YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(a(x1)) -> b(x1)
  b(x1) -> c(x1)
  c(b(x1)) -> a(b(c(x1)))
  c(x1) -> x1
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    b#(x1) -> c#(x1)
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(b(c(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(x1)
    b(x1) -> c(x1)
    c(b(x1)) -> a(b(c(x1)))
    c(x1) -> x1
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     b#(x1) -> c#(x1)
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> b#(c(x1))
     c#(b(x1)) -> a#(b(c(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(x1)
     b(x1) -> c(x1)
     c(b(x1)) -> a(b(c(x1)))
     c(x1) -> x1
    graph:
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> b#(c(x1)) -> b#(x1) -> c#(x1)
     c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(x1)
     b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
     b#(x1) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
     b#(x1) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     a#(a(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> x1
      a(a(x1)) -> b(x1)
      b(x1) -> c(x1)
      c(b(x1)) -> a(b(c(x1)))
      c(x1) -> x1
     interpretation:
      [c#](x0) = [0 0 0]x0,
      
      [b#](x0) = [0 0 0]x0,
      
      [a#](x0) = [-& 0  0 ]x0 + [0],
      
                [0  -& -&]     [-&]
      [c](x0) = [1  0  0 ]x0 + [0 ]
                [1  0  0 ]     [0 ],
      
                [1 0 0]     [0]
      [b](x0) = [1 0 0]x0 + [0]
                [1 0 0]     [0],
      
                [0 0 0]     [0]
      [a](x0) = [1 0 0]x0 + [1]
                [0 1 1]     [1]
     orientation:
      a#(a(x1)) = [1 1 1]x1 + [1] >= [0 0 0]x1 = b#(x1)
      
      b#(x1) = [0 0 0]x1 >= [0 0 0]x1 = c#(x1)
      
      c#(b(x1)) = [1 0 0]x1 + [0] >= [0 0 0]x1 = c#(x1)
      
      c#(b(x1)) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = b#(c(x1))
      
      c#(b(x1)) = [1 0 0]x1 + [0] >= [1 0 0]x1 + [0] = a#(b(c(x1)))
      
              [0 0 0]     [0]           
      a(x1) = [1 0 0]x1 + [1] >= x1 = x1
              [0 1 1]     [1]           
      
                 [1 1 1]     [1]    [1 0 0]     [0]        
      a(a(x1)) = [1 1 1]x1 + [1] >= [1 0 0]x1 + [0] = b(x1)
                 [2 2 2]     [2]    [1 0 0]     [0]        
      
              [1 0 0]     [0]    [0  -& -&]     [-&]        
      b(x1) = [1 0 0]x1 + [0] >= [1  0  0 ]x1 + [0 ] = c(x1)
              [1 0 0]     [0]    [1  0  0 ]     [0 ]        
      
                 [1 0 0]     [0]    [1 0 0]     [0]              
      c(b(x1)) = [2 1 1]x1 + [1] >= [2 1 1]x1 + [1] = a(b(c(x1)))
                 [2 1 1]     [1]    [2 1 1]     [1]              
      
              [0  -& -&]     [-&]           
      c(x1) = [1  0  0 ]x1 + [0 ] >= x1 = x1
              [1  0  0 ]     [0 ]           
     problem:
      DPs:
       b#(x1) -> c#(x1)
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> b#(c(x1))
       c#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(x1)
       b(x1) -> c(x1)
       c(b(x1)) -> a(b(c(x1)))
       c(x1) -> x1
     Restore Modifier:
      DPs:
       b#(x1) -> c#(x1)
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> b#(c(x1))
       c#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(x1)
       b(x1) -> c(x1)
       c(b(x1)) -> a(b(c(x1)))
       c(x1) -> x1
      EDG Processor:
       DPs:
        b#(x1) -> c#(x1)
        c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> b#(c(x1))
        c#(b(x1)) -> a#(b(c(x1)))
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(x1)
        b(x1) -> c(x1)
        c(b(x1)) -> a(b(c(x1)))
        c(x1) -> x1
       graph:
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
        c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
        c#(b(x1)) -> b#(c(x1)) -> b#(x1) -> c#(x1)
        b#(x1) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        b#(x1) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
        b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
       SCC Processor:
        #sccs: 1
        #rules: 3
        #arcs: 7/16
        DPs:
         c#(b(x1)) -> c#(x1)
         c#(b(x1)) -> b#(c(x1))
         b#(x1) -> c#(x1)
        TRS:
         a(x1) -> x1
         a(a(x1)) -> b(x1)
         b(x1) -> c(x1)
         c(b(x1)) -> a(b(c(x1)))
         c(x1) -> x1
        Arctic Interpretation Processor:
         dimension: 3
         usable rules:
          a(x1) -> x1
          a(a(x1)) -> b(x1)
          b(x1) -> c(x1)
          c(b(x1)) -> a(b(c(x1)))
          c(x1) -> x1
         interpretation:
          [c#](x0) = [0 0 0]x0,
          
          [b#](x0) = [0 0 0]x0,
          
                    [0  -& 0 ]  
          [c](x0) = [0  0  0 ]x0
                    [0  0  0 ]  ,
          
                    [0 1 0]  
          [b](x0) = [0 0 0]x0
                    [1 0 1]  ,
          
                    [0 0 0]  
          [a](x0) = [0 1 0]x0
                    [0 1 0]  
         orientation:
          c#(b(x1)) = [1 1 1]x1 >= [0 0 0]x1 = c#(x1)
          
          c#(b(x1)) = [1 1 1]x1 >= [0 0 0]x1 = b#(c(x1))
          
          b#(x1) = [0 0 0]x1 >= [0 0 0]x1 = c#(x1)
          
                  [0 0 0]             
          a(x1) = [0 1 0]x1 >= x1 = x1
                  [0 1 0]             
          
                     [0 1 0]      [0 1 0]          
          a(a(x1)) = [1 2 1]x1 >= [0 0 0]x1 = b(x1)
                     [1 2 1]      [1 0 1]          
          
                  [0 1 0]      [0  -& 0 ]          
          b(x1) = [0 0 0]x1 >= [0  0  0 ]x1 = c(x1)
                  [1 0 1]      [0  0  0 ]          
          
                     [1 1 1]      [1 1 1]                
          c(b(x1)) = [1 1 1]x1 >= [1 1 1]x1 = a(b(c(x1)))
                     [1 1 1]      [1 1 1]                
          
                  [0  -& 0 ]             
          c(x1) = [0  0  0 ]x1 >= x1 = x1
                  [0  0  0 ]             
         problem:
          DPs:
           b#(x1) -> c#(x1)
          TRS:
           a(x1) -> x1
           a(a(x1)) -> b(x1)
           b(x1) -> c(x1)
           c(b(x1)) -> a(b(c(x1)))
           c(x1) -> x1
         Restore Modifier:
          DPs:
           b#(x1) -> c#(x1)
          TRS:
           a(x1) -> x1
           a(a(x1)) -> b(x1)
           b(x1) -> c(x1)
           c(b(x1)) -> a(b(c(x1)))
           c(x1) -> x1
          EDG Processor:
           DPs:
            b#(x1) -> c#(x1)
           TRS:
            a(x1) -> x1
            a(a(x1)) -> b(x1)
            b(x1) -> c(x1)
            c(b(x1)) -> a(b(c(x1)))
            c(x1) -> x1
           graph:
            
           Qed