YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   a#(x1) -> b#(b(x1))
   a#(b(b(x1))) -> a#(x1)
   a#(b(b(x1))) -> c#(a(x1))
   a#(b(b(x1))) -> c#(c(a(x1)))
   a#(b(b(x1))) -> c#(c(c(a(x1))))
   a#(b(b(x1))) -> b#(c(c(c(a(x1)))))
   a#(b(b(x1))) -> b#(b(c(c(c(a(x1))))))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> c#(c(c(x1)))
   c#(c(c(b(b(x1))))) -> a#(x1)
  TRS:
   a(x1) -> b(b(x1))
   a(b(b(x1))) -> b(b(c(c(c(a(x1))))))
   b(b(x1)) -> c(c(c(x1)))
   c(c(c(b(b(x1))))) -> a(x1)
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> c#(a(x1))
    a#(b(b(x1))) -> c#(c(a(x1)))
    a#(b(b(x1))) -> c#(c(c(a(x1))))
    a#(b(b(x1))) -> b#(c(c(c(a(x1)))))
    a#(b(b(x1))) -> b#(b(c(c(c(a(x1))))))
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(c(x1))
    b#(b(x1)) -> c#(c(c(x1)))
    c#(c(c(b(b(x1))))) -> a#(x1)
   TRS:
    a(x1) -> b(b(x1))
    a(b(b(x1))) -> b(b(c(c(c(a(x1))))))
    b(b(x1)) -> c(c(c(x1)))
    c(c(c(b(b(x1))))) -> a(x1)
   graph:
    c#(c(c(b(b(x1))))) -> a#(x1) ->
    a#(b(b(x1))) -> b#(b(c(c(c(a(x1))))))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(b(b(x1))) -> b#(c(c(c(a(x1)))))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(b(b(x1))) -> c#(c(c(a(x1))))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(b(b(x1))) -> c#(c(a(x1)))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(b(b(x1))) -> c#(a(x1))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(x1) -> b#(b(x1))
    c#(c(c(b(b(x1))))) -> a#(x1) -> a#(x1) -> b#(x1)
    b#(b(x1)) -> c#(c(c(x1))) -> c#(c(c(b(b(x1))))) -> a#(x1)
    b#(b(x1)) -> c#(c(x1)) -> c#(c(c(b(b(x1))))) -> a#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(c(b(b(x1))))) -> a#(x1)
    a#(b(b(x1))) -> c#(c(c(a(x1)))) -> c#(c(c(b(b(x1))))) -> a#(x1)
    a#(b(b(x1))) -> c#(c(a(x1))) -> c#(c(c(b(b(x1))))) -> a#(x1)
    a#(b(b(x1))) -> c#(a(x1)) -> c#(c(c(b(b(x1))))) -> a#(x1)
    a#(b(b(x1))) -> b#(c(c(c(a(x1))))) ->
    b#(b(x1)) -> c#(c(c(x1)))
    a#(b(b(x1))) -> b#(c(c(c(a(x1))))) -> b#(b(x1)) -> c#(c(x1))
    a#(b(b(x1))) -> b#(c(c(c(a(x1))))) -> b#(b(x1)) -> c#(x1)
    a#(b(b(x1))) -> b#(b(c(c(c(a(x1)))))) ->
    b#(b(x1)) -> c#(c(c(x1)))
    a#(b(b(x1))) -> b#(b(c(c(c(a(x1)))))) ->
    b#(b(x1)) -> c#(c(x1))
    a#(b(b(x1))) -> b#(b(c(c(c(a(x1)))))) -> b#(b(x1)) -> c#(x1)
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(b(c(c(c(a(x1))))))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(c(c(c(a(x1)))))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(c(c(a(x1))))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(c(a(x1)))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(a(x1))
    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
    a#(b(b(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(c(x1)))
    a#(x1) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(x1))
    a#(x1) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1)
    a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(c(c(x1)))
    a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(c(x1))
    a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c#](x0) = 4x0,
     
     [b#](x0) = 2x0 + 1,
     
     [a#](x0) = 4x0 + 10,
     
     [c](x0) = x0,
     
     [b](x0) = 2x0 + 4,
     
     [a](x0) = 4x0 + 12
    orientation:
     a#(x1) = 4x1 + 10 >= 2x1 + 1 = b#(x1)
     
     a#(x1) = 4x1 + 10 >= 4x1 + 9 = b#(b(x1))
     
     a#(b(b(x1))) = 16x1 + 58 >= 4x1 + 10 = a#(x1)
     
     a#(b(b(x1))) = 16x1 + 58 >= 16x1 + 48 = c#(a(x1))
     
     a#(b(b(x1))) = 16x1 + 58 >= 16x1 + 48 = c#(c(a(x1)))
     
     a#(b(b(x1))) = 16x1 + 58 >= 16x1 + 48 = c#(c(c(a(x1))))
     
     a#(b(b(x1))) = 16x1 + 58 >= 8x1 + 25 = b#(c(c(c(a(x1)))))
     
     a#(b(b(x1))) = 16x1 + 58 >= 16x1 + 57 = b#(b(c(c(c(a(x1))))))
     
     b#(b(x1)) = 4x1 + 9 >= 4x1 = c#(x1)
     
     b#(b(x1)) = 4x1 + 9 >= 4x1 = c#(c(x1))
     
     b#(b(x1)) = 4x1 + 9 >= 4x1 = c#(c(c(x1)))
     
     c#(c(c(b(b(x1))))) = 16x1 + 48 >= 4x1 + 10 = a#(x1)
     
     a(x1) = 4x1 + 12 >= 4x1 + 12 = b(b(x1))
     
     a(b(b(x1))) = 16x1 + 60 >= 16x1 + 60 = b(b(c(c(c(a(x1))))))
     
     b(b(x1)) = 4x1 + 12 >= x1 = c(c(c(x1)))
     
     c(c(c(b(b(x1))))) = 4x1 + 12 >= 4x1 + 12 = a(x1)
    problem:
     DPs:
      
     TRS:
      a(x1) -> b(b(x1))
      a(b(b(x1))) -> b(b(c(c(c(a(x1))))))
      b(b(x1)) -> c(c(c(x1)))
      c(c(c(b(b(x1))))) -> a(x1)
    Qed