YES
Input TRS:
      1: a(b(c(x1))) -> c(b(a(x1)))
      2: C(B(A(x1))) -> A(B(C(x1)))
      3: b(a(C(x1))) -> C(a(b(x1)))
      4: c(A(B(x1))) -> B(A(c(x1)))
      5: A(c(b(x1))) -> b(c(A(x1)))
      6: B(C(a(x1))) -> a(C(B(x1)))
      7: a(A(x1)) -> x1
      8: A(a(x1)) -> x1
      9: b(B(x1)) -> x1
      10: B(b(x1)) -> x1
      11: c(C(x1)) -> x1
      12: C(c(x1)) -> x1
Number of strict rules: 12
Direct POLO(bPol) ... removes: 8 5 10 7 9
      a 	w: x1 + 1
      b 	w: x1 + 1
      c 	w: x1
      C 	w: x1
      B 	w: x1
      A 	w: 2 * x1 + 1
Number of strict rules: 7
Direct POLO(bPol) ... removes: 12 11
      a 	w: 2 * x1 + 1
      b 	w: x1 + 1
      c 	w: 2 * x1 + 1
      C 	w: x1 + 1
      B 	w: 2 * x1 + 1
      A 	w: x1 + 1
Number of strict rules: 5
Direct POLO(bPol) ... removes: 6
      a 	w: 2 * x1 + 2
      b 	w: x1
      c 	w: x1
      C 	w: x1
      B 	w: 2 * x1 + 1
      A 	w: x1
Number of strict rules: 4
Direct POLO(bPol) ... removes: 2
      a 	w: x1
      b 	w: x1
      c 	w: x1
      C 	w: 2 * x1
      B 	w: x1
      A 	w: x1 + 1
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4 3
      a 	w: x1
      b 	w: 2 * x1 + 1
      c 	w: 2 * x1 + 1
      C 	w: x1 + 15092
      B 	w: x1 + 1
      A 	w: x1
Number of strict rules: 1
Direct POLO(bPol) ... removes: 1
      a 	w: 2 * x1
      b 	w: x1
      c 	w: x1 + 22315
      C 	w: x1
      B 	w: x1
      A 	w: x1 + 1
Number of strict rules: 0