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: 1
    usable rules:
     a(a(x1)) -> b(a(c(x1)))
     b(b(x1)) -> a(a(x1))
     c(b(x1)) -> a(x1)
    interpretation:
     [c#](x0) = 5x0,
     
     [c](x0) = x0,
     
     [a#](x0) = 3x0,
     
     [b#](x0) = 3x0,
     
     [a](x0) = 2x0,
     
     [b](x0) = 2x0
    orientation:
     a#(a(x1)) = 5x1 >= 5x1 = c#(x1)
     
     a#(a(x1)) = 5x1 >= 3x1 = a#(c(x1))
     
     a#(a(x1)) = 5x1 >= 5x1 = b#(a(c(x1)))
     
     b#(b(x1)) = 5x1 >= 3x1 = a#(x1)
     
     b#(b(x1)) = 5x1 >= 5x1 = a#(a(x1))
     
     c#(b(x1)) = 7x1 >= 3x1 = a#(x1)
     
     a(a(x1)) = 4x1 >= 4x1 = b(a(c(x1)))
     
     b(b(x1)) = 4x1 >= 4x1 = a(a(x1))
     
     c(b(x1)) = 2x1 >= 2x1 = a(x1)
    problem:
     DPs:
      a#(a(x1)) -> c#(x1)
      a#(a(x1)) -> b#(a(c(x1)))
      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:
      a#(a(x1)) -> c#(x1)
      a#(a(x1)) -> b#(a(c(x1)))
      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:
       a#(a(x1)) -> c#(x1)
       a#(a(x1)) -> b#(a(c(x1)))
       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:
       b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1)
       b#(b(x1)) -> a#(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:
                   [0  -&]  
         [c](x0) = [0  -&]x0,
         
         [a#](x0) = [-& 0 ]x0 + [0],
         
         [b#](x0) = [0  -&]x0,
         
                   [0  0 ]     [-&]
         [a](x0) = [3  -&]x0 + [0 ],
         
                   [3 0]     [0]
         [b](x0) = [3 0]x0 + [0]
        orientation:
         b#(b(x1)) = [3 0]x1 + [0] >= [3  -&]x1 + [0] = a#(a(x1))
         
         a#(a(x1)) = [3  -&]x1 + [0] >= [0  -&]x1 = b#(a(c(x1)))
         
                    [3 0]     [0]    [3  -&]     [0]              
         a(a(x1)) = [3 3]x1 + [0] >= [3  -&]x1 + [0] = b(a(c(x1)))
         
                    [6 3]     [3]    [3 0]     [0]           
         b(b(x1)) = [6 3]x1 + [3] >= [3 3]x1 + [0] = a(a(x1))
         
                    [3 0]     [0]    [0  0 ]     [-&]        
         c(b(x1)) = [3 0]x1 + [0] >= [3  -&]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:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1