YES

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

Proof:
 DP Processor:
  DPs:
   a#(c(x1)) -> a#(x1)
   a#(c(x1)) -> a#(a(x1))
   a#(c(x1)) -> c#(a(a(x1)))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(b(x1)) -> x1
   a(c(x1)) -> b(c(a(a(x1))))
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> c#(a(a(x1)))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(b(x1)) -> x1
    a(c(x1)) -> b(c(a(a(x1))))
    c(b(x1)) -> a(c(x1))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(c(x1)) -> c#(a(a(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(c(x1)) -> a#(a(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> c#(a(a(x1))) -> c#(b(x1)) -> a#(c(x1))
    a#(c(x1)) -> c#(a(a(x1))) -> c#(b(x1)) -> c#(x1)
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(a(a(x1)))
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(a(x1)))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(a(x1))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [c#](x0) = 12x0,
     
     [a#](x0) = 10x0,
     
     [c](x0) = 2x0,
     
     [a](x0) = x0,
     
     [b](x0) = x0
    orientation:
     a#(c(x1)) = 12x1 >= 10x1 = a#(x1)
     
     a#(c(x1)) = 12x1 >= 10x1 = a#(a(x1))
     
     a#(c(x1)) = 12x1 >= 12x1 = c#(a(a(x1)))
     
     c#(b(x1)) = 12x1 >= 12x1 = c#(x1)
     
     c#(b(x1)) = 12x1 >= 12x1 = a#(c(x1))
     
     a(b(x1)) = x1 >= x1 = x1
     
     a(c(x1)) = 2x1 >= 2x1 = b(c(a(a(x1))))
     
     c(b(x1)) = 2x1 >= 2x1 = a(c(x1))
    problem:
     DPs:
      a#(c(x1)) -> c#(a(a(x1)))
      c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> a#(c(x1))
     TRS:
      a(b(x1)) -> x1
      a(c(x1)) -> b(c(a(a(x1))))
      c(b(x1)) -> a(c(x1))
    EDG Processor:
     DPs:
      a#(c(x1)) -> c#(a(a(x1)))
      c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> a#(c(x1))
     TRS:
      a(b(x1)) -> x1
      a(c(x1)) -> b(c(a(a(x1))))
      c(b(x1)) -> a(c(x1))
     graph:
      c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
      c#(b(x1)) -> a#(c(x1)) -> a#(c(x1)) -> c#(a(a(x1)))
      a#(c(x1)) -> c#(a(a(x1))) -> c#(b(x1)) -> c#(x1)
      a#(c(x1)) -> c#(a(a(x1))) -> c#(b(x1)) -> a#(c(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [-& 1 ]x0 + [0],
       
       [a#](x0) = [-& 3 ]x0 + [0],
       
                 [0  2 ]     [3]
       [c](x0) = [-& 0 ]x0 + [1],
       
                 [-& 0 ]     [1]
       [a](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [b](x0) = [0  2 ]x0 + [3]
      orientation:
       a#(c(x1)) = [-& 3 ]x1 + [4] >= [-& 1 ]x1 + [2] = c#(a(a(x1)))
       
       c#(b(x1)) = [1 3]x1 + [4] >= [-& 1 ]x1 + [0] = c#(x1)
       
       c#(b(x1)) = [1 3]x1 + [4] >= [-& 3 ]x1 + [4] = a#(c(x1))
       
                  [0  2 ]     [3]           
       a(b(x1)) = [-& 0 ]x1 + [0] >= x1 = x1
       
                  [-& 0 ]     [1]    [-& 0 ]     [1]                 
       a(c(x1)) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = b(c(a(a(x1))))
       
                  [2 4]     [5]    [-& 0 ]     [1]           
       c(b(x1)) = [0 2]x1 + [3] >= [0  2 ]x1 + [3] = a(c(x1))
      problem:
       DPs:
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(b(x1)) -> x1
        a(c(x1)) -> b(c(a(a(x1))))
        c(b(x1)) -> a(c(x1))
      EDG Processor:
       DPs:
        c#(b(x1)) -> a#(c(x1))
       TRS:
        a(b(x1)) -> x1
        a(c(x1)) -> b(c(a(a(x1))))
        c(b(x1)) -> a(c(x1))
       graph:
        
       Qed