#const max = 10.
#const size = 30.
order(1, size).
order(2, size).
order(3, size).
order(4, size).

width(1).
width(2).
width(3).
width(4).

pattern(1, 1, 0).
pattern(1, 2, 1).
pattern(1, 3, 0).
pattern(1, 4, 3).

pattern(2, 1, 1).
pattern(2, 2, 0).
pattern(2, 3, 1).
pattern(2, 4, 2).

pattern(3, 1, 1).
pattern(3, 2, 2).
pattern(3, 3, 0).
pattern(3, 4, 2).

pattern(4, 1, 0).
pattern(4, 2, 1).
pattern(4, 3, 2).
pattern(4, 4, 1).

pattern(5, 1, 3).
pattern(5, 2, 1).
pattern(5, 3, 1).
pattern(5, 4, 1).

pattern(6, 1, 2).
pattern(6, 2, 4).
pattern(6, 3, 0).
pattern(6, 4, 1).

pattern(7, 1, 0).
pattern(7, 2, 6).
pattern(7, 3, 1).
pattern(7, 4, 0).

pattern(8, 1, 1).
pattern(8, 2, 5).
pattern(8, 3, 1).
pattern(8, 4, 0).

pattern(9, 1, 4).
pattern(9, 2, 2).
pattern(9, 3, 1).
pattern(9, 4, 0).


1 { cut(I, 0..max) } 1:- pattern(I, _, _).
:- order(W, L), #sum { J * K: pattern(I, W, J), cut(I, K)} < L.

total(N) :- N = #sum {J, I : cut(I, J)}.
#minimize {N: total(N)}.

#show cut/2.
#show total/1.