YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(b(x1))
   b#(b(c(x1))) -> a#(x1)
   b#(b(c(x1))) -> c#(a(x1))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
   b#(b(x1)) -> a#(a(a(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> a#(c(x1))
   c#(a(x1)) -> b#(a(c(x1)))
  TRS:
   a(a(x1)) -> b(x1)
   b(a(x1)) -> a(b(x1))
   b(b(c(x1))) -> c(a(x1))
   b(b(x1)) -> a(a(a(x1)))
   c(a(x1)) -> b(a(c(x1)))
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    b#(b(c(x1))) -> a#(x1)
    b#(b(c(x1))) -> c#(a(x1))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> a#(a(a(x1)))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> a#(c(x1))
    c#(a(x1)) -> b#(a(c(x1)))
   TRS:
    a(a(x1)) -> b(x1)
    b(a(x1)) -> a(b(x1))
    b(b(c(x1))) -> c(a(x1))
    b(b(x1)) -> a(a(a(x1)))
    c(a(x1)) -> b(a(c(x1)))
   graph:
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(c(x1)))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(a(x1)))
    c#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(x1))
    c#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(x1)
    c#(a(x1)) -> b#(a(c(x1))) -> b#(b(c(x1))) -> c#(a(x1))
    c#(a(x1)) -> b#(a(c(x1))) -> b#(b(c(x1))) -> a#(x1)
    c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> a#(b(x1))
    c#(a(x1)) -> b#(a(c(x1))) -> b#(a(x1)) -> b#(x1)
    c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
    b#(b(c(x1))) -> c#(a(x1)) -> c#(a(x1)) -> b#(a(c(x1)))
    b#(b(c(x1))) -> c#(a(x1)) -> c#(a(x1)) -> a#(c(x1))
    b#(b(c(x1))) -> c#(a(x1)) -> c#(a(x1)) -> c#(x1)
    b#(b(c(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> a#(a(a(x1))) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
    b#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    b#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    b#(a(x1)) -> b#(x1) -> b#(b(c(x1))) -> c#(a(x1))
    b#(a(x1)) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(c(x1))) -> c#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c#](x0) = 12x0 + 28,
     
     [b#](x0) = 4x0 + 10,
     
     [a#](x0) = 4x0 + 4,
     
     [c](x0) = 3x0 + 8,
     
     [b](x0) = x0 + 3,
     
     [a](x0) = x0 + 2
    orientation:
     a#(a(x1)) = 4x1 + 12 >= 4x1 + 10 = b#(x1)
     
     b#(a(x1)) = 4x1 + 18 >= 4x1 + 10 = b#(x1)
     
     b#(a(x1)) = 4x1 + 18 >= 4x1 + 16 = a#(b(x1))
     
     b#(b(c(x1))) = 12x1 + 54 >= 4x1 + 4 = a#(x1)
     
     b#(b(c(x1))) = 12x1 + 54 >= 12x1 + 52 = c#(a(x1))
     
     b#(b(x1)) = 4x1 + 22 >= 4x1 + 4 = a#(x1)
     
     b#(b(x1)) = 4x1 + 22 >= 4x1 + 12 = a#(a(x1))
     
     b#(b(x1)) = 4x1 + 22 >= 4x1 + 20 = a#(a(a(x1)))
     
     c#(a(x1)) = 12x1 + 52 >= 12x1 + 28 = c#(x1)
     
     c#(a(x1)) = 12x1 + 52 >= 12x1 + 36 = a#(c(x1))
     
     c#(a(x1)) = 12x1 + 52 >= 12x1 + 50 = b#(a(c(x1)))
     
     a(a(x1)) = x1 + 4 >= x1 + 3 = b(x1)
     
     b(a(x1)) = x1 + 5 >= x1 + 5 = a(b(x1))
     
     b(b(c(x1))) = 3x1 + 14 >= 3x1 + 14 = c(a(x1))
     
     b(b(x1)) = x1 + 6 >= x1 + 6 = a(a(a(x1)))
     
     c(a(x1)) = 3x1 + 14 >= 3x1 + 13 = b(a(c(x1)))
    problem:
     DPs:
      
     TRS:
      a(a(x1)) -> b(x1)
      b(a(x1)) -> a(b(x1))
      b(b(c(x1))) -> c(a(x1))
      b(b(x1)) -> a(a(a(x1)))
      c(a(x1)) -> b(a(c(x1)))
    Qed