include "tree.mzn";
include "subgraph.mzn";  

predicate fzn_path(int: N, int: E, array[int] of int: from, array[int] of int: to,
                   var int: s, var int: t, array[int] of var bool: ns, array[int] of var bool: es) =
    let { array[1..2*E] of int: dfrom = from ++ to;
          array[1..2*E] of int: dto   = to ++ from;
          array[1..2*E] of var bool: des;
    } in
        /* ensure that the directed edges selected agree with undirected edges */
        forall(e in 1..E)(es[e] <-> (des[e] \/ des[e+E])) /\
        /* duplicate the edges so that the we can use directed graph path */
        fzn_dpath(N,2*E,dfrom,dto,s,t,ns,des);
   
%-----------------------------------------------------------------------------%