YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> b#(b(a(a(x1))))
   b#(c(x1)) -> a#(x1)
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> c(b(b(a(a(x1)))))
   b(c(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> c(b(b(a(a(x1)))))
    b(c(x1)) -> a(x1)
   graph:
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 3
    interpretation:
     [b#](x0) = [0 0 0]x0 + [1],
     
     [a#](x0) = [-& -& 0 ]x0 + [0],
     
               [0  0  1 ]     [0]
     [c](x0) = [0  -& 0 ]x0 + [0]
               [0  -& 0 ]     [0],
     
               [0  0  0 ]     [1]
     [b](x0) = [0  1  1 ]x0 + [0]
               [0  0  -&]     [1],
     
               [0  -& 1 ]     [0 ]
     [a](x0) = [-& 0  0 ]x0 + [0 ]
               [-& 0  0 ]     [-&]
    orientation:
     a#(a(b(x1))) = [0 1 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(x1)
     
     a#(a(b(x1))) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = a#(a(x1))
     
     a#(a(b(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = b#(a(a(x1)))
     
     a#(a(b(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = b#(b(a(a(x1))))
     
     b#(c(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(x1)
     
             [0  -& 1 ]     [0 ]           
     a(x1) = [-& 0  0 ]x1 + [0 ] >= x1 = x1
             [-& 0  0 ]     [-&]           
     
                   [1 2 2]     [2]    [1 2 2]     [2]                    
     a(a(b(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = c(b(b(a(a(x1)))))
                   [0 1 1]     [1]    [0 1 1]     [1]                    
     
                [0 0 1]     [1]    [0  -& 1 ]     [0 ]        
     b(c(x1)) = [1 0 1]x1 + [1] >= [-& 0  0 ]x1 + [0 ] = a(x1)
                [0 0 1]     [1]    [-& 0  0 ]     [-&]        
    problem:
     DPs:
      a#(a(b(x1))) -> b#(a(a(x1)))
      a#(a(b(x1))) -> b#(b(a(a(x1))))
     TRS:
      a(x1) -> x1
      a(a(b(x1))) -> c(b(b(a(a(x1)))))
      b(c(x1)) -> a(x1)
    EDG Processor:
     DPs:
      a#(a(b(x1))) -> b#(a(a(x1)))
      a#(a(b(x1))) -> b#(b(a(a(x1))))
     TRS:
      a(x1) -> x1
      a(a(b(x1))) -> c(b(b(a(a(x1)))))
      b(c(x1)) -> a(x1)
     graph:
      
     Qed