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)))
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(a(x1)) -> x1
      b(b(x1)) -> a(b(c(x1)))
      c(c(x1)) -> b(b(b(x1)))
     interpretation:
      [c#](x0) = [0  -& -&]x0 + [0],
      
      [b#](x0) = [0  0  -&]x0 + [0],
      
                [1  0  -&]     [1]
      [c](x0) = [0  -& -&]x0 + [0]
                [1  0  0 ]     [0],
      
                [-& -& -&]     [0]
      [b](x0) = [1  0  -&]x0 + [1]
                [0  1  -&]     [0],
      
                [0  -& -&]     [0]
      [a](x0) = [0  -& 0 ]x0 + [1]
                [1  0  0 ]     [0]
     orientation:
      c#(c(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [1] = b#(b(b(x1)))
      
      b#(b(x1)) = [1  0  -&]x1 + [1] >= [0  -& -&]x1 + [0] = c#(x1)
      
      c#(c(x1)) = [1  0  -&]x1 + [1] >= [0  0  -&]x1 + [0] = b#(x1)
      
      b#(b(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [1] = b#(c(x1))
      
      c#(c(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [1] = b#(b(x1))
      
                 [0  -& -&]     [0]           
      a(a(x1)) = [1  0  0 ]x1 + [1] >= x1 = x1
                 [1  0  0 ]     [1]           
      
                 [-& -& -&]     [0]    [-& -& -&]     [0]              
      b(b(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [1] = a(b(c(x1)))
                 [2  1  -&]     [2]    [2  1  -&]     [2]              
      
                 [2  1  -&]     [2]    [-& -& -&]     [0]              
      c(c(x1)) = [1  0  -&]x1 + [1] >= [1  0  -&]x1 + [1] = b(b(b(x1)))
                 [2  1  0 ]     [2]    [2  1  -&]     [2]              
     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)))
     Restore Modifier:
      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
         usable rules:
          a(a(x1)) -> x1
          b(b(x1)) -> a(b(c(x1)))
          c(c(x1)) -> b(b(b(x1)))
         interpretation:
          [b#](x0) = [1 0 0]x0 + [0],
          
                    [-& -& 0 ]     [0 ]
          [c](x0) = [0  -& 1 ]x0 + [-&]
                    [0  -& 1 ]     [1 ],
          
                    [0  -& 1 ]     [1]
          [b](x0) = [1  -& 0 ]x0 + [0]
                    [-& -& -&]     [0],
          
                    [-& 0  1 ]     [0 ]
          [a](x0) = [0  1  0 ]x0 + [0 ]
                    [-& -& 0 ]     [-&]
         orientation:
          b#(b(x1)) = [1  -& 2 ]x1 + [2] >= [0  -& 1 ]x1 + [1] = b#(c(x1))
          
                     [0  1  1 ]     [0 ]           
          a(a(x1)) = [1  2  1 ]x1 + [1 ] >= x1 = x1
                     [-& -& 0 ]     [-&]           
          
                     [0  -& 1 ]     [1]    [0  -& 1 ]     [1]              
          b(b(x1)) = [1  -& 2 ]x1 + [2] >= [1  -& 2 ]x1 + [2] = a(b(c(x1)))
                     [-& -& -&]     [0]    [-& -& -&]     [0]              
          
                     [0  -& 1 ]     [1]    [0  -& 1 ]     [1]              
          c(c(x1)) = [1  -& 2 ]x1 + [2] >= [1  -& 2 ]x1 + [2] = b(b(b(x1)))
                     [1  -& 2 ]     [2]    [-& -& -&]     [0]              
         problem:
          DPs:
           
          TRS:
           a(a(x1)) -> x1
           b(b(x1)) -> a(b(c(x1)))
           c(c(x1)) -> b(b(b(x1)))
         Qed