% *****************************************************************************
% **  Succesor                                                                *
% *****************************************************************************
% succ(+UG, -PL, -SL)                                                         *
% First, find normalized version of UG graph G.                               *
% Then find all predecessor and successors pairs.                             *
% SL is a successor of PL if:                                                 *
% i) SL is f path: [v_1, v_2, .., v_n] and PL is f path: [u_1, u_2, .., u_m], *
% ii) m <= n,                                                                 *
% iii) for i = 1..m, there is e(u_i, v_i) in G.                               *
% *****************************************************************************
succ(UG, PL, SL) :- normalize(UG, G), nPermuting(G), lsucc(G, PL, SL).

lsucc(G, [], SL) :- fPath(SL, G).
lsucc(G, [V], [U]) :- graphVtx(V, G), graphVtx(U, G), e(V, U, G).
lsucc(G, [V], [U1|[U2|SL]]) :- graphVtx(V, G), graphVtx(U1, G), graphVtx(U2, G), e(V, U1, G), f(U1, U2, G), lsucc(G, [], [U2|SL]).
lsucc(G, [V1|[V2|PL]], [U1|[U2|SL]]) :- graphVtx(V1, G), graphVtx(U1, G), graphVtx(V2, G), graphVtx(U2, G), f(V1, V2, G), f(U1, U2, G), e(V1, U1, G), lsucc(G, [V2|PL], [U2|SL])