YES
Input TRS:
      1: a(x1) -> b(b(x1))
      2: a(b(b(x1))) -> b(b(c(c(c(a(x1))))))
      3: b(b(x1)) -> c(c(c(x1)))
      4: c(c(c(b(b(x1))))) -> a(x1)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 3
      a 	w: x1 + 15444
      b 	w: x1 + 7722
      c 	w: x1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(b(b(x1))) -> #c(c(c(a(x1))))
     #2: #a(b(b(x1))) -> #c(c(a(x1)))
     #3: #a(b(b(x1))) -> #c(a(x1))
     #4: #a(b(b(x1))) -> #a(x1)
     #5: #c(c(c(b(b(x1))))) -> #a(x1)
Number of SCCs: 1, DPs: 3
  SCC { #1 #4 #5 }
POLO(Sum)... succeeded.
      a 	w: x1 + 23596
      b 	w: x1 + 11798
      c 	w: x1
      #c 	w: x1
      #a 	w: x1 + 1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #1 #4 #5
Number of SCCs: 0, DPs: 0