YES

TRS:

  and(true(),X) -> activate(X)
  and(false(),Y) -> false()
  if(true(),X,Y) -> activate(X)
  if(false(),X,Y) -> activate(Y)
  add(0(),X) -> activate(X)
  add(s(X),Y) -> s(n__add(activate(X),activate(Y)))
  first(0(),X) -> nil()
  first(s(X),cons(Y,Z)) -> cons(activate(Y),n__first(activate(X),activate(Z)))
  from(X) -> cons(activate(X),n__from(n__s(activate(X))))
  add(X1,X2) -> n__add(X1,X2)
  first(X1,X2) -> n__first(X1,X2)
  from(X) -> n__from(X)
  s(X) -> n__s(X)
  activate(n__add(X1,X2)) -> add(X1,X2)
  activate(n__first(X1,X2)) -> first(X1,X2)
  activate(n__from(X)) -> from(X)
  activate(n__s(X)) -> s(X)
  activate(X) -> X

max/plus interpretations on N:

  and_A(x1,x2) = max{13, 1 + x1, 4 + x2}
  and#_A(x1,x2) = max{13, 1 + x1, 4 + x2}
  true_A = 0
  true#_A = 0
  activate_A(x1) = max{13, 3 + x1}
  activate#_A(x1) = max{13, 3 + x1}
  false_A = 2
  false#_A = 2
  if_A(x1,x2,x3) = max{0, 12 + x1, 4 + x2, 13 + x3}
  if#_A(x1,x2,x3) = max{0, 12 + x1, 4 + x2, 13 + x3}
  add_A(x1,x2) = max{24, 5 + x1, 14 + x2}
  add#_A(x1,x2) = max{24, 5 + x1, 14 + x2}
  0_A = 16
  0#_A = 16
  s_A(x1) = max{7, x1}
  s#_A(x1) = max{7, x1}
  n__add_A(x1,x2) = max{21, 2 + x1, 11 + x2}
  n__add#_A(x1,x2) = max{21, 2 + x1, 11 + x2}
  first_A(x1,x2) = max{12, 7 + x1, 14 + x2}
  first#_A(x1,x2) = max{12, 7 + x1, 14 + x2}
  nil_A = 15
  nil#_A = 15
  cons_A(x1,x2) = max{10, 2 + x1, x2}
  cons#_A(x1,x2) = max{10, 2 + x1, x2}
  n__first_A(x1,x2) = max{8, 4 + x1, 11 + x2}
  n__first#_A(x1,x2) = max{8, 4 + x1, 11 + x2}
  from_A(x1) = max{26, 16 + x1}
  from#_A(x1) = max{26, 16 + x1}
  n__from_A(x1) = max{26, 13 + x1}
  n__from#_A(x1) = max{26, 13 + x1}
  n__s_A(x1) = max{6, x1}
  n__s#_A(x1) = max{6, x1}

precedence:

  and = if > activate = nil = from > add = 0 = first = n__from > true = false = s = n__add = cons = n__first > n__s