YES

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

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