YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> c#(b(x1))
   c#(b(x1)) -> a#(x1)
   c#(b(x1)) -> a#(a(x1))
   c#(b(x1)) -> a#(a(a(x1)))
   a#(a(a(a(x1)))) -> c#(x1)
   a#(a(a(a(x1)))) -> b#(c(x1))
  TRS:
   b(c(x1)) -> c(b(x1))
   c(b(x1)) -> a(a(a(x1)))
   a(a(a(a(x1)))) -> b(c(x1))
  TDG Processor:
   DPs:
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> c#(b(x1))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
    c#(b(x1)) -> a#(a(a(x1)))
    a#(a(a(a(x1)))) -> c#(x1)
    a#(a(a(a(x1)))) -> b#(c(x1))
   TRS:
    b(c(x1)) -> c(b(x1))
    c(b(x1)) -> a(a(a(x1)))
    a(a(a(a(x1)))) -> b(c(x1))
   graph:
    a#(a(a(a(x1)))) -> c#(x1) -> c#(b(x1)) -> a#(a(a(x1)))
    a#(a(a(a(x1)))) -> c#(x1) -> c#(b(x1)) -> a#(a(x1))
    a#(a(a(a(x1)))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(a(a(a(x1)))) -> b#(c(x1)) -> b#(c(x1)) -> c#(b(x1))
    a#(a(a(a(x1)))) -> b#(c(x1)) -> b#(c(x1)) -> b#(x1)
    c#(b(x1)) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> b#(c(x1))
    c#(b(x1)) -> a#(a(a(x1))) -> a#(a(a(a(x1)))) -> c#(x1)
    c#(b(x1)) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(c(x1))
    c#(b(x1)) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> c#(x1)
    c#(b(x1)) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(c(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(a(a(x1)))) -> c#(x1)
    b#(c(x1)) -> c#(b(x1)) -> c#(b(x1)) -> a#(a(a(x1)))
    b#(c(x1)) -> c#(b(x1)) -> c#(b(x1)) -> a#(a(x1))
    b#(c(x1)) -> c#(b(x1)) -> c#(b(x1)) -> a#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [a#](x0) = x0,
     
     [c#](x0) = 15x0,
     
     [b#](x0) = 3x0,
     
     [a](x0) = 6x0,
     
     [b](x0) = 3x0,
     
     [c](x0) = 15x0
    orientation:
     b#(c(x1)) = 18x1 >= 3x1 = b#(x1)
     
     b#(c(x1)) = 18x1 >= 18x1 = c#(b(x1))
     
     c#(b(x1)) = 18x1 >= x1 = a#(x1)
     
     c#(b(x1)) = 18x1 >= 6x1 = a#(a(x1))
     
     c#(b(x1)) = 18x1 >= 12x1 = a#(a(a(x1)))
     
     a#(a(a(a(x1)))) = 18x1 >= 15x1 = c#(x1)
     
     a#(a(a(a(x1)))) = 18x1 >= 18x1 = b#(c(x1))
     
     b(c(x1)) = 18x1 >= 18x1 = c(b(x1))
     
     c(b(x1)) = 18x1 >= 18x1 = a(a(a(x1)))
     
     a(a(a(a(x1)))) = 24x1 >= 18x1 = b(c(x1))
    problem:
     DPs:
      b#(c(x1)) -> c#(b(x1))
      a#(a(a(a(x1)))) -> b#(c(x1))
     TRS:
      b(c(x1)) -> c(b(x1))
      c(b(x1)) -> a(a(a(x1)))
      a(a(a(a(x1)))) -> b(c(x1))
    EDG Processor:
     DPs:
      b#(c(x1)) -> c#(b(x1))
      a#(a(a(a(x1)))) -> b#(c(x1))
     TRS:
      b(c(x1)) -> c(b(x1))
      c(b(x1)) -> a(a(a(x1)))
      a(a(a(a(x1)))) -> b(c(x1))
     graph:
      a#(a(a(a(x1)))) -> b#(c(x1)) -> b#(c(x1)) -> c#(b(x1))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4