       b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 4/16
       DPs:
        b#(b(x1)) -> b#(c(x1))
       TRS:
        a(a(x1)) -> x1
        b(b(x1)) -> a(b(c(x1)))
        c(c(x1)) -> b(b(b(x1)))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [b#](x0) = [0 0 1]x0 + [0],
         
                   [1  -& 0 ]     [1]
         [c](x0) = [1  -& 0 ]x0 + [0]
                   [0  -& -&]     [0],
         
                   [-& -& -&]     [0]
         [b](x0) = [0  -& 1 ]x0 + [0]
                   [1  -& 0 ]     [1],
         
                   [0  -& -&]     [0]
         [a](x0) = [0  1  0 ]x0 + [0]
                   [0  0  -&]     [0]
        orientation:
         b#(b(x1)) = [2  -& 1 ]x1 + [2] >= [1  -& 0 ]x1 + [1] = b#(c(x1))
         
                    [0  -& -&]     [0]           
         a(a(x1)) = [1  2  1 ]x1 + [1] >= x1 = x1
                    [0  1  0 ]     [0]           
         
                    [-& -& -&]     [0]    [-& -& -&]     [0]              
         b(b(x1)) = [2  -& 1 ]x1 + [2] >= [2  -& 1 ]x1 + [2] = a(b(c(x1)))
                    [1  -& 0 ]     [1]    [1  -& 0 ]     [1]              
         
                    [2  -& 1 ]     [2]    [-& -& -&]     [0]              
         c(c(x1)) = [2  -& 1 ]x1 + [2] >= [2  -& 1 ]x1 + [2] = b(b(b(x1)))
                    [1  -& 0 ]     [1]    [1  -& 0 ]     [1]              
        problem:
         DPs:
          
         TRS:
          a(a(x1)) -> x1
          b(b(x1)) -> a(b(c(x1)))
          c(c(x1)) -> b(b(b(x1)))
        Qed