YES
Input TRS:
      1: a(b(x1)) -> C(x1)
      2: b(c(x1)) -> A(x1)
      3: c(a(x1)) -> B(x1)
      4: A(C(x1)) -> b(x1)
      5: C(B(x1)) -> a(x1)
      6: B(A(x1)) -> c(x1)
      7: a(a(a(a(x1)))) -> A(A(A(x1)))
      8: A(A(A(A(x1)))) -> a(a(a(x1)))
      9: b(b(b(b(x1)))) -> B(B(B(x1)))
      10: B(B(B(B(x1)))) -> b(b(b(x1)))
      11: c(c(c(c(x1)))) -> C(C(C(x1)))
      12: C(C(C(C(x1)))) -> c(c(c(x1)))
      13: B(a(a(a(x1)))) -> c(A(A(A(x1))))
      14: A(A(A(b(x1)))) -> a(a(a(C(x1))))
      15: C(b(b(b(x1)))) -> a(B(B(B(x1))))
      16: B(B(B(c(x1)))) -> b(b(b(A(x1))))
      17: A(c(c(c(x1)))) -> b(C(C(C(x1))))
      18: C(C(C(a(x1)))) -> c(c(c(B(x1))))
      19: a(A(x1)) -> x1
      20: A(a(x1)) -> x1
      21: b(B(x1)) -> x1
      22: B(b(x1)) -> x1
      23: c(C(x1)) -> x1
      24: C(c(x1)) -> x1
Number of strict rules: 24
Direct POLO(bPol) ... removes: 18 4 15 8 1 3 16 21 19 17 22 5 10 7 20 14 12 23 24 11 9 13 6 2
      a 	w: 2 * x1 + 2
      b 	w: 2 * x1 + 2
      c 	w: 2 * x1 + 2
      C 	w: 2 * x1 + 1
      B 	w: 2 * x1 + 1
      A 	w: 2 * x1 + 1
Number of strict rules: 0