YES

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

Proof:
 DP Processor:
  DPs:
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> c#(a(x1))
   c#(b(x1)) -> c#(c(a(x1)))
   c#(b(x1)) -> a#(c(c(a(x1))))
  TRS:
   a(b(x1)) -> x1
   a(c(x1)) -> b(b(x1))
   c(b(x1)) -> a(c(c(a(x1))))
  TDG Processor:
   DPs:
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> c#(a(x1))
    c#(b(x1)) -> c#(c(a(x1)))
    c#(b(x1)) -> a#(c(c(a(x1))))
   TRS:
    a(b(x1)) -> x1
    a(c(x1)) -> b(b(x1))
    c(b(x1)) -> a(c(c(a(x1))))
   graph:
    c#(b(x1)) -> c#(c(a(x1))) -> c#(b(x1)) -> a#(c(c(a(x1))))
    c#(b(x1)) -> c#(c(a(x1))) -> c#(b(x1)) -> c#(c(a(x1)))
    c#(b(x1)) -> c#(c(a(x1))) -> c#(b(x1)) -> c#(a(x1))
    c#(b(x1)) -> c#(c(a(x1))) -> c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> a#(c(c(a(x1))))
    c#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> c#(c(a(x1)))
    c#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> c#(a(x1))
    c#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     c#(b(x1)) -> c#(c(a(x1)))
     c#(b(x1)) -> c#(a(x1))
    TRS:
     a(b(x1)) -> x1
     a(c(x1)) -> b(b(x1))
     c(b(x1)) -> a(c(c(a(x1))))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(b(x1)) -> x1
      a(c(x1)) -> b(b(x1))
      c(b(x1)) -> a(c(c(a(x1))))
     interpretation:
      [c#](x0) = [0 0]x0 + [0],
      
                [1 1]     [2]
      [c](x0) = [0 1]x0 + [0],
      
                [0  -&]     [-&]
      [a](x0) = [0  -&]x0 + [0 ],
      
                [0 0]     [0]
      [b](x0) = [1 0]x0 + [2]
     orientation:
      c#(b(x1)) = [1 0]x1 + [2] >= [1  -&]x1 + [2] = c#(c(a(x1)))
      
      c#(b(x1)) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = c#(a(x1))
      
                 [0 0]     [0]           
      a(b(x1)) = [0 0]x1 + [0] >= x1 = x1
      
                 [1 1]     [2]    [1 0]     [2]           
      a(c(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = b(b(x1))
      
                 [2 1]     [3]    [2  -&]     [3]                 
      c(b(x1)) = [2 1]x1 + [3] >= [2  -&]x1 + [3] = a(c(c(a(x1))))
     problem:
      DPs:
       c#(b(x1)) -> c#(c(a(x1)))
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> b(b(x1))
       c(b(x1)) -> a(c(c(a(x1))))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(c(a(x1)))
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> b(b(x1))
       c(b(x1)) -> a(c(c(a(x1))))
      EDG Processor:
       DPs:
        c#(b(x1)) -> c#(c(a(x1)))
       TRS:
        a(b(x1)) -> x1
        a(c(x1)) -> b(b(x1))
        c(b(x1)) -> a(c(c(a(x1))))
       graph:
        c#(b(x1)) -> c#(c(a(x1))) -> c#(b(x1)) -> c#(c(a(x1)))
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(b(x1)) -> x1
         a(c(x1)) -> b(b(x1))
         c(b(x1)) -> a(c(c(a(x1))))
        interpretation:
         [c#](x0) = [0 1 0]x0 + [0],
         
                   [0  1  0 ]     [1]
         [c](x0) = [-& 0  -&]x0 + [0]
                   [0  1  0 ]     [0],
         
                   [1  -& 0 ]     [0]
         [a](x0) = [0  -& -&]x0 + [0]
                   [1  -& 0 ]     [1],
         
                   [-& 0  -&]     [0]
         [b](x0) = [1  -& 0 ]x0 + [1]
                   [0  0  0 ]     [1]
        orientation:
         c#(b(x1)) = [2 0 1]x1 + [2] >= [1  -& 0 ]x1 + [1] = c#(c(a(x1)))
         
                    [0  1  0 ]     [1]           
         a(b(x1)) = [-& 0  -&]x1 + [0] >= x1 = x1
                    [0  1  0 ]     [1]           
         
                    [1 2 1]     [2]    [1  -& 0 ]     [1]           
         a(c(x1)) = [0 1 0]x1 + [1] >= [0  1  0 ]x1 + [1] = b(b(x1))
                    [1 2 1]     [2]    [1  0  0 ]     [1]           
         
                    [2  0  1 ]     [2]    [2  -& 1 ]     [2]                 
         c(b(x1)) = [1  -& 0 ]x1 + [1] >= [1  -& 0 ]x1 + [1] = a(c(c(a(x1))))
                    [2  0  1 ]     [2]    [2  -& 1 ]     [2]                 
        problem:
         DPs:
          
         TRS:
          a(b(x1)) -> x1
          a(c(x1)) -> b(b(x1))
          c(b(x1)) -> a(c(c(a(x1))))
        Qed