YES

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

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