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