FindInstance (and Solve, ...) abysmally slow on a fully determined system of linear equations and inequalities: why?

In the comments, Daniel Lichtblau wrote:

[...] I believe the number of explicit inequalities figures into the method choice heuristic so that could be the cause of worse-than-linear complexity.

So it would seem that FindInstance made an unfortunate choice in tackling this, admittedly odd, set of inequalities.

One possible work-around would be to use smaller, non-overlapping, subsets of inequalities: a!=b!=c!=d&&e!=f!=g!=h and to filter the solution set returned by FindInstance.


No one has upgraded this post in a long time and as Danny promised all the problems the OP posted have been dealt with. In v 11.1 for instance, the last one now runs in a lot less than 150 seconds.

Timing[FindInstance[{
    s!=e!=n!=d!=m!=o!=r!=y,
    s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0},
    {s,e,n,d,m,o,r,y},Integers]]


{0.01, {{s -> 9, e -> 5, n -> 6, d -> 7, m -> 1, o -> 0, r -> 8, y -> 2}}}