YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(c(a(x1)))
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(c(b(x1)))
  TRS:
   a(b(x1)) -> b(c(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   b(a(x1)) -> a(c(b(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1)))
   TRS:
    a(b(x1)) -> b(c(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    b(a(x1)) -> a(c(b(x1)))
   graph:
    b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> 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#(a(x1)) -> a#(c(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> b#(c(a(x1)))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> a#(c(b(x1)))
    a#(b(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> 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)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   EDG Processor:
    DPs:
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> b#(c(a(x1)))
     b#(c(x1)) -> b#(x1)
     b#(c(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(c(b(x1)))
    TRS:
     a(b(x1)) -> b(c(a(x1)))
     b(c(x1)) -> c(b(b(x1)))
     b(a(x1)) -> a(c(b(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#(a(x1)) -> b#(x1)
     b#(c(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(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#(a(x1)) -> b#(x1)
     b#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1)
     a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    SCC Processor:
     #sccs: 2
     #rules: 4
     #arcs: 16/36
     DPs:
      a#(b(x1)) -> a#(x1)
     TRS:
      a(b(x1)) -> b(c(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      b(a(x1)) -> a(c(b(x1)))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0 + -6,
       
       [c](x0) = 10,
       
       [a](x0) = 5x0 + 13,
       
       [b](x0) = 2x0 + 0
      orientation:
       a#(b(x1)) = 2x1 + 0 >= x1 + -6 = a#(x1)
       
       a(b(x1)) = 7x1 + 13 >= 12 = b(c(a(x1)))
       
       b(c(x1)) = 12 >= 10 = c(b(b(x1)))
       
       b(a(x1)) = 7x1 + 15 >= 15 = a(c(b(x1)))
      problem:
       DPs:
        
       TRS:
        a(b(x1)) -> b(c(a(x1)))
        b(c(x1)) -> c(b(b(x1)))
        b(a(x1)) -> a(c(b(x1)))
      Qed
     
     DPs:
      b#(c(x1)) -> b#(b(x1))
      b#(a(x1)) -> b#(x1)
      b#(c(x1)) -> b#(x1)
     TRS:
      a(b(x1)) -> b(c(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      b(a(x1)) -> a(c(b(x1)))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0,
       
       [c](x0) = x0 + -2,
       
       [a](x0) = 5x0 + 12,
       
       [b](x0) = x0 + -12
      orientation:
       b#(c(x1)) = x1 + -2 >= x1 + -12 = b#(b(x1))
       
       b#(a(x1)) = 5x1 + 12 >= x1 = b#(x1)
       
       b#(c(x1)) = x1 + -2 >= x1 = b#(x1)
       
       a(b(x1)) = 5x1 + 12 >= 5x1 + 12 = b(c(a(x1)))
       
       b(c(x1)) = x1 + -2 >= x1 + -2 = c(b(b(x1)))
       
       b(a(x1)) = 5x1 + 12 >= 5x1 + 12 = a(c(b(x1)))
      problem:
       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)))
        b(a(x1)) -> a(c(b(x1)))
      EDG Processor:
       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)))
        b(a(x1)) -> a(c(b(x1)))
       graph:
        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)) -> b#(b(x1))
        b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
       Matrix Interpretation Processor: dim=4
        
        interpretation:
         [b#](x0) = [0 0 0 1]x0,
         
                   [0 0 0 0]     [0]
                   [0 0 0 0]     [0]
         [c](x0) = [0 0 0 0]x0 + [0]
                   [1 0 0 1]     [1],
         
                   [0 0 0 0]  
                   [0 1 0 0]  
         [a](x0) = [0 0 1 0]x0
                   [0 1 1 0]  ,
         
                   [0 0 0 0]     [0]
                   [0 1 1 0]     [0]
         [b](x0) = [0 0 0 0]x0 + [1]
                   [1 0 0 1]     [0]
        orientation:
         b#(c(x1)) = [1 0 0 1]x1 + [1] >= [1 0 0 1]x1 = b#(b(x1))
         
         b#(c(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 1]x1 = b#(x1)
         
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
                    [0 1 1 0]     [0]    [0 0 0 0]     [0]              
         a(b(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(c(a(x1)))
                    [0 1 1 0]     [1]    [0 1 1 0]     [1]              
         
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
         b(c(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = c(b(b(x1)))
                    [1 0 0 1]     [1]    [1 0 0 1]     [1]              
         
                    [0 0 0 0]     [0]    [0]              
                    [0 1 1 0]     [0]    [0]              
         b(a(x1)) = [0 0 0 0]x1 + [1] >= [0] = a(c(b(x1)))
                    [0 1 1 0]     [0]    [0]              
        problem:
         DPs:
          
         TRS:
          a(b(x1)) -> b(c(a(x1)))
          b(c(x1)) -> c(b(b(x1)))
          b(a(x1)) -> a(c(b(x1)))
        Qed