YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> a#(x1)
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> a#(c(x1))
   a#(x1) -> b#(x1)
   a#(x1) -> c#(b(x1))
   c#(c(c(x1))) -> b#(x1)
  TRS:
   b(c(x1)) -> a(x1)
   b(b(x1)) -> a(c(x1))
   a(x1) -> c(b(x1))
   c(c(c(x1))) -> b(x1)
  TDG Processor:
   DPs:
    b#(c(x1)) -> a#(x1)
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> a#(c(x1))
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    c#(c(c(x1))) -> b#(x1)
   TRS:
    b(c(x1)) -> a(x1)
    b(b(x1)) -> a(c(x1))
    a(x1) -> c(b(x1))
    c(c(c(x1))) -> b(x1)
   graph:
    c#(c(c(x1))) -> b#(x1) -> b#(b(x1)) -> a#(c(x1))
    c#(c(c(x1))) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    c#(c(c(x1))) -> b#(x1) -> b#(c(x1)) -> a#(x1)
    a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(x1)
    a#(x1) -> b#(x1) -> b#(b(x1)) -> a#(c(x1))
    a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    a#(x1) -> b#(x1) -> b#(c(x1)) -> a#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(c(x1))) -> b#(x1)
    b#(b(x1)) -> a#(c(x1)) -> a#(x1) -> c#(b(x1))
    b#(b(x1)) -> a#(c(x1)) -> a#(x1) -> b#(x1)
    b#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
    b#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [c#](x0) = 1x0,
     
     [a#](x0) = 3x0,
     
     [b#](x0) = 3x0,
     
     [a](x0) = 3x0,
     
     [b](x0) = 2x0,
     
     [c](x0) = 1x0
    orientation:
     b#(c(x1)) = 4x1 >= 3x1 = a#(x1)
     
     b#(b(x1)) = 5x1 >= 1x1 = c#(x1)
     
     b#(b(x1)) = 5x1 >= 4x1 = a#(c(x1))
     
     a#(x1) = 3x1 >= 3x1 = b#(x1)
     
     a#(x1) = 3x1 >= 3x1 = c#(b(x1))
     
     c#(c(c(x1))) = 3x1 >= 3x1 = b#(x1)
     
     b(c(x1)) = 3x1 >= 3x1 = a(x1)
     
     b(b(x1)) = 4x1 >= 4x1 = a(c(x1))
     
     a(x1) = 3x1 >= 3x1 = c(b(x1))
     
     c(c(c(x1))) = 3x1 >= 2x1 = b(x1)
    problem:
     DPs:
      a#(x1) -> b#(x1)
      a#(x1) -> c#(b(x1))
      c#(c(c(x1))) -> b#(x1)
     TRS:
      b(c(x1)) -> a(x1)
      b(b(x1)) -> a(c(x1))
      a(x1) -> c(b(x1))
      c(c(c(x1))) -> b(x1)
    EDG Processor:
     DPs:
      a#(x1) -> b#(x1)
      a#(x1) -> c#(b(x1))
      c#(c(c(x1))) -> b#(x1)
     TRS:
      b(c(x1)) -> a(x1)
      b(b(x1)) -> a(c(x1))
      a(x1) -> c(b(x1))
      c(c(c(x1))) -> b(x1)
     graph:
      a#(x1) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(x1)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/9