YES
Input TRS:
      1: a(l(x1)) -> l(a(x1))
      2: a(c(x1)) -> c(a(x1))
      3: c(a(r(x1))) -> r(a(x1))
      4: l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1)))))))
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(c(x1)) -> #c(a(x1))
     #2: #a(c(x1)) -> #a(x1)
     #3: #c(a(r(x1))) -> #a(x1)
     #4: #a(l(x1)) -> #l(a(x1))
     #5: #a(l(x1)) -> #a(x1)
     #6: #l(r(a(a(x1)))) -> #a(a(l(c(c(c(r(x1)))))))
     #7: #l(r(a(a(x1)))) -> #a(l(c(c(c(r(x1))))))
     #8: #l(r(a(a(x1)))) -> #l(c(c(c(r(x1)))))
     #9: #l(r(a(a(x1)))) -> #c(c(c(r(x1))))
     #10: #l(r(a(a(x1)))) -> #c(c(r(x1)))
     #11: #l(r(a(a(x1)))) -> #c(r(x1))
Number of SCCs: 1, DPs: 7
  SCC { #1..7 }
POLO(Sum)... succeeded.
      a 	w: x1 + 8946
      r 	w: x1 + 15923
      l 	w: x1 + 46823
      c 	w: x1
      #c 	w: x1
      #l 	w: x1 + 46824
      #a 	w: x1 + 8947
    USABLE RULES: { 1..4 }
    Removed DPs: #1 #3 #5 #7
Number of SCCs: 1, DPs: 3
  SCC { #2 #4 #6 }
POLO(Sum)... succeeded.
      a 	w: x1
      r 	w: 18458
      l 	w: 74051
      c 	w: x1 + 1
      #c 	w: x1
      #l 	w: 82998
      #a 	w: x1 + 8947
    USABLE RULES: { 1..4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #4 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded.
      a 	w: max(x1 + 55771, 0)
      r 	w: 111544
      l 	w: max(x1 + 2, 0)
      c 	w: max(x1 - 37181, 0)
      #c 	w: 0
      #l 	w: max(x1 - 55768, 0)
      #a 	w: max(x1 + 1, 0)
    USABLE RULES: { 1..4 }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0