YES

Problem:
 a(b(c(x1))) -> c(b(a(x1)))
 C(B(A(x1))) -> A(B(C(x1)))
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 a(A(x1)) -> x1
 A(a(x1)) -> x1
 b(B(x1)) -> x1
 B(b(x1)) -> x1
 c(C(x1)) -> x1
 C(c(x1)) -> x1

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