#!/bin/sh
# -*- coding: utf-8 -*-
# Copyright (C) 2017 Laboratoire de Recherche et Développement
# de l'Epita (LRDE).
#
# This file is part of Spot, a model checking library.
#
# Spot is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# Spot is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
# License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

. ./defs
set -e

cat >formulas <<'EOF'
0
F!(!b <-> FGb)
1
a W F(a -> b)
((0 R Xa) R a) -> Fa
!Xa & (Gb R (Xa W 0))
(1 U b) | F(Fb W (a <-> FXa))
(a M 1) | (!a W a)
(G!a W ((b M 1) -> Fa)) -> !a
!a xor (a <-> b)
b & (a <-> b)
b
(a | b | (a -> b)) R b
Xa
!b
!Fb | !Xb
!(b | Gb)
XXX(b | Gb)
(a & F(a | FG(a W b))) U a
FGXb M (!b M b)
a
((a & !b) W Ga) W a
(b <-> FGb) M 1
X!b
FX!(a xor !a)
Fb R (a & (a <-> b))
XXb | (b W 0)
1 U (b xor !b)
G!(b M 1) W (1 U b)
!(Fa M Xa)


(!b U b) U X(!a -> Fb)
(b | (Fa R (b W a))) M 1
1 U (a xor b)
XF!b
X(!(!b | (a M b)) -> XXa)
(FXXF(a R Fa) R Xb) U XFb
!Gb
F(Xb xor XXb)
F(XF!a & (Fb U !a))
!b M 1
b M Fb
!(a xor (b xor ((b W Ga) -> b)))
!(a -> (a & !a)) xor !(a U !b)
!(0 R !b)
Fa M FXb
Fa & (Fa | (!a -> Gb))
Xb M X!a
Gb xor (b W !b)
F!(a | (b W a))
F(1 U b)
F(!a M 1)
XF((b <-> (a <-> b)) | Fb)
F(a U !b)
(!a | b) U (1 U F(a M !b))
!(Xb -> (b W a))
!(0 R !X(Fb U a))
X((a -> b) M 1)
Fb M F(a W b)
FXF(a <-> (Xb -> b))
Xa | !((b W 0) & (a | Fb))


!(F!b M 1)
X(!a W Xb)
!Fb xor G((b xor (Xa M b)) U b)
(0 R b) R (a R Xa)
Gb
a W X(b | Xb)
a W b
X(Xb & (!Ga R Ga))
!Fb
a & GXa
XX(X(a xor b) W 0)
!a -> ((a xor !GFa) W 0)
b M Gb
Xa R XXG(!a & (Fa W Gb))
G!b W b
G(b | G!a)
a xor ((!Xb M 1) & (b M a))

G(b xor (a <-> !a))
!((a | (XXa & (a M Gb))) U b)
!(!b -> b) W a
b | !(b M 1)
G((Fa W !a) xor !(0 R b))
0 R ((Ga xor Xb) -> (0 R a))
G!Xa
!(X!b M a)
!(!b M a) W !a
G(a & X!Xb)
Xb -> Gb
(b | X!b) W a
b W (!b xor (!a M FXb))


((b M 1) M 1) xor (a xor Ga)
b <-> (a M 1)
a xor F(!X!Fa xor (b U Xa))
G!(!b R (Xb W b))
(Fa & Xb) | G(b U Ga)
!(a R Gb) R !a
!(Gb U a)
(FXb & XGa) xor F(Xa M 1)
Gb <-> !((1 U a) -> b)
(a U b) & ((b U a) R FX!Ga)
Xb <-> F!a
!(a xor F(1 U Fb))
Fa <-> G(a R b)
a | (Fb <-> XXFa)
(a U b) & (b <-> FX!b)
X!a -> (((b -> a) xor (a W 0)) M Gb)
XX!(b U (X(0 R b) R a))
XX(Ga <-> (Xa | !(b U Xa)))
b xor Fa
(Fb M a) xor X(Fa U Fb)
b xor (Fb | (a W Gb))
!a & X(Ga -> G(a xor b))
(a xor XF!a) | X((a | (b R a)) -> b)
((a U XFb) W Fb) -> FX!a
X(a U Fb) -> !G!a
Fa R X(b & X(X(b R a) -> b))
a M (G!b R Xb)
(!a R a) | (Fa xor XFb)
XF(b | Gb) M ((b R a) R !a)
!a xor (0 R ((b -> a) -> Gb))

(Ga | Fb) M 1
!G(F(b & Fa) W b)
F!b -> (1 U (b W a))
((0 R b) M 1) U XXa
1 U (b & Ga)
a & F(!b W Gb)
!((a <-> Gb) R (Fa -> Fb))
!G(!a M 1)
FG(b & Ga)
(Xa W 0) M 1
a xor !(Fb W Fa)
1 U (a & Ga)
a W ((a M G(0 R Fb)) -> a)
F((b -> F(a W 0)) W 0)
G(1 U Ga)
!(Fb W 0)
F(!XFXb M Xa)
b | (Gb M F(a & Fa))
a R !(0 R G(b & Fa))
b W F(b R a)
((a <-> b) W G!a) U !(!b M 1)
F(Fb xor !Xa)
!FX(G(1 U b) R (1 U Xa))
X(F!Fb M Xa)
FGa
FGXb
Fa -> XXG(1 U Gb)
XXFa U Ga
a & F!X(a | XFa)
F(a | Gb)
EOF

cat formulas | ltlcross \
  --timeout=60 \
  '{1} ltl2tgba %f >%T' \
  '{2} case `ltlfilt -f %f --format=%%[w]h` in *P*) ltl2tgba -B %f | autfilt\
    --dca ;; *) ltl2tgba -B %f;; esac >%O'

for i in 4 5 6 7 8 9 10
do
  for acc in "min even" "min odd" "max even" "max odd";
  do
    randaut -A "parity $acc $i" a b c > input.hoa
    autfilt --dca input.hoa > res.hoa
    autfilt input.hoa --included-in=res.hoa
  done
done