YES

TRS:

  active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N))))
  active(sqr(0())) -> mark(0())
  active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X))))
  active(dbl(0())) -> mark(0())
  active(dbl(s(X))) -> mark(s(s(dbl(X))))
  active(add(0(),X)) -> mark(X)
  active(add(s(X),Y)) -> mark(s(add(X,Y)))
  active(first(0(),X)) -> mark(nil())
  active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
  mark(terms(X)) -> active(terms(mark(X)))
  mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
  mark(recip(X)) -> active(recip(mark(X)))
  mark(sqr(X)) -> active(sqr(mark(X)))
  mark(s(X)) -> active(s(X))
  mark(0()) -> active(0())
  mark(add(X1,X2)) -> active(add(mark(X1),mark(X2)))
  mark(dbl(X)) -> active(dbl(mark(X)))
  mark(first(X1,X2)) -> active(first(mark(X1),mark(X2)))
  mark(nil()) -> active(nil())
  terms(mark(X)) -> terms(X)
  terms(active(X)) -> terms(X)
  cons(mark(X1),X2) -> cons(X1,X2)
  cons(X1,mark(X2)) -> cons(X1,X2)
  cons(active(X1),X2) -> cons(X1,X2)
  cons(X1,active(X2)) -> cons(X1,X2)
  recip(mark(X)) -> recip(X)
  recip(active(X)) -> recip(X)
  sqr(mark(X)) -> sqr(X)
  sqr(active(X)) -> sqr(X)
  s(mark(X)) -> s(X)
  s(active(X)) -> s(X)
  add(mark(X1),X2) -> add(X1,X2)
  add(X1,mark(X2)) -> add(X1,X2)
  add(active(X1),X2) -> add(X1,X2)
  add(X1,active(X2)) -> add(X1,X2)
  dbl(mark(X)) -> dbl(X)
  dbl(active(X)) -> dbl(X)
  first(mark(X1),X2) -> first(X1,X2)
  first(X1,mark(X2)) -> first(X1,X2)
  first(active(X1),X2) -> first(X1,X2)
  first(X1,active(X2)) -> first(X1,X2)

max/plus interpretations on N:

  active_A(x1) = max{53, x1}
  active#_A(x1) = max{120, 52 + x1}
  terms_A(x1) = max{235, 165 + x1}
  terms#_A(x1) = max{122, 123}
  mark_A(x1) = max{53, 41 + x1}
  mark#_A(x1) = max{119, 121 + x1}
  cons_A(x1,x2) = max{0, x1, 0}
  cons#_A(x1,x2) = max{118, 121, 66}
  recip_A(x1) = max{83, 13 + x1}
  recip#_A(x1) = max{204, 204}
  sqr_A(x1) = max{82, 40 + x1}
  sqr#_A(x1) = max{118, 132}
  s_A(x1) = max{3, 1}
  s#_A(x1) = max{54, 1}
  0_A = 7
  0#_A = 124
  add_A(x1,x2) = max{141, x1, 71 + x2}
  add#_A(x1,x2) = max{0, 0, 0}
  dbl_A(x1) = max{11, x1}
  dbl#_A(x1) = max{130, 131}
  first_A(x1,x2) = max{140, 59 + x1, 70 + x2}
  first#_A(x1,x2) = max{115, 116, 117}
  nil_A = 54
  nil#_A = 123

precedence:

  mark > recip > active > terms > s > sqr > add = dbl > 0 > nil > first > cons