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
     usable rules:
      a(x1) -> c(b(x1))
      b(a(x1)) -> a(c(x1))
      c(c(c(x1))) -> b(a(x1))
     interpretation:
      [b#](x0) = x0,
      
      [c](x0) = 2x0,
      
      [a#](x0) = 2x0,
      
      [c#](x0) = x0,
      
      [a](x0) = 4x0,
      
      [b](x0) = 2x0
     orientation:
      a#(x1) = 2x1 >= x1 = b#(x1)
      
      a#(x1) = 2x1 >= 2x1 = c#(b(x1))
      
      b#(a(x1)) = 4x1 >= x1 = c#(x1)
      
      b#(a(x1)) = 4x1 >= 4x1 = a#(c(x1))
      
      c#(c(c(x1))) = 4x1 >= 2x1 = a#(x1)
      
      c#(c(c(x1))) = 4x1 >= 4x1 = b#(a(x1))
      
      a(x1) = 4x1 >= 4x1 = c(b(x1))
      
      b(a(x1)) = 6x1 >= 6x1 = a(c(x1))
      
      c(c(c(x1))) = 6x1 >= 6x1 = 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))
     Restore Modifier:
      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
        usable rules:
         a(x1) -> c(b(x1))
         b(a(x1)) -> a(c(x1))
         c(c(c(x1))) -> b(a(x1))
        interpretation:
         [b#](x0) = [1 0]x0,
         
                   [0 1]  
         [c](x0) = [0 1]x0,
         
         [a#](x0) = [2 2]x0,
         
         [c#](x0) = [1 2]x0,
         
                   [1 2]  
         [a](x0) = [1 1]x0,
         
                   [1 1]  
         [b](x0) = [0 0]x0
        orientation:
         a#(x1) = [2 2]x1 >= [2 2]x1 = c#(b(x1))
         
         b#(a(x1)) = [2 3]x1 >= [2 3]x1 = a#(c(x1))
         
         c#(c(c(x1))) = [3 4]x1 >= [2 3]x1 = b#(a(x1))
         
                 [1 2]      [1 1]             
         a(x1) = [1 1]x1 >= [1 1]x1 = c(b(x1))
         
                    [2 3]      [2 3]             
         b(a(x1)) = [1 2]x1 >= [1 2]x1 = a(c(x1))
         
                       [2 3]      [2 3]             
         c(c(c(x1))) = [2 3]x1 >= [1 2]x1 = b(a(x1))
        problem:
         DPs:
          a#(x1) -> c#(b(x1))
          b#(a(x1)) -> a#(c(x1))
         TRS:
          a(x1) -> c(b(x1))
          b(a(x1)) -> a(c(x1))
          c(c(c(x1))) -> b(a(x1))
        Restore Modifier:
         DPs:
          a#(x1) -> c#(b(x1))
          b#(a(x1)) -> a#(c(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))
          TRS:
           a(x1) -> c(b(x1))
           b(a(x1)) -> a(c(x1))
           c(c(c(x1))) -> b(a(x1))
          graph:
           b#(a(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1))
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4