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:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [C](x0) = 8x0,
   
   [B](x0) = x0,
   
   [A](x0) = 4x0,
   
   [a](x0) = 3x0,
   
   [b](x0) = 11x0,
   
   [c](x0) = 5x0
  orientation:
   a(b(c(x1))) = 19x1 >= 19x1 = c(b(a(x1)))
   
   C(B(A(x1))) = 12x1 >= 12x1 = A(B(C(x1)))
   
   b(a(C(x1))) = 22x1 >= 22x1 = C(a(b(x1)))
   
   c(A(B(x1))) = 9x1 >= 9x1 = B(A(c(x1)))
   
   A(c(b(x1))) = 20x1 >= 20x1 = b(c(A(x1)))
   
   B(C(a(x1))) = 11x1 >= 11x1 = a(C(B(x1)))
   
   a(A(x1)) = 7x1 >= x1 = x1
   
   A(a(x1)) = 7x1 >= x1 = x1
   
   b(B(x1)) = 11x1 >= x1 = x1
   
   B(b(x1)) = 11x1 >= x1 = x1
   
   c(C(x1)) = 13x1 >= x1 = x1
   
   C(c(x1)) = 13x1 >= x1 = x1
  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)))
  String Reversal Processor:
   c(b(a(x1))) -> a(b(c(x1)))
   A(B(C(x1))) -> C(B(A(x1)))
   C(a(b(x1))) -> b(a(C(x1)))
   B(A(c(x1))) -> c(A(B(x1)))
   b(c(A(x1))) -> A(c(b(x1)))
   a(C(B(x1))) -> B(C(a(x1)))
   Bounds Processor:
    bound: 0
    enrichment: match
    automaton:
     final states: {17,14,11,8,5,1}
     transitions:
      f60() -> 2*
      a0(2) -> 18*
      a0(9) -> 10*
      a0(4) -> 1*
      b0(10) -> 8*
      b0(2) -> 15*
      b0(3) -> 4*
      c0(15) -> 16*
      c0(2) -> 3*
      c0(13) -> 11*
      C0(7) -> 5*
      C0(2) -> 9*
      C0(18) -> 19*
      B0(2) -> 12*
      B0(19) -> 17*
      B0(6) -> 7*
      A0(12) -> 13*
      A0(2) -> 6*
      A0(16) -> 14*
      1 -> 3,16
      5 -> 6,13
      8 -> 9,19
      11 -> 12,7
      14 -> 15,4
      17 -> 18,10
    problem:
     
    Qed