#! /bin/sh
# -*- coding: utf-8 -*-
# Copyright (C) 2012, 2013, 2014 Laboratoire de Recherche et
# Developpement 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 || exit 1
set -e

cat >reduceu.txt <<EOF
Xa | GFb, Xa | GFb
X(a | GXFb), Xa | GFb
Xa & GFb, Xa & GFb
X(a & GXFb), Xa & GFb

F(a & b & GFc & FGd), F(a & b) & G(Fc & FGd)
Fa | Fb | GFc | GFd, F(a|b) | GF(c | d)
Fa | Fb | GFc | GFd | FGe, F(a|b) | F(G(e) | GF(c | d))
Ga | Gb | GFd | FGe | FGf, Ga | Gb | F(GFd | Ge | Gf)

G(Ga & Fb & c & GFd), G(a&c) & G(Fb & Fd)
G(Ga & GFb & c & GFd), G(a&c) & G(Fb & Fd)
G(a & GFb & c & GFd), G(a&c) & G(Fb & Fd)
G(Ga & Fb & c & GFd & FGe), G(a & c) & G(Fb & Fd & FGe)
G(Ga & XFGb & c & FGd & FGe), FG(b & d & e) & G(a & c)
G(Ga & GXFb & c & FGd & FGe & Fc), G(Fb & FG(d & e)) & G(a & c)
Ga & Gb & GFd & FGe & FGf, G(Fd & FG(e & f)) & G(a & b)
G(Ga & Gb & GFd & FGe) & FGf, G(Fd & FG(e & f)) & G(a & b)

a U (b | Fc), (a U b) | Fc
a W (b | Fc), (a W b) | Fc
a U (b & GFc), (a U b) & GFc
# Unchanged
a W (b & GFc), a W (b & GFc)
# Unchanged
(a | Gc) W g, (a | Gc) W g
# Unchanged
(a | Gc) U g, (a | Gc) U g
(a & GFc) M b, (a M b) & GFc
# Unchanged
(a | GFc) M b, (a | GFc) M b
# Unchanged
(a & GFc) R b, (a & GFc) R b
# Unchanged
(a | GFc) R b, (a | GFc) R b
a R (b & Gc), (a R b) & Gc
a M (b & Gc), (a M b) & Gc
EOF

run 0 ../reduceu reduceu.txt
