YES
Input TRS:
      1: a(a(a(a(x1)))) -> b(b(x1))
      2: b(b(a(a(x1)))) -> a(a(b(b(x1))))
      3: b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
      4: b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
      5: c(c(a(a(x1)))) -> b(b(a(a(c(c(x1))))))
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 5
      a 	w: x1 + 20538
      b 	w: x1 + 41076
      c 	w: 2 * x1 + 15922
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #b(b(a(a(x1)))) -> #a(a(b(b(x1))))
     #2: #b(b(a(a(x1)))) -> #a(b(b(x1)))
     #3: #b(b(a(a(x1)))) -> #b(b(x1))
     #4: #b(b(a(a(x1)))) -> #b(x1)
     #5: #b(b(b(b(c(c(x1)))))) -> #a(a(x1))
     #6: #b(b(b(b(c(c(x1)))))) -> #a(x1)
     #7: #a(a(a(a(x1)))) -> #b(b(x1))
     #8: #a(a(a(a(x1)))) -> #b(x1)
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      a 	w: x1 + 2
      b 	w: x1 + 1
      c 	w: x1 + 20163
      #a 	w: x1
      #b 	w: x1
    USABLE RULES: { 1..3 }
    Removed DPs: #1..8
Number of SCCs: 0, DPs: 0