YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> b#(b(x1))
   a#(a(x1)) -> b#(b(b(x1)))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> c#(c(c(x1)))
   c#(c(c(c(x1)))) -> b#(x1)
   c#(c(c(c(x1)))) -> a#(b(x1))
  TRS:
   a(a(x1)) -> b(b(b(x1)))
   b(b(x1)) -> c(c(c(x1)))
   c(c(c(c(x1)))) -> a(b(x1))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c#](x0) = x0 + 13,
    
    [b#](x0) = x0 + 17,
    
    [a#](x0) = x0 + 21,
    
    [c](x0) = x0 + 6,
    
    [b](x0) = x0 + 9,
    
    [a](x0) = x0 + 15
   orientation:
    a#(a(x1)) = x1 + 36 >= x1 + 17 = b#(x1)
    
    a#(a(x1)) = x1 + 36 >= x1 + 26 = b#(b(x1))
    
    a#(a(x1)) = x1 + 36 >= x1 + 35 = b#(b(b(x1)))
    
    b#(b(x1)) = x1 + 26 >= x1 + 13 = c#(x1)
    
    b#(b(x1)) = x1 + 26 >= x1 + 19 = c#(c(x1))
    
    b#(b(x1)) = x1 + 26 >= x1 + 25 = c#(c(c(x1)))
    
    c#(c(c(c(x1)))) = x1 + 31 >= x1 + 17 = b#(x1)
    
    c#(c(c(c(x1)))) = x1 + 31 >= x1 + 30 = a#(b(x1))
    
    a(a(x1)) = x1 + 30 >= x1 + 27 = b(b(b(x1)))
    
    b(b(x1)) = x1 + 18 >= x1 + 18 = c(c(c(x1)))
    
    c(c(c(c(x1)))) = x1 + 24 >= x1 + 24 = a(b(x1))
   problem:
    DPs:
     
    TRS:
     a(a(x1)) -> b(b(b(x1)))
     b(b(x1)) -> c(c(c(x1)))
     c(c(c(c(x1)))) -> a(b(x1))
   Qed