YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> c#(a(x1))
   a#(b(x1)) -> b#(c(a(x1)))
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(c(x1)) -> c#(b(b(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> a#(c(x1))
  TRS:
   a(b(x1)) -> b(c(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   c(a(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> b#(c(a(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> c#(b(b(x1)))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> a#(c(x1))
   TRS:
    a(b(x1)) -> b(c(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    c(a(x1)) -> a(c(x1))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> c#(b(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> a#(c(x1))
    b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> a#(c(x1)) -> a#(b(x1)) -> b#(c(a(x1)))
    c#(a(x1)) -> a#(c(x1)) -> a#(b(x1)) -> c#(a(x1))
    c#(a(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> c#(b(b(x1)))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> c#(a(x1)) -> c#(a(x1)) -> a#(c(x1))
    a#(b(x1)) -> c#(a(x1)) -> c#(a(x1)) -> c#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = 0,
     
     [c#](x0) = 0,
     
     [a#](x0) = x0 + 0,
     
     [c](x0) = 0,
     
     [a](x0) = x0 + 0,
     
     [b](x0) = x0 + 8
    orientation:
     a#(b(x1)) = x1 + 8 >= x1 + 0 = a#(x1)
     
     a#(b(x1)) = x1 + 8 >= 0 = c#(a(x1))
     
     a#(b(x1)) = x1 + 8 >= 0 = b#(c(a(x1)))
     
     b#(c(x1)) = 0 >= 0 = b#(x1)
     
     b#(c(x1)) = 0 >= 0 = b#(b(x1))
     
     b#(c(x1)) = 0 >= 0 = c#(b(b(x1)))
     
     c#(a(x1)) = 0 >= 0 = c#(x1)
     
     c#(a(x1)) = 0 >= 0 = a#(c(x1))
     
     a(b(x1)) = x1 + 8 >= 8 = b(c(a(x1)))
     
     b(c(x1)) = 8 >= 0 = c(b(b(x1)))
     
     c(a(x1)) = 0 >= 0 = a(c(x1))
    problem:
     DPs:
      a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> c#(b(b(x1)))
      c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> a#(c(x1))
     TRS:
      a(b(x1)) -> b(c(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      c(a(x1)) -> a(c(x1))
    EDG Processor:
     DPs:
      a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> c#(b(b(x1)))
      c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> a#(c(x1))
     TRS:
      a(b(x1)) -> b(c(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      c(a(x1)) -> a(c(x1))
     graph:
      b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> c#(b(b(x1)))
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(b(x1)))
      b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(x1)
      b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> a#(c(x1))
      c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
      c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
      c#(a(x1)) -> a#(c(x1)) -> a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     SCC Processor:
      #sccs: 3
      #rules: 4
      #arcs: 12/36
      DPs:
       b#(c(x1)) -> b#(b(x1))
       b#(c(x1)) -> b#(x1)
      TRS:
       a(b(x1)) -> b(c(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       c(a(x1)) -> a(c(x1))
      Matrix Interpretation Processor: dim=4
       
       interpretation:
        [b#](x0) = [1 1 0 0]x0,
        
                  [0 0 0 0]     [1]
                  [1 1 0 0]     [0]
        [c](x0) = [1 0 0 0]x0 + [0]
                  [0 0 0 0]     [0],
        
                  [0 0 0 0]     [1]
                  [1 0 1 1]     [0]
        [a](x0) = [0 0 0 0]x0 + [1]
                  [0 0 0 1]     [0],
        
                  [1 0 0 0]     [0]
                  [0 1 0 0]     [0]
        [b](x0) = [0 0 1 1]x0 + [0]
                  [0 0 0 0]     [1]
       orientation:
        b#(c(x1)) = [1 1 0 0]x1 + [1] >= [1 1 0 0]x1 = b#(b(x1))
        
        b#(c(x1)) = [1 1 0 0]x1 + [1] >= [1 1 0 0]x1 = b#(x1)
        
                   [0 0 0 0]     [1]    [0 0 0 0]     [1]              
                   [1 0 1 1]     [1]    [1 0 1 1]     [1]              
        a(b(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(c(a(x1)))
                   [0 0 0 0]     [1]    [0 0 0 0]     [1]              
        
                   [0 0 0 0]     [1]    [0 0 0 0]     [1]              
                   [1 1 0 0]     [0]    [1 1 0 0]     [0]              
        b(c(x1)) = [1 0 0 0]x1 + [0] >= [1 0 0 0]x1 + [0] = c(b(b(x1)))
                   [0 0 0 0]     [1]    [0 0 0 0]     [0]              
        
                   [0 0 0 0]     [1]    [0 0 0 0]     [1]           
                   [1 0 1 1]     [1]    [1 0 0 0]     [1]           
        c(a(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a(c(x1))
                   [0 0 0 0]     [0]    [0 0 0 0]     [0]           
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> b(c(a(x1)))
         b(c(x1)) -> c(b(b(x1)))
         c(a(x1)) -> a(c(x1))
       Qed
      
      DPs:
       c#(a(x1)) -> c#(x1)
      TRS:
       a(b(x1)) -> b(c(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       c(a(x1)) -> a(c(x1))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [c#](x0) = 2x0,
        
        [c](x0) = x0,
        
        [a](x0) = 1x0,
        
        [b](x0) = x0
       orientation:
        c#(a(x1)) = 3x1 >= 2x1 = c#(x1)
        
        a(b(x1)) = 1x1 >= 1x1 = b(c(a(x1)))
        
        b(c(x1)) = x1 >= x1 = c(b(b(x1)))
        
        c(a(x1)) = 1x1 >= 1x1 = a(c(x1))
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> b(c(a(x1)))
         b(c(x1)) -> c(b(b(x1)))
         c(a(x1)) -> a(c(x1))
       Qed
      
      DPs:
       a#(b(x1)) -> a#(x1)
      TRS:
       a(b(x1)) -> b(c(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       c(a(x1)) -> a(c(x1))
      Arctic Interpretation Processor:
       dimension: 1
       interpretation:
        [a#](x0) = 6x0 + 0,
        
        [c](x0) = 0,
        
        [a](x0) = x0 + 0,
        
        [b](x0) = 2x0 + 3
       orientation:
        a#(b(x1)) = 8x1 + 9 >= 6x1 + 0 = a#(x1)
        
        a(b(x1)) = 2x1 + 3 >= 3 = b(c(a(x1)))
        
        b(c(x1)) = 3 >= 0 = c(b(b(x1)))
        
        c(a(x1)) = 0 >= 0 = a(c(x1))
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> b(c(a(x1)))
         b(c(x1)) -> c(b(b(x1)))
         c(a(x1)) -> a(c(x1))
       Qed