YES

TRS:

  a__and(true(),X) -> mark(X)
  a__and(false(),Y) -> false()
  a__if(true(),X,Y) -> mark(X)
  a__if(false(),X,Y) -> mark(Y)
  a__add(0(),X) -> mark(X)
  a__add(s(X),Y) -> s(add(X,Y))
  a__first(0(),X) -> nil()
  a__first(s(X),cons(Y,Z)) -> cons(Y,first(X,Z))
  a__from(X) -> cons(X,from(s(X)))
  mark(and(X1,X2)) -> a__and(mark(X1),X2)
  mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
  mark(add(X1,X2)) -> a__add(mark(X1),X2)
  mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
  mark(from(X)) -> a__from(X)
  mark(true()) -> true()
  mark(false()) -> false()
  mark(0()) -> 0()
  mark(s(X)) -> s(X)
  mark(nil()) -> nil()
  mark(cons(X1,X2)) -> cons(X1,X2)
  a__and(X1,X2) -> and(X1,X2)
  a__if(X1,X2,X3) -> if(X1,X2,X3)
  a__add(X1,X2) -> add(X1,X2)
  a__first(X1,X2) -> first(X1,X2)
  a__from(X) -> from(X)

linear polynomial interpretations on N:

  a__and_A(x1,x2) = x1 + x2 + 2
  a__and#_A(x1,x2) = x2 + 2
  true_A = 0
  true#_A = 0
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 1
  false_A = 1
  false#_A = 0
  a__if_A(x1,x2,x3) = x1 + x2 + x3 + 3
  a__if#_A(x1,x2,x3) = x2 + x3 + 3
  a__add_A(x1,x2) = x1 + x2 + 3
  a__add#_A(x1,x2) = x2 + 3
  0_A = 1
  0#_A = 1
  s_A(x1) = x1
  s#_A(x1) = 0
  add_A(x1,x2) = x1 + x2 + 3
  add#_A(x1,x2) = 2
  a__first_A(x1,x2) = x1 + x2 + 2
  a__first#_A(x1,x2) = 3
  nil_A = 1
  nil#_A = 0
  cons_A(x1,x2) = x2
  cons#_A(x1,x2) = 0
  first_A(x1,x2) = x1 + x2 + 2
  first#_A(x1,x2) = 2
  a__from_A(x1) = x1 + 1
  a__from#_A(x1) = 1
  from_A(x1) = x1 + 1
  from#_A(x1) = 0
  and_A(x1,x2) = x1 + x2 + 2
  and#_A(x1,x2) = x2
  if_A(x1,x2,x3) = x1 + x2 + x3 + 3
  if#_A(x1,x2,x3) = x3 + 2

precedence:

  false = and > a__and = mark > a__if = a__add = 0 = a__first = a__from > true = s = add = nil = cons = first = from = if