YES
Input TRS:
      1: f(x1) -> n(c(c(x1)))
      2: c(f(x1)) -> f(c(c(x1)))
      3: c(c(x1)) -> c(x1)
      4: n(s(x1)) -> f(s(s(x1)))
      5: n(f(x1)) -> f(n(x1))
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #c(f(x1)) -> #f(c(c(x1)))
     #2: #c(f(x1)) -> #c(c(x1))
     #3: #c(f(x1)) -> #c(x1)
     #4: #n(f(x1)) -> #f(n(x1))
     #5: #n(f(x1)) -> #n(x1)
     #6: #f(x1) -> #n(c(c(x1)))
     #7: #f(x1) -> #c(c(x1))
     #8: #f(x1) -> #c(x1)
     #9: #n(s(x1)) -> #f(s(s(x1)))
Number of SCCs: 1, DPs: 9
  SCC { #1..9 }
POLO(Sum)... succeeded.
      s 	w: 20977
      n 	w: x1
      c 	w: 0
      f 	w: x1
      #f 	w: 0
      #c 	w: 0
      #n 	w: x1
    USABLE RULES: { 1..5 }
    Removed DPs: #9
Number of SCCs: 1, DPs: 8
  SCC { #1..8 }
POLO(Sum)... succeeded.
      s 	w: 18458
      n 	w: x1 + 25908
      c 	w: x1
      f 	w: x1 + 25908
      #f 	w: x1 + 25907
      #c 	w: x1
      #n 	w: x1 + 25907
    USABLE RULES: { 1..5 }
    Removed DPs: #1..3 #5 #7 #8
Number of SCCs: 1, DPs: 2
  SCC { #4 #6 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      s 	w: [25469;20259]
      n 	w: [1,1;0,1] * x1 + [1;0]
      c 	w: [1,0;0,0] * x1
      f 	w: x1 + [20260;0]
      #f 	w: x1 + [1;0]
      #c 	w: [0;0]
      #n 	w: [1,1;0,1] * x1
    USABLE RULES: { 1..5 }
    Removed DPs: #4 #6
Number of SCCs: 0, DPs: 0