YES
Input TRS:
      1: a(c(a(x1))) -> c(a(c(x1)))
      2: a(a(b(x1))) -> a(d(b(x1)))
      3: a(b(x1)) -> b(a(a(x1)))
      4: d(d(x1)) -> a(d(b(x1)))
      5: b(b(x1)) -> b(c(x1))
      6: a(d(c(x1))) -> c(a(x1))
      7: b(c(x1)) -> a(a(a(x1)))
Number of strict rules: 7
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(a(b(x1))) -> #a(d(b(x1)))
     #2: #a(a(b(x1))) -> #d(b(x1))
     #3: #a(d(c(x1))) -> #a(x1)
     #4: #b(c(x1)) -> #a(a(a(x1)))
     #5: #b(c(x1)) -> #a(a(x1))
     #6: #b(c(x1)) -> #a(x1)
     #7: #b(b(x1)) -> #b(c(x1))
     #8: #a(b(x1)) -> #b(a(a(x1)))
     #9: #a(b(x1)) -> #a(a(x1))
     #10: #a(b(x1)) -> #a(x1)
     #11: #a(c(a(x1))) -> #a(c(x1))
     #12: #d(d(x1)) -> #a(d(b(x1)))
     #13: #d(d(x1)) -> #d(b(x1))
     #14: #d(d(x1)) -> #b(x1)
Number of SCCs: 2, DPs: 10
  SCC { #11 }
POLO(Sum)... succeeded.
      a 	w: x1 + 1
      d 	w: 0
      b 	w: 0
      c 	w: x1 + 28958
      #d 	w: 0
      #a 	w: x1
      #b 	w: 0
    USABLE RULES: { }
    Removed DPs: #11
Number of SCCs: 1, DPs: 9
  SCC { #1 #3..10 }
POLO(Sum)... succeeded.
      a 	w: x1
      d 	w: x1
      b 	w: x1 + 32287
      c 	w: x1
      #d 	w: 0
      #a 	w: x1
      #b 	w: x1 + 32286
    USABLE RULES: { 1..3 5..7 }
    Removed DPs: #4..10
Number of SCCs: 1, DPs: 2
  SCC { #1 #3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      a 	s: [1]	p: 1	w: x1
      d 	s: [1]	p: 0	w: x1
      b 	s: []	p: 2	w: x1 + 1
      c 	s: 1
      #d 	s: []	p: 0	w: 1
      #a 	s: [1]	p: 0	w: x1 + 1
      #b 	s: []	p: 0	w: 1
    USABLE RULES: { 1..3 5..7 }
    Removed DPs: #1 #3
Number of SCCs: 0, DPs: 0