YES

TRS:

  is_empty(nil()) -> true()
  is_empty(cons(x,l)) -> false()
  hd(cons(x,l)) -> x
  tl(cons(x,l)) -> l
  append(l1,l2) -> ifappend(l1,l2,l1)
  ifappend(l1,l2,nil()) -> l2
  ifappend(l1,l2,cons(x,l)) -> cons(x,append(l,l2))

linear polynomial interpretations on N:

  is_empty_A(x1) = 0
  is_empty#_A(x1) = 2
  nil_A = 1
  nil#_A = 0
  true_A = 0
  true#_A = 1
  cons_A(x1,x2) = x1 + x2 + 2
  cons#_A(x1,x2) = 4
  false_A = 0
  false#_A = 3
  hd_A(x1) = x1
  hd#_A(x1) = x1
  tl_A(x1) = x1
  tl#_A(x1) = x1
  append_A(x1,x2) = x1 + x2 + 1
  append#_A(x1,x2) = x1 + x2 + 4
  ifappend_A(x1,x2,x3) = x2 + x3 + 1
  ifappend#_A(x1,x2,x3) = x2 + x3 + 3

precedence:

  ifappend > is_empty = nil = cons = hd = tl = append > true = false