YES
Input TRS:
      1: a(x1) -> b(x1)
      2: a(b(x1)) -> b(c(a(x1)))
      3: b(x1) -> c(x1)
      4: c(b(x1)) -> a(x1)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 3
      a 	w: 2 * x1 + 21239
      b 	w: 2 * x1 + 21239
      c 	w: x1
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(b(x1)) -> #c(a(x1))
     #2: #a(b(x1)) -> #a(x1)
     #3: #c(b(x1)) -> #a(x1)
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... succeeded.
      a 	w: x1 + 21240
      b 	w: x1 + 21240
      c 	w: x1
      #c 	w: x1
      #a 	w: x1 + 1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0