YES
Input TRS:
      1: a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
      2: a__sqr(0()) -> 0()
      3: a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
      4: a__dbl(0()) -> 0()
      5: a__dbl(s(X)) -> s(s(dbl(X)))
      6: a__add(0(),X) -> mark(X)
      7: a__add(s(X),Y) -> s(add(X,Y))
      8: a__first(0(),X) -> nil()
      9: a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
      10: mark(terms(X)) -> a__terms(mark(X))
      11: mark(sqr(X)) -> a__sqr(mark(X))
      12: mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
      13: mark(dbl(X)) -> a__dbl(mark(X))
      14: mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
      15: mark(cons(X1,X2)) -> cons(mark(X1),X2)
      16: mark(recip(X)) -> recip(mark(X))
      17: mark(s(X)) -> s(X)
      18: mark(0()) -> 0()
      19: mark(nil()) -> nil()
      20: a__terms(X) -> terms(X)
      21: a__sqr(X) -> sqr(X)
      22: a__add(X1,X2) -> add(X1,X2)
      23: a__dbl(X) -> dbl(X)
      24: a__first(X1,X2) -> first(X1,X2)
Number of strict rules: 24
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a__add(0(),X) -> #mark(X)
     #2: #mark(dbl(X)) -> #a__dbl(mark(X))
     #3: #mark(dbl(X)) -> #mark(X)
     #4: #a__first(s(X),cons(Y,Z)) -> #mark(Y)
     #5: #mark(sqr(X)) -> #a__sqr(mark(X))
     #6: #mark(sqr(X)) -> #mark(X)
     #7: #mark(add(X1,X2)) -> #a__add(mark(X1),mark(X2))
     #8: #mark(add(X1,X2)) -> #mark(X1)
     #9: #mark(add(X1,X2)) -> #mark(X2)
     #10: #mark(first(X1,X2)) -> #a__first(mark(X1),mark(X2))
     #11: #mark(first(X1,X2)) -> #mark(X1)
     #12: #mark(first(X1,X2)) -> #mark(X2)
     #13: #mark(terms(X)) -> #a__terms(mark(X))
     #14: #mark(terms(X)) -> #mark(X)
     #15: #mark(recip(X)) -> #mark(X)
     #16: #a__terms(N) -> #a__sqr(mark(N))
     #17: #a__terms(N) -> #mark(N)
     #18: #mark(cons(X1,X2)) -> #mark(X1)
Number of SCCs: 1, DPs: 15
  SCC { #1 #3 #4 #6..15 #17 #18 }
POLO(Sum)... succeeded.
      s 	w: 1
      #a__first	w: x1 + x2
      recip	w: x1 + 23612
      dbl	w: x1 + 1
      #a__add	w: x2 + 18755
      a__add	w: x1 + x2 + 18755
      a__dbl	w: x1 + 1
      a__sqr	w: x1 + 29534
      #a__terms	w: x1 + 1
      #mark	w: x1
      0 	w: 1
      nil	w: 2
      #a__dbl	w: 0
      mark	w: x1
      first	w: x1 + x2 + 1
      a__first	w: x1 + x2 + 1
      cons	w: x1 + 19335
      add	w: x1 + x2 + 18755
      sqr	w: x1 + 29534
      a__terms	w: x1 + 72481
      #a__sqr	w: 0
      terms	w: x1 + 72481
    USABLE RULES: { 1..24 }
    Removed DPs: #1 #3 #4 #6 #8..15 #17 #18
Number of SCCs: 0, DPs: 0