YES

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

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