YES

TRS:

  active(and(true(),X)) -> mark(X)
  active(and(false(),Y)) -> mark(false())
  active(if(true(),X,Y)) -> mark(X)
  active(if(false(),X,Y)) -> mark(Y)
  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)))
  active(from(X)) -> mark(cons(X,from(s(X))))
  mark(and(X1,X2)) -> active(and(mark(X1),X2))
  mark(true()) -> active(true())
  mark(false()) -> active(false())
  mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3))
  mark(add(X1,X2)) -> active(add(mark(X1),X2))
  mark(0()) -> active(0())
  mark(s(X)) -> active(s(X))
  mark(first(X1,X2)) -> active(first(mark(X1),mark(X2)))
  mark(nil()) -> active(nil())
  mark(cons(X1,X2)) -> active(cons(X1,X2))
  mark(from(X)) -> active(from(X))
  and(mark(X1),X2) -> and(X1,X2)
  and(X1,mark(X2)) -> and(X1,X2)
  and(active(X1),X2) -> and(X1,X2)
  and(X1,active(X2)) -> and(X1,X2)
  if(mark(X1),X2,X3) -> if(X1,X2,X3)
  if(X1,mark(X2),X3) -> if(X1,X2,X3)
  if(X1,X2,mark(X3)) -> if(X1,X2,X3)
  if(active(X1),X2,X3) -> if(X1,X2,X3)
  if(X1,active(X2),X3) -> if(X1,X2,X3)
  if(X1,X2,active(X3)) -> if(X1,X2,X3)
  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)
  s(mark(X)) -> s(X)
  s(active(X)) -> s(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)
  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)
  from(mark(X)) -> from(X)
  from(active(X)) -> from(X)

linear polynomial interpretations on N:

  active_A(x1) = x1
  active#_A(x1) = x1
  and_A(x1,x2) = x1 + x2 + 3
  and#_A(x1,x2) = x1 + x2 + 5
  true_A = 0
  true#_A = 0
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 4
  false_A = 0
  false#_A = 2
  if_A(x1,x2,x3) = x1 + x2 + x3 + 5
  if#_A(x1,x2,x3) = x1 + x2 + x3 + 5
  add_A(x1,x2) = x1 + x2 + 3
  add#_A(x1,x2) = 6
  0_A = 2
  0#_A = 1
  s_A(x1) = 1
  s#_A(x1) = 3
  first_A(x1,x2) = x1 + x2 + 6
  first#_A(x1,x2) = 7
  nil_A = 1
  nil#_A = 0
  cons_A(x1,x2) = 1
  cons#_A(x1,x2) = 6
  from_A(x1) = 7
  from#_A(x1) = 3

precedence:

  add > active > false = if > and = mark > true = 0 = s = first = from > nil = cons