YES

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

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