YES
Input TRS:
      1: a(x1) -> b(c(x1))
      2: a(b(x1)) -> b(a(x1))
      3: d(c(x1)) -> d(a(x1))
      4: a(c(x1)) -> c(a(x1))
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(b(x1)) -> #a(x1)
     #2: #d(c(x1)) -> #d(a(x1))
     #3: #d(c(x1)) -> #a(x1)
     #4: #a(c(x1)) -> #a(x1)
Number of SCCs: 2, DPs: 3
  SCC { #2 }
POLO(Sum)... succeeded.
      a 	w: x1 + 1
      d 	w: 0
      b 	w: 1
      c 	w: x1 + 2
      #d 	w: x1
      #a 	w: 0
    USABLE RULES: { 1 2 4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #1 #4 }
POLO(Sum)... succeeded.
      a 	w: x1 + 1
      d 	w: 0
      b 	w: x1 + 1
      c 	w: x1
      #d 	w: x1
      #a 	w: x1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 1
  SCC { #4 }
POLO(Sum)... succeeded.
      a 	w: x1 + 1
      d 	w: 0
      b 	w: 1
      c 	w: x1 + 7720
      #d 	w: x1
      #a 	w: x1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #4
Number of SCCs: 0, DPs: 0