YES

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

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