YES

TRS:

  first(0(),X) -> nil()
  first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
  from(X) -> cons(X,n__from(n__s(X)))
  first(X1,X2) -> n__first(X1,X2)
  from(X) -> n__from(X)
  s(X) -> n__s(X)
  activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
  activate(n__from(X)) -> from(activate(X))
  activate(n__s(X)) -> s(activate(X))
  activate(X) -> X

linear polynomial interpretations on N:

  first_A(x1,x2) = x1 + x2 + 3
  first#_A(x1,x2) = x2 + 4
  0_A = 1
  0#_A = 1
  nil_A = 0
  nil#_A = 0
  s_A(x1) = x1
  s#_A(x1) = 1
  cons_A(x1,x2) = x2
  cons#_A(x1,x2) = 3
  n__first_A(x1,x2) = x1 + x2 + 3
  n__first#_A(x1,x2) = x2 + 3
  activate_A(x1) = x1
  activate#_A(x1) = x1 + 2
  from_A(x1) = x1 + 3
  from#_A(x1) = 4
  n__from_A(x1) = x1 + 3
  n__from#_A(x1) = 1
  n__s_A(x1) = x1
  n__s#_A(x1) = 0

precedence:

  first = 0 > nil = cons = n__first > activate > from > n__from = n__s > s