YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> a#(c(x1))
   a#(a(x1)) -> b#(a(c(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
   c#(b(x1)) -> a#(x1)
  TRS:
   a(a(x1)) -> b(a(c(x1)))
   b(b(x1)) -> a(a(x1))
   c(b(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> a#(c(x1))
    a#(a(x1)) -> b#(a(c(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(a(x1)) -> b(a(c(x1)))
    b(b(x1)) -> a(a(x1))
    c(b(x1)) -> a(x1)
   graph:
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(x1))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(x1)))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(c(x1)))
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1))
    a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(a(x1)) -> b(a(c(x1)))
     b(b(x1)) -> a(a(x1))
     c(b(x1)) -> a(x1)
    interpretation:
     [b#](x0) = [-& 1 ]x0 + [0],
     
     [c#](x0) = [-& 0 ]x0 + [0],
     
     [a#](x0) = [-& 1 ]x0 + [0],
     
               [-& 0 ]     [0]
     [b](x0) = [0  1 ]x0 + [3],
     
               [-& 0 ]     [0]
     [c](x0) = [-& 0 ]x0 + [2],
     
               [0  0 ]     [0]
     [a](x0) = [-& 1 ]x0 + [3]
    orientation:
     a#(a(x1)) = [-& 2 ]x1 + [4] >= [-& 0 ]x1 + [0] = c#(x1)
     
     a#(a(x1)) = [-& 2 ]x1 + [4] >= [-& 1 ]x1 + [3] = a#(c(x1))
     
     a#(a(x1)) = [-& 2 ]x1 + [4] >= [-& 2 ]x1 + [4] = b#(a(c(x1)))
     
     b#(b(x1)) = [1 2]x1 + [4] >= [-& 1 ]x1 + [0] = a#(x1)
     
     b#(b(x1)) = [1 2]x1 + [4] >= [-& 2 ]x1 + [4] = a#(a(x1))
     
     c#(b(x1)) = [0 1]x1 + [3] >= [-& 1 ]x1 + [0] = a#(x1)
     
                [0  1 ]     [3]    [-& 1 ]     [3]              
     a(a(x1)) = [-& 2 ]x1 + [4] >= [-& 2 ]x1 + [4] = b(a(c(x1)))
     
                [0 1]     [3]    [0  1 ]     [3]           
     b(b(x1)) = [1 2]x1 + [4] >= [-& 2 ]x1 + [4] = a(a(x1))
     
                [0 1]     [3]    [0  0 ]     [0]        
     c(b(x1)) = [0 1]x1 + [3] >= [-& 1 ]x1 + [3] = a(x1)
    problem:
     DPs:
      a#(a(x1)) -> b#(a(c(x1)))
      b#(b(x1)) -> a#(a(x1))
      c#(b(x1)) -> a#(x1)
     TRS:
      a(a(x1)) -> b(a(c(x1)))
      b(b(x1)) -> a(a(x1))
      c(b(x1)) -> a(x1)
    Restore Modifier:
     DPs:
      a#(a(x1)) -> b#(a(c(x1)))
      b#(b(x1)) -> a#(a(x1))
      c#(b(x1)) -> a#(x1)
     TRS:
      a(a(x1)) -> b(a(c(x1)))
      b(b(x1)) -> a(a(x1))
      c(b(x1)) -> a(x1)
     EDG Processor:
      DPs:
       a#(a(x1)) -> b#(a(c(x1)))
       b#(b(x1)) -> a#(a(x1))
       c#(b(x1)) -> a#(x1)
      TRS:
       a(a(x1)) -> b(a(c(x1)))
       b(b(x1)) -> a(a(x1))
       c(b(x1)) -> a(x1)
      graph:
       b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(x1)))
       c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(x1)))
       a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(x1))
      SCC Processor:
       #sccs: 1
       #rules: 2
       #arcs: 3/9
       DPs:
        b#(b(x1)) -> a#(a(x1))
        a#(a(x1)) -> b#(a(c(x1)))
       TRS:
        a(a(x1)) -> b(a(c(x1)))
        b(b(x1)) -> a(a(x1))
        c(b(x1)) -> a(x1)
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(a(x1)) -> b(a(c(x1)))
         b(b(x1)) -> a(a(x1))
         c(b(x1)) -> a(x1)
        interpretation:
         [b#](x0) = [-& 0 ]x0 + [0],
         
         [a#](x0) = [0 0]x0 + [0],
         
                   [0 1]     [0]
         [b](x0) = [0 1]x0 + [1],
         
                   [-& 0 ]     [0]
         [c](x0) = [-& 0 ]x0 + [0],
         
                   [0 1]     [1]
         [a](x0) = [0 0]x0 + [0]
        orientation:
         b#(b(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = a#(a(x1))
         
         a#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(a(c(x1)))
         
                    [1 1]     [1]    [-& 1 ]     [1]              
         a(a(x1)) = [0 1]x1 + [1] >= [-& 1 ]x1 + [1] = b(a(c(x1)))
         
                    [1 2]     [2]    [1 1]     [1]           
         b(b(x1)) = [1 2]x1 + [2] >= [0 1]x1 + [1] = a(a(x1))
         
                    [0 1]     [1]    [0 1]     [1]        
         c(b(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [0] = a(x1)
        problem:
         DPs:
          b#(b(x1)) -> a#(a(x1))
         TRS:
          a(a(x1)) -> b(a(c(x1)))
          b(b(x1)) -> a(a(x1))
          c(b(x1)) -> a(x1)
        Restore Modifier:
         DPs:
          b#(b(x1)) -> a#(a(x1))
         TRS:
          a(a(x1)) -> b(a(c(x1)))
          b(b(x1)) -> a(a(x1))
          c(b(x1)) -> a(x1)
         EDG Processor:
          DPs:
           b#(b(x1)) -> a#(a(x1))
          TRS:
           a(a(x1)) -> b(a(c(x1)))
           b(b(x1)) -> a(a(x1))
           c(b(x1)) -> a(x1)
          graph:
           
          Qed