YES
Input TRS:
      1: terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
      2: sqr(0()) -> 0()
      3: sqr(s(X)) -> s(add(sqr(X),dbl(X)))
      4: dbl(0()) -> 0()
      5: dbl(s(X)) -> s(s(dbl(X)))
      6: add(0(),X) -> X
      7: add(s(X),Y) -> s(add(X,Y))
      8: first(0(),X) -> nil()
      9: first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
      10: terms(X) -> n__terms(X)
      11: s(X) -> n__s(X)
      12: first(X1,X2) -> n__first(X1,X2)
      13: activate(n__terms(X)) -> terms(activate(X))
      14: activate(n__s(X)) -> s(activate(X))
      15: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
      16: activate(X) -> X
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #activate(n__terms(X)) -> #terms(activate(X))
     #2: #activate(n__terms(X)) -> #activate(X)
     #3: #first(s(X),cons(Y,Z)) -> #activate(Z)
     #4: #activate(n__s(X)) -> #s(activate(X))
     #5: #activate(n__s(X)) -> #activate(X)
     #6: #add(s(X),Y) -> #s(add(X,Y))
     #7: #add(s(X),Y) -> #add(X,Y)
     #8: #dbl(s(X)) -> #s(s(dbl(X)))
     #9: #dbl(s(X)) -> #s(dbl(X))
     #10: #dbl(s(X)) -> #dbl(X)
     #11: #sqr(s(X)) -> #s(add(sqr(X),dbl(X)))
     #12: #sqr(s(X)) -> #add(sqr(X),dbl(X))
     #13: #sqr(s(X)) -> #sqr(X)
     #14: #sqr(s(X)) -> #dbl(X)
     #15: #terms(N) -> #sqr(N)
     #16: #activate(n__first(X1,X2)) -> #first(activate(X1),activate(X2))
     #17: #activate(n__first(X1,X2)) -> #activate(X1)
     #18: #activate(n__first(X1,X2)) -> #activate(X2)
Number of SCCs: 4, DPs: 9
  SCC { #13 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      n__first	w: 0
      recip	w: 0
      activate	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #activate	w: 0
      n__s	w: 0
      #sqr	w: x1
      0 	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      n__terms	w: 0
      cons	w: 0
      #add	w: 0
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #13
Number of SCCs: 3, DPs: 8
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      n__first	w: 0
      recip	w: 0
      activate	w: 0
      dbl	w: 0
      #dbl	w: x1
      #terms	w: 0
      #activate	w: 0
      n__s	w: 0
      #sqr	w: 0
      0 	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      n__terms	w: 0
      cons	w: 0
      #add	w: 0
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 2, DPs: 7
  SCC { #7 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      n__first	w: 0
      recip	w: 0
      activate	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #activate	w: 0
      n__s	w: 0
      #sqr	w: 0
      0 	w: 0
      #s 	w: 0
      #first	w: 0
      nil	w: 0
      first	w: 0
      n__terms	w: 0
      cons	w: 0
      #add	w: x1
      add	w: 0
      sqr	w: 0
      terms	w: 0
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 6
  SCC { #2 #3 #5 #16..18 }
POLO(Sum)... succeeded.
      s 	w: x1
      n__first	w: x1 + x2 + 31893
      recip	w: 1
      activate	w: x1
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #activate	w: x1
      n__s	w: x1
      #sqr	w: 0
      0 	w: 0
      #s 	w: 0
      #first	w: x2 + 1
      nil	w: 0
      first	w: x1 + x2 + 31893
      n__terms	w: x1 + 20977
      cons	w: x2
      #add	w: 0
      add	w: x2 + 1
      sqr	w: 1
      terms	w: x1 + 20977
    USABLE RULES: { 1..16 }
    Removed DPs: #2 #3 #16..18
Number of SCCs: 1, DPs: 1
  SCC { #5 }
POLO(Sum)... succeeded.
      s 	w: x1
      n__first	w: x1 + x2 + 9727
      recip	w: 1
      activate	w: 0
      dbl	w: 0
      #dbl	w: 0
      #terms	w: 0
      #activate	w: x1
      n__s	w: x1 + 2
      #sqr	w: 0
      0 	w: 0
      #s 	w: 0
      #first	w: 1
      nil	w: 2
      first	w: 1
      n__terms	w: x1 + 20975
      cons	w: x2
      #add	w: 0
      add	w: 1
      sqr	w: 1
      terms	w: x1 + 20974
    USABLE RULES: { 2 }
    Removed DPs: #5
Number of SCCs: 0, DPs: 0