DOMAINS
IntList = integer*
IntLists = IntList*

PREDICATES
max(integer, integer, integer)
maxElement(IntList, integer)
maxWithIdx(integer, integer, integer, integer, integer, integer)
maxMaxIdx(IntLists, integer, integer, integer)
maxMaxInList(IntLists, integer, integer)

GOAL
clearwindow,
maxMaxInList([[2, 3, 1], [5, 4, 3, 1, 0], [1, 2, 7], [6, 1], [3, 2, 0]], Idx, Maximum),
write(Maximum),
nl,
write(Idx).

CLAUSES
max(X, Y, X) :-
    X > Y,!.
max(_, Y, Y).

maxElement([], -32768) :- !.
maxElement([Head|Tail], MaxEl) :-
    maxElement(Tail, TailMax),
    max(Head, TailMax, MaxEl).

maxWithIdx(A, AIdx, B, _, A, AIdx) :-
    A > B,!.
maxWithIdx(_, _, B, BIdx, B, BIdx).

maxMaxIdx([], _, -32768, -1) :- !.
maxMaxIdx([Head|Tail], Idx, CurrMax, CurrIdx) :-
    NextIdx = Idx + 1,
    maxMaxIdx(Tail, NextIdx, TailMax, TailMaxIdx),
    maxElement(Head, HeadMax),
    maxWithIdx(HeadMax, Idx, TailMax, TailMaxIdx, CurrMax, CurrIdx).

maxMaxInList(List, Idx, Maximum) :-
    maxMaxIdx(List, 0, Maximum, Idx).