(VAR x y z t)
(THEORY (AC app plus))
(RULES
  if(true, x, y) -> x
  if(false, x, y) -> y
  eq(0, 0) -> true
  eq(0, s(x)) -> false
  eq(s(x), s(y)) -> eq(x, y)
  plus(empty, x) -> x
  app(x, empty) -> empty
  app(x, app(empty, z)) -> app(empty, z)
  app(x, plus(y, z)) -> plus(app(x, y), app(x, z))
  app(x, app(plus(y, z), t)) -> app(plus(app(x, y), app(x, z)), t)
  app(singl(x), singl(y)) -> if(eq(x, y), singl(x), empty)
)