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)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
     [a#](x0) = [0 2]x0,
     
     [c#](x0) = [1 2]x0 + [1],
     
     [b#](x0) = [1 2]x0 + [3],
     
               [1 0]     [1]
     [a](x0) = [1 1]x0 + [0],
     
               [1 0]     [1]
     [b](x0) = [2 1]x0 + [1],
     
               [1 0]     [2]
     [c](x0) = [2 1]x0 + [0]
    orientation:
     b#(c(x1)) = [5 2]x1 + [5] >= [1 2]x1 + [3] = b#(x1)
     
     b#(c(x1)) = [5 2]x1 + [5] >= [5 2]x1 + [4] = c#(b(x1))
     
     c#(b(x1)) = [5 2]x1 + [4] >= [0 2]x1 = a#(x1)
     
     c#(b(x1)) = [5 2]x1 + [4] >= [2 2]x1 = a#(a(x1))
     
     c#(b(x1)) = [5 2]x1 + [4] >= [4 2]x1 + [2] = a#(a(a(x1)))
     
     a#(a(a(a(x1)))) = [6 2]x1 + [6] >= [1 2]x1 + [1] = c#(x1)
     
     a#(a(a(a(x1)))) = [6 2]x1 + [6] >= [5 2]x1 + [5] = b#(c(x1))
     
                [1 0]     [3]    [1 0]     [3]           
     b(c(x1)) = [4 1]x1 + [5] >= [4 1]x1 + [3] = c(b(x1))
     
                [1 0]     [3]    [1 0]     [3]              
     c(b(x1)) = [4 1]x1 + [3] >= [3 1]x1 + [3] = a(a(a(x1)))
     
                      [1 0]     [4]    [1 0]     [3]           
     a(a(a(a(x1)))) = [4 1]x1 + [6] >= [4 1]x1 + [5] = b(c(x1))
    problem:
     DPs:
      
     TRS:
      b(c(x1)) -> c(b(x1))
      c(b(x1)) -> a(a(a(x1)))
      a(a(a(a(x1)))) -> b(c(x1))
    Qed