YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> c#(a(x1))
   a#(b(x1)) -> b#(c(a(x1)))
   b#(x1) -> c#(x1)
   c#(b(x1)) -> a#(x1)
  TRS:
   a(x1) -> b(x1)
   a(b(x1)) -> b(c(a(x1)))
   b(x1) -> c(x1)
   c(b(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> b#(c(a(x1)))
    b#(x1) -> c#(x1)
    c#(b(x1)) -> a#(x1)
   TRS:
    a(x1) -> b(x1)
    a(b(x1)) -> b(c(a(x1)))
    b(x1) -> c(x1)
    c(b(x1)) -> a(x1)
   graph:
    c#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    c#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
    c#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
    b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(a(x1))) -> b#(x1) -> c#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(x1) -> b#(x1) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [c#](x0) = 6x0,
     
     [b#](x0) = 15x0,
     
     [a#](x0) = 15x0,
     
     [c](x0) = x0,
     
     [b](x0) = 10x0,
     
     [a](x0) = 10x0
    orientation:
     a#(x1) = 15x1 >= 15x1 = b#(x1)
     
     a#(b(x1)) = 25x1 >= 15x1 = a#(x1)
     
     a#(b(x1)) = 25x1 >= 16x1 = c#(a(x1))
     
     a#(b(x1)) = 25x1 >= 25x1 = b#(c(a(x1)))
     
     b#(x1) = 15x1 >= 6x1 = c#(x1)
     
     c#(b(x1)) = 16x1 >= 15x1 = a#(x1)
     
     a(x1) = 10x1 >= 10x1 = b(x1)
     
     a(b(x1)) = 20x1 >= 20x1 = b(c(a(x1)))
     
     b(x1) = 10x1 >= x1 = c(x1)
     
     c(b(x1)) = 10x1 >= 10x1 = a(x1)
    problem:
     DPs:
      a#(x1) -> b#(x1)
      a#(b(x1)) -> b#(c(a(x1)))
     TRS:
      a(x1) -> b(x1)
      a(b(x1)) -> b(c(a(x1)))
      b(x1) -> c(x1)
      c(b(x1)) -> a(x1)
    EDG Processor:
     DPs:
      a#(x1) -> b#(x1)
      a#(b(x1)) -> b#(c(a(x1)))
     TRS:
      a(x1) -> b(x1)
      a(b(x1)) -> b(c(a(x1)))
      b(x1) -> c(x1)
      c(b(x1)) -> a(x1)
     graph:
      
     Qed