YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> c#(x1)
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> c#(a(x1))
   c#(c(x1)) -> a#(b(c(a(x1))))
  TRS:
   a(x1) -> b(x1)
   a(b(b(x1))) -> c(x1)
   c(c(x1)) -> a(b(c(a(x1))))
  TDG Processor:
   DPs:
    a#(b(b(x1))) -> c#(x1)
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> c#(a(x1))
    c#(c(x1)) -> a#(b(c(a(x1))))
   TRS:
    a(x1) -> b(x1)
    a(b(b(x1))) -> c(x1)
    c(c(x1)) -> a(b(c(a(x1))))
   graph:
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(c(a(x1))))
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1))
    c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1)
    c#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> c#(x1)
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1))))
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> c#(a(x1))
    a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [c#](x0) = 4x0,
     
     [a#](x0) = 2x0,
     
     [c](x0) = 3x0,
     
     [b](x0) = 1x0,
     
     [a](x0) = 1x0
    orientation:
     a#(b(b(x1))) = 4x1 >= 4x1 = c#(x1)
     
     c#(c(x1)) = 7x1 >= 2x1 = a#(x1)
     
     c#(c(x1)) = 7x1 >= 5x1 = c#(a(x1))
     
     c#(c(x1)) = 7x1 >= 7x1 = a#(b(c(a(x1))))
     
     a(x1) = 1x1 >= 1x1 = b(x1)
     
     a(b(b(x1))) = 3x1 >= 3x1 = c(x1)
     
     c(c(x1)) = 6x1 >= 6x1 = a(b(c(a(x1))))
    problem:
     DPs:
      a#(b(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(c(a(x1))))
     TRS:
      a(x1) -> b(x1)
      a(b(b(x1))) -> c(x1)
      c(c(x1)) -> a(b(c(a(x1))))
    EDG Processor:
     DPs:
      a#(b(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(c(a(x1))))
     TRS:
      a(x1) -> b(x1)
      a(b(b(x1))) -> c(x1)
      c(c(x1)) -> a(b(c(a(x1))))
     graph:
      c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1)
      a#(b(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(c(a(x1))))
     CDG Processor:
      DPs:
       a#(b(b(x1))) -> c#(x1)
       c#(c(x1)) -> a#(b(c(a(x1))))
      TRS:
       a(x1) -> b(x1)
       a(b(b(x1))) -> c(x1)
       c(c(x1)) -> a(b(c(a(x1))))
      graph:
       c#(c(x1)) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> c#(x1)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 1/4