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(a(x1))))) -> A(A(A(x1)))
      8: A(A(A(A(x1)))) -> a(a(a(a(x1))))
      9: b(b(b(b(b(x1))))) -> B(B(B(x1)))
      10: B(B(B(B(x1)))) -> b(b(b(b(x1))))
      11: c(c(c(c(c(x1))))) -> C(C(C(x1)))
      12: C(C(C(C(x1)))) -> c(c(c(c(x1))))
      13: B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
      14: A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
      15: C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
      16: B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
      17: A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
      18: C(C(C(a(x1)))) -> c(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: 4 8 1 3 21 19 22 5 10 7 20 12 23 24 11 9 6 2
      a 	w: x1 + 34134
      b 	w: x1 + 34134
      c 	w: x1 + 34134
      C 	w: x1 + 51201
      B 	w: x1 + 51201
      A 	w: x1 + 51201
Number of strict rules: 6
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #B(a(a(a(a(x1))))) -> #A(A(A(x1)))
     #2: #B(a(a(a(a(x1))))) -> #A(A(x1))
     #3: #B(a(a(a(a(x1))))) -> #A(x1)
     #4: #A(A(A(b(x1)))) -> #C(x1)
     #5: #A(c(c(c(c(x1))))) -> #C(C(C(x1)))
     #6: #A(c(c(c(c(x1))))) -> #C(C(x1))
     #7: #A(c(c(c(c(x1))))) -> #C(x1)
     #8: #B(B(B(c(x1)))) -> #A(x1)
     #9: #C(b(b(b(b(x1))))) -> #B(B(B(x1)))
     #10: #C(b(b(b(b(x1))))) -> #B(B(x1))
     #11: #C(b(b(b(b(x1))))) -> #B(x1)
     #12: #C(C(C(a(x1)))) -> #B(x1)
Number of SCCs: 1, DPs: 12
  SCC { #1..12 }
POLO(Sum)... succeeded.
      a 	w: x1 + 63928
      b 	w: x1 + 63928
      #B 	w: x1
      c 	w: x1 + 63928
      C 	w: x1 + 95892
      B 	w: x1 + 95892
      #C 	w: x1 + 127854
      A 	w: x1 + 95892
      #A 	w: x1 + 63927
    USABLE RULES: { 13..18 }
    Removed DPs: #1..12
Number of SCCs: 0, DPs: 0