1%-----------------------------------------------------------------------------%
2% Requires that the array 'x' is strictly lexicographically less than array 'y'.
3% Compares them from first to last element, regardless of indices
4%-----------------------------------------------------------------------------%
5
6predicate fzn_lex_less_int(array[int] of var int: x,
7                           array[int] of var int: y) =
8    assert(length(x) == length(y),
9        "lex_less_int(\(x), \(y)): arrays of different lengths")
10    /\
11    fzn_lex_less_int__MIP(x, y)
12    ;
13
14predicate fzn_lex_less_int__MIP(array[int] of var int: x,
15                                array[int] of var int: y) =
16    let { int: lx = min(index_set(x)),
17          int: ux = max(index_set(x)),
18          int: ly = min(index_set(y)),
19          int: uy = max(index_set(y)),
20          int: size = min(ux - lx, uy - ly),
21          array[0..size] of var 0..1: fEQ;
22          array[0..size] of var 0..1: fLT;
23    } in
24        sum(fLT) == 1
25        /\
26        fEQ[0] + fLT[0] == 1
27        /\
28        forall(i in 1..size) (
29            fEQ[i-1] == fEQ[i] + fLT[i]
30        )
31        /\
32        forall(i in 0..size) (
33            aux_int_eq_if_1(x[lx+i], y[ly+i], fEQ[i])
34            /\
35            aux_int_lt_if_1(x[lx+i], y[ly+i], fLT[i])
36        )
37    ;
38
39%-----------------------------------------------------------------------------%
40