clear_graph.

add_cons(a>=10@required),add_cons(a+b=c@required),add_cons(c+25=d@strong).
add_cons(d=75@prefer).
add_cons(b>=20@required).

show_graph.

c(11,[10],[],([d]','[d=75])-prefer-t).
c(10,[9],[11],(strong','[c]','[d]','[c+25=d]','g','t)-strong-f).
c(9,[8,1],[10],(required','[b,a]','[c]','[a+b=c]','g','t)-required-f).
c(8,[],[9],(required','[]','[b]','[b>=20]','x','t)-required-g).
c(1,[],[9],(required','[]','[a]','[a>=10]','x','t)-required-g).

v(a,1,required).
v(b,8,required).
v(c,9,required).
v(d,10,strong).
yes

execute.

d=75É75
c=50É50
a=10É30
b=20É40
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph.

add_cons(a=5@weak),add_cons(a=b@required),add_cons(b=c@required),add_cons(c=d@required),add_cons(d=e@required).
add_cons(c=7@strong).

show_graph.

c(4,[6],[5],(strong','[c]','[d]','[c=d]','x','x)-required-f).
c(5,[4],[],(strong','[d]','[e]','[d=e]','x','x)-required-f).
c(9,[8],[],([a]','[a=5])-weak-t).
c(8,[7],[9],(strong','[b]','[a]','[a=b]','x','t)-required-f).
c(7,[6],[8],(strong','[c]','[b]','[b=c]','x','t)-required-f).
c(6,[],[4,7],(strong','[]','[c]','[c=7]','x','t)-strong-f).

v(c,6,strong).
v(d,4,strong).
v(e,5,strong).
v(b,7,strong).
v(a,8,strong).
yes

execute.

c=7É7
d=7É7
e=7É7
b=7É7
a=7É7
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph.
add_cons(a=5@strong),add_cons(b=4@weak),add_cons(a+b=c@required),add_cons(d=7@prefer),add_cons(c+d=e@required),add_cons(e=54@weakest).

show_graph.

c(6,[5],[],([e]','[e=54])-weakest-t).
c(5,[3,4],[6],(weak','[c,d]','[e]','[c+d=e]','x','t)-required-f).
c(3,[2,1],[5],(weak','[b,a]','[c]','[a+b=c]','x','t)-required-f).
c(4,[],[5],(prefer','[]','[d]','[d=7]','x','t)-prefer-f).
c(2,[],[3],(weak','[]','[b]','[b=4]','x','t)-weak-f).
c(1,[],[3],(strong','[]','[a]','[a=5]','x','t)-strong-f).

v(a,1,strong).
v(b,2,weak).
v(c,3,weak).
v(d,4,prefer).
v(e,5,weak).
yes

execute.

d=7É7
b=4É4
a=5É5
c=9É9
e=16É16
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph.

add_cons(a>=5@required),add_cons(c=7@required),add_cons(a=b+c@required),add_cons(a=d@prefer),add_cons(b=e@prefer),add_cons(b=f@strong).

show_graph.

c(2,[],[3],(required','[]','[c]','[c=7]','x','x)-required-f).
c(4,[1],[],(prefer','[a]','[d]','[a=d]','g','x)-prefer-f).
c(1,[],[3,4],(required','[]','[a]','[a>=5]','x','x)-required-g).
c(5,[3],[],(prefer','[b]','[e]','[b=e]','g','x)-prefer-f).
c(6,[3],[],(strong','[b]','[f]','[b=f]','g','x)-strong-f).
c(3,[2,1],[5,6],(required','[c,a]','[b]','[a=b+c]','g','x)-required-f).

v(a,1,required).
v(c,2,required).
v(b,3,required).
v(d,4,prefer).
v(e,5,prefer).
v(f,6,strong).
yes

execute.

c=7É7
a=5É +inf
d=5É +inf
b= -2É +inf
e= -2É +inf
f= -2É +inf
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph.

add_cons(a=5@weak),add_cons(b=5@weak),add_cons(a+b=c@required),add_cons(a>=10@required),add_cons(b>=10@required),add_cons(c=100@weak),add_cons(c+25=d@required).

show_graph.

c(4,[],[3,8],(required','[]','[a]','[a>=10]','x','t)-required-g).
c(6,[],[3,8],(required','[]','[b]','[b>=10]','x','t)-required-g).
c(8,[6,4,3],[],([b,a,c]','[c=100,a=5,b=5])-weak-t).
c(9,[3],[],(required','[c]','[d]','[c+25=d]','g','x)-required-f).
c(3,[4,6],[8,9],(required','[b,a]','[c]','[a+b=c]','g','t)-required-f).

v(a,4,required).
v(b,6,required).
v(c,3,required).
v(d,9,required).
yes

execute.

a=10É10
c=100É100
b=90É90
d=125É125
yes

(add_cons(d=<10@strong)).
yes
execute.

d=45É45
c=20É20
a=10É10
b=10É10
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph,
add_cons(a=5@weak),
add_cons(b=5@weak),
add_cons(a+b=c@required),
add_cons(c=100@weak),
add_cons(a>=10@required),
add_cons(c+25=d@required),
add_cons(d=<100@strong),
add_cons(b>=20@required),
add_cons(a=50@prefer),
add_cons(d=200@weak).

show_graph.

c(9,[14],[15],([d]','[d=<100])-strong-t).
c(14,[13],[9,16],(required','[c]','[d]','[c+25=d]','g','t)-required-f).
c(7,[],[13,15,16],(required','[]','[a]','[a>=10]','x','t)-required-g).
c(12,[],[13,16],(required','[]','[b]','[b>=20]','x','t)-required-g).
c(13,[12,7],[14,16],(required','[b,a]','[c]','[a+b=c]','g','t)-required-f).
c(15,[7,9],[16],([a]','[a=50])-prefer-t).
c(16,[15,13,12,7,14],[],([a,b,c,d]','[d=200,c=100,b=5,a=5])-weak-t).

v(a,7,required).
v(b,12,required).
v(c,13,required).
v(d,14,required).
yes

(execute).

d=100É100
c=75É75
b=25É25
a=50É50
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph,add_cons(a>=10@strong),add_cons(a+b=c@required),add_cons(b>=20@required),add_cons(c+25=d@weak).
add_cons(b=<25@weak).
add_cons(a=<20@weak).
yes
show_graph.

c(5,[3],[],(weak','[c]','[d]','[c+25=d]','g','x)-weak-f).
c(3,[1,4],[5],(strong','[b,a]','[c]','[a+b=c]','g','x)-required-f).
c(6,[4],[],([b]','[b=<25])-weak-t).
c(4,[],[3,6],(required','[]','[b]','[b>=20]','x','t)-required-g).
c(7,[1],[],([a]','[a=<20])-weak-t).
c(1,[],[3,7],(strong','[]','[a]','[a>=10]','x','t)-strong-g).

v(a,1,strong).
v(b,4,required).
v(c,3,strong).
v(d,5,weak).
yes

(execute).

a=10É20
c=30É45
b=20É25
d=55É70
yes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear_graph,
add_cons(x>=0@required),add_cons(x+y=<6@strong),add_cons(y>=4@required),add_cons(2*x>=y@weak).
show_graph.

c(3,[],[2,4],(required','[]','[y]','[y>=4]','x','t)-required-g).
c(1,[],[2,4],(required','[]','[x]','[x>=0]','x','t)-required-g).
c(4,[3,1,2],[],([y,x]','[2*x>=y])-weak-t).
c(2,[1,3],[4],([y,x]','[x+y=<6])-strong-t).

v(x,1,required).
v(y,3,required).
yes

execute.

x=2É2
y=4É4
yes