%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% simple constraint solver for inequalities between variables
%% thom fruehwirth ECRC 950519, LMU 980207, 980311
%%
%% ported to hProlog by Tom Schrijvers 

:- module(leq,[]).
:- use_module(library(chr)).

:- constraints leq/2.
reflexivity  @ leq(X,X) <=> true.
antisymmetry @ leq(X,Y), leq(Y,X) <=> X = Y.
idempotence  @ leq(X,Y) \ leq(X,Y) <=> true.
transitivity @ leq(X,Y), leq(Y,Z) ==> leq(X,Z).

time(N):-
	cputime(X),
	length(L,N),
	genleq(L,Last),
	L=[First|_],
	leq(Last,First),
	cputime( Now),
	Time is Now-X,
	write(N-Time), nl.

genleq([Last],Last) :- ! .
genleq([X,Y|Xs],Last):-
	leq(X,Y),
	genleq([Y|Xs],Last).

cputime( Ts) :- 
	statistics( runtime, [Tm,_]),
	Ts is Tm/1000.