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(a__add(a__sqr(mark(X)),a__dbl(mark(X))))
      4: a__dbl(0()) -> 0()
      5: a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
      6: a__add(0(),X) -> mark(X)
      7: a__add(s(X),Y) -> s(a__add(mark(X),mark(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(mark(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: #a__add(s(X),Y) -> #a__add(mark(X),mark(Y))
     #14: #a__add(s(X),Y) -> #mark(X)
     #15: #a__add(s(X),Y) -> #mark(Y)
     #16: #mark(terms(X)) -> #a__terms(mark(X))
     #17: #mark(terms(X)) -> #mark(X)
     #18: #a__dbl(s(X)) -> #a__dbl(mark(X))
     #19: #a__dbl(s(X)) -> #mark(X)
     #20: #mark(s(X)) -> #mark(X)
     #21: #mark(recip(X)) -> #mark(X)
     #22: #a__sqr(s(X)) -> #a__add(a__sqr(mark(X)),a__dbl(mark(X)))
     #23: #a__sqr(s(X)) -> #a__sqr(mark(X))
     #24: #a__sqr(s(X)) -> #mark(X)
     #25: #a__sqr(s(X)) -> #a__dbl(mark(X))
     #26: #a__sqr(s(X)) -> #mark(X)
     #27: #a__terms(N) -> #a__sqr(mark(N))
     #28: #a__terms(N) -> #mark(N)
     #29: #mark(cons(X1,X2)) -> #mark(X1)
Number of SCCs: 1, DPs: 29
  SCC { #1..29 }
POLO(Sum)... POLO(max)... succeeded.
      s 	w: x1
      #a__first	w: max(x2 + 19308)
      recip	w: x1 + 1
      dbl	w: x1 + 32287
      #a__add	w: max(x1 + 19306, x2 + 19307)
      a__add	w: max(x1, x2 + 11799)
      a__dbl	w: x1 + 32287
      a__sqr	w: x1 + 44086
      #a__terms	w: x1 + 63393
      #mark	w: x1 + 19306
      0 	w: 8368
      nil	w: 4
      #a__dbl	w: x1 + 19307
      mark	w: x1
      first	w: max(x1 + 1, x2 + 3)
      a__first	w: max(x1 + 1, x2 + 3)
      cons	w: max(x1 + 4)
      add	w: max(x1, x2 + 11799)
      sqr	w: x1 + 44086
      a__terms	w: x1 + 44091
      #a__sqr	w: x1 + 63392
      terms	w: x1 + 44091
    USABLE RULES: { 1..24 }
    Removed DPs: #1..4 #6 #9..12 #15..17 #19 #21 #24..29
Number of SCCs: 2, DPs: 9
  SCC { #18 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #a__first	s: [2,1]	p: 0
      recip	s: [1]	p: 0
      dbl	s: [1]	p: 1
      #a__add	s: [1,2]	p: 0
      a__add	s: [2,1]	p: 1
      a__dbl	s: [1]	p: 1
      a__sqr	s: [1]	p: 2
      #a__terms	s: 1
      #mark	s: []	p: 0
      0 	s: []	p: 3
      nil	s: []	p: 4
      #a__dbl	s: 1
      mark	s: 1
      first	s: []	p: 4
      a__first	s: []	p: 4
      cons	s: []	p: 0
      add	s: [2,1]	p: 1
      sqr	s: [1]	p: 2
      a__terms	s: []	p: 3
      #a__sqr	s: 1
      terms	s: []	p: 3
    USABLE RULES: { 1..24 }
    Removed DPs: #18
Number of SCCs: 1, DPs: 8
  SCC { #5 #7 #8 #13 #14 #20 #22 #23 }
POLO(Sum)... POLO(max)... QLPOS... succeeded.
      s 	s: [1]	p: 0
      #a__first	s: [2,1]	p: 0
      recip	s: [1]	p: 0
      dbl	s: [1]	p: 1
      #a__add	s: 1
      a__add	s: [2,1]	p: 1
      a__dbl	s: [1]	p: 1
      a__sqr	s: [1]	p: 2
      #a__terms	s: 1
      #mark	s: 1
      0 	s: []	p: 3
      nil	s: []	p: 4
      #a__dbl	s: []	p: 0
      mark	s: 1
      first	s: []	p: 4
      a__first	s: []	p: 4
      cons	s: []	p: 0
      add	s: [2,1]	p: 1
      sqr	s: [1]	p: 2
      a__terms	s: []	p: 3
      #a__sqr	s: [1]	p: 2
      terms	s: []	p: 3
    USABLE RULES: { 1..24 }
    Removed DPs: #7 #8 #13 #14 #20 #22 #23
Number of SCCs: 0, DPs: 0