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{48, 0, 34 + x2}
  and#_A(x1,x2) = max{60, 60, 62 + x2}
  true_A = 1
  true#_A = 0
  activate_A(x1) = max{48, 34 + x1}
  activate#_A(x1) = max{62, 61 + x1}
  false_A = 35
  false#_A = 61
  if_A(x1,x2,x3) = max{48, 0, 34 + x2, 34 + x3}
  if#_A(x1,x2,x3) = max{62, 0, 61 + x2, 61 + x3}
  add_A(x1,x2) = max{12, 71 + x1, 35 + x2}
  add#_A(x1,x2) = max{4, 84 + x1, 61 + x2}
  0_A = 0
  0#_A = 93
  s_A(x1) = max{77, -23 + x1}
  s#_A(x1) = max{1, 3}
  n__add_A(x1,x2) = max{36, 37 + x1, 24 + x2}
  n__add#_A(x1,x2) = max{62, 60, 3}
  first_A(x1,x2) = max{46, 45 + x1, 80 + x2}
  first#_A(x1,x2) = max{91, 90 + x1, 106 + x2}
  nil_A = 80
  nil#_A = 92
  cons_A(x1,x2) = max{47, -1 + x1, -43 + x2}
  cons#_A(x1,x2) = max{66, 64, -32 + x2}
  n__first_A(x1,x2) = max{10, 31 + x1, 46 + x2}
  n__first#_A(x1,x2) = max{62, 62, 91}
  from_A(x1) = max{56, 46 + x1}
  from#_A(x1) = max{65, 67 + x1}
  n__from_A(x1) = max{5, 22 + x1}
  n__from#_A(x1) = max{64, 64}
  n__s_A(x1) = max{77, -57 + x1}
  n__s#_A(x1) = max{0, 2}

precedence:

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