YES
Input TRS:
      1: a(a(b(b(x1)))) -> C(C(x1))
      2: b(b(c(c(x1)))) -> A(A(x1))
      3: c(c(a(a(x1)))) -> B(B(x1))
      4: A(A(C(C(x1)))) -> b(b(x1))
      5: C(C(B(B(x1)))) -> a(a(x1))
      6: B(B(A(A(x1)))) -> c(c(x1))
      7: a(a(a(a(a(a(a(a(a(a(x1)))))))))) -> A(A(A(A(A(A(x1))))))
      8: A(A(A(A(A(A(A(A(x1)))))))) -> a(a(a(a(a(a(a(a(x1))))))))
      9: b(b(b(b(b(b(b(b(b(b(x1)))))))))) -> B(B(B(B(B(B(x1))))))
      10: B(B(B(B(B(B(B(B(x1)))))))) -> b(b(b(b(b(b(b(b(x1))))))))
      11: c(c(c(c(c(c(c(c(c(c(x1)))))))))) -> C(C(C(C(C(C(x1))))))
      12: C(C(C(C(C(C(C(C(x1)))))))) -> c(c(c(c(c(c(c(c(x1))))))))
      13: B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> c(c(A(A(A(A(A(A(x1))))))))
      14: A(A(A(A(A(A(b(b(x1)))))))) -> a(a(a(a(a(a(a(a(C(C(x1))))))))))
      15: C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> a(a(B(B(B(B(B(B(x1))))))))
      16: B(B(B(B(B(B(c(c(x1)))))))) -> b(b(b(b(b(b(b(b(A(A(x1))))))))))
      17: A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> b(b(C(C(C(C(C(C(x1))))))))
      18: C(C(C(C(C(C(a(a(x1)))))))) -> c(c(c(c(c(c(c(c(B(B(x1))))))))))
      19: a(a(A(A(x1)))) -> x1
      20: A(A(a(a(x1)))) -> x1
      21: b(b(B(B(x1)))) -> x1
      22: B(B(b(b(x1)))) -> x1
      23: c(c(C(C(x1)))) -> x1
      24: C(C(c(c(x1)))) -> x1
Number of strict rules: 24
Direct POLO(bPol) ... removes: 4 8 1 3 21 19 22 5 10 7 20 12 23 24 11 9 6 2
      a 	w: x1 + 1182
      b 	w: x1 + 1182
      c 	w: x1 + 1182
      C 	w: x1 + 1773
      B 	w: x1 + 1773
      A 	w: x1 + 1773
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(A(A(A(A(A(x1))))))
     #2: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(A(A(A(A(x1)))))
     #3: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(A(A(A(x1))))
     #4: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(A(A(x1)))
     #5: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(A(x1))
     #6: #B(B(a(a(a(a(a(a(a(a(x1)))))))))) -> #A(x1)
     #7: #A(A(A(A(A(A(b(b(x1)))))))) -> #C(C(x1))
     #8: #A(A(A(A(A(A(b(b(x1)))))))) -> #C(x1)
     #9: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(C(C(C(C(C(x1))))))
     #10: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(C(C(C(C(x1)))))
     #11: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(C(C(C(x1))))
     #12: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(C(C(x1)))
     #13: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(C(x1))
     #14: #A(A(c(c(c(c(c(c(c(c(x1)))))))))) -> #C(x1)
     #15: #B(B(B(B(B(B(c(c(x1)))))))) -> #A(A(x1))
     #16: #B(B(B(B(B(B(c(c(x1)))))))) -> #A(x1)
     #17: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(B(B(B(B(B(x1))))))
     #18: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(B(B(B(B(x1)))))
     #19: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(B(B(B(x1))))
     #20: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(B(B(x1)))
     #21: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(B(x1))
     #22: #C(C(b(b(b(b(b(b(b(b(x1)))))))))) -> #B(x1)
     #23: #C(C(C(C(C(C(a(a(x1)))))))) -> #B(B(x1))
     #24: #C(C(C(C(C(C(a(a(x1)))))))) -> #B(x1)
Number of SCCs: 1, DPs: 24
  SCC { #1..24 }
POLO(Sum)... succeeded.
      a 	w: x1 + 28918
      b 	w: x1 + 28918
      #B 	w: x1
      c 	w: x1 + 28918
      C 	w: x1 + 43377
      B 	w: x1 + 43377
      #C 	w: x1 + 115670
      A 	w: x1 + 43377
      #A 	w: x1 + 57835
    USABLE RULES: { 13..18 }
    Removed DPs: #1..24
Number of SCCs: 0, DPs: 0