YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [B](x0) = 3x0,
   
   [A](x0) = 3x0,
   
   [c](x0) = 2x0,
   
   [C](x0) = 3x0,
   
   [a](x0) = 2x0,
   
   [b](x0) = 2x0
  orientation:
   a(a(b(b(x1)))) = 8x1 >= 6x1 = C(C(x1))
   
   b(b(c(c(x1)))) = 8x1 >= 6x1 = A(A(x1))
   
   c(c(a(a(x1)))) = 8x1 >= 6x1 = B(B(x1))
   
   A(A(C(C(x1)))) = 12x1 >= 4x1 = b(b(x1))
   
   C(C(B(B(x1)))) = 12x1 >= 4x1 = a(a(x1))
   
   B(B(A(A(x1)))) = 12x1 >= 4x1 = c(c(x1))
   
   a(a(a(a(a(a(a(a(a(a(x1)))))))))) = 20x1 >= 18x1 = A(A(A(A(A(A(x1))))))
   
   A(A(A(A(A(A(A(A(x1)))))))) = 24x1 >= 16x1 = a(a(a(a(a(a(a(a(x1))))))))
   
   b(b(b(b(b(b(b(b(b(b(x1)))))))))) = 20x1 >= 18x1 = B(B(B(B(B(B(x1))))))
   
   B(B(B(B(B(B(B(B(x1)))))))) = 24x1 >= 16x1 = b(b(b(b(b(b(b(b(x1))))))))
   
   c(c(c(c(c(c(c(c(c(c(x1)))))))))) = 20x1 >= 18x1 = C(C(C(C(C(C(x1))))))
   
   C(C(C(C(C(C(C(C(x1)))))))) = 24x1 >= 16x1 = c(c(c(c(c(c(c(c(x1))))))))
   
   B(B(a(a(a(a(a(a(a(a(x1)))))))))) = 22x1 >= 22x1 = c(c(A(A(A(A(A(A(x1))))))))
   
   A(A(A(A(A(A(b(b(x1)))))))) = 22x1 >= 22x1 = a(a(a(a(a(a(a(a(C(C(x1))))))))))
   
   C(C(b(b(b(b(b(b(b(b(x1)))))))))) = 22x1 >= 22x1 = a(a(B(B(B(B(B(B(x1))))))))
   
   B(B(B(B(B(B(c(c(x1)))))))) = 22x1 >= 22x1 = b(b(b(b(b(b(b(b(A(A(x1))))))))))
   
   A(A(c(c(c(c(c(c(c(c(x1)))))))))) = 22x1 >= 22x1 = b(b(C(C(C(C(C(C(x1))))))))
   
   C(C(C(C(C(C(a(a(x1)))))))) = 22x1 >= 22x1 = c(c(c(c(c(c(c(c(B(B(x1))))))))))
   
   a(a(A(A(x1)))) = 10x1 >= x1 = x1
   
   A(A(a(a(x1)))) = 10x1 >= x1 = x1
   
   b(b(B(B(x1)))) = 10x1 >= x1 = x1
   
   B(B(b(b(x1)))) = 10x1 >= x1 = x1
   
   c(c(C(C(x1)))) = 10x1 >= x1 = x1
   
   C(C(c(c(x1)))) = 10x1 >= x1 = x1
  problem:
   B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> c(c(A(A(A(A(A(A(x1))))))))
   A(A(A(A(A(A(b(b(x1)))))))) -> a(a(a(a(a(a(a(a(C(C(x1))))))))))
   C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> a(a(B(B(B(B(B(B(x1))))))))
   B(B(B(B(B(B(c(c(x1)))))))) -> b(b(b(b(b(b(b(b(A(A(x1))))))))))
   A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> b(b(C(C(C(C(C(C(x1))))))))
   C(C(C(C(C(C(a(a(x1)))))))) -> c(c(c(c(c(c(c(c(B(B(x1))))))))))
  String Reversal Processor:
   a(a(a(a(a(a(a(a(B(B(x1)))))))))) -> A(A(A(A(A(A(c(c(x1))))))))
   b(b(A(A(A(A(A(A(x1)))))))) -> C(C(a(a(a(a(a(a(a(a(x1))))))))))
   b(b(b(b(b(b(b(b(C(C(x1)))))))))) -> B(B(B(B(B(B(a(a(x1))))))))
   c(c(B(B(B(B(B(B(x1)))))))) -> A(A(b(b(b(b(b(b(b(b(x1))))))))))
   c(c(c(c(c(c(c(c(A(A(x1)))))))))) -> C(C(C(C(C(C(b(b(x1))))))))
   a(a(C(C(C(C(C(C(x1)))))))) -> B(B(c(c(c(c(c(c(c(c(x1))))))))))
   Bounds Processor:
    bound: 0
    enrichment: match
    automaton:
     final states: {42,36,26,20,10,1}
     transitions:
      f60() -> 2*
      A0(35) -> 26*
      A0(5) -> 6*
      A0(7) -> 8*
      A0(34) -> 35*
      A0(9) -> 1*
      A0(4) -> 5*
      A0(6) -> 7*
      A0(8) -> 9*
      c0(45) -> 46*
      c0(47) -> 48*
      c0(2) -> 3*
      c0(44) -> 45*
      c0(4) -> 43*
      c0(46) -> 47*
      c0(43) -> 44*
      c0(3) -> 4*
      C0(40) -> 41*
      C0(37) -> 38*
      C0(39) -> 40*
      C0(19) -> 10*
      C0(41) -> 36*
      C0(38) -> 39*
      C0(28) -> 37*
      C0(18) -> 19*
      a0(15) -> 16*
      a0(17) -> 18*
      a0(12) -> 13*
      a0(2) -> 11*
      a0(14) -> 15*
      a0(16) -> 17*
      a0(11) -> 12*
      a0(13) -> 14*
      B0(25) -> 20*
      B0(22) -> 23*
      B0(12) -> 21*
      B0(49) -> 42*
      B0(24) -> 25*
      B0(21) -> 22*
      B0(48) -> 49*
      B0(23) -> 24*
      b0(30) -> 31*
      b0(32) -> 33*
      b0(27) -> 28*
      b0(2) -> 27*
      b0(29) -> 30*
      b0(31) -> 32*
      b0(33) -> 34*
      b0(28) -> 29*
      1 -> 11,12,13,14,15,16,17,18
      10 -> 27,28
      20 -> 27,28,29,30,31,32,33,34
      26 -> 3,4
      36 -> 3,4,43,44,45,46,47,48
      42 -> 11,12
    problem:
     
    Qed