YES

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

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