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(activate(X1),X2)
  activate(n__first(X1,X2)) -> first(activate(X1),activate(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{1, 5 + x1, 1 + x2}
  and#_A(x1,x2) = max{1, 5 + x1, 1 + x2}
  true_A = 0
  true#_A = 0
  activate_A(x1) = max{5, x1}
  activate#_A(x1) = max{5, x1}
  false_A = 0
  false#_A = 0
  if_A(x1,x2,x3) = max{0, x1, 5 + x2, 1 + x3}
  if#_A(x1,x2,x3) = max{0, x1, 5 + x2, 1 + x3}
  add_A(x1,x2) = max{6, 3 + x1, 8 + x2}
  add#_A(x1,x2) = max{6, 3 + x1, 8 + x2}
  0_A = 1
  0#_A = 1
  s_A(x1) = max{13, x1}
  s#_A(x1) = max{13, x1}
  n__add_A(x1,x2) = max{7, 3 + x1, 8 + x2}
  n__add#_A(x1,x2) = max{7, 3 + x1, 8 + x2}
  first_A(x1,x2) = max{23, 12 + x1, 18 + x2}
  first#_A(x1,x2) = max{23, 12 + x1, 18 + x2}
  nil_A = 0
  nil#_A = 0
  cons_A(x1,x2) = max{4, 6 + x1, x2}
  cons#_A(x1,x2) = max{4, 6 + x1, x2}
  n__first_A(x1,x2) = max{23, 12 + x1, 18 + x2}
  n__first#_A(x1,x2) = max{23, 12 + x1, 18 + x2}
  from_A(x1) = max{25, 12 + x1}
  from#_A(x1) = max{25, 12 + x1}
  n__from_A(x1) = max{25, 12 + x1}
  n__from#_A(x1) = max{25, 12 + x1}
  n__s_A(x1) = max{13, x1}
  n__s#_A(x1) = max{13, x1}

precedence:

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