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