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%doesprovidethoroughcheckingforsmallexamples.(Giventhe
combinatorics,large
%examplesareoutofthequestion.
well_defined_for(LIST):-
not(ordering_counterexample(LIST,A1,A2)),
not(nil_minimal_counterexample(LIST,A)).
%Ifthereisanelementnotgreaterthannil,thispredicate
determinesitsidentity.
nil_minimal_counterexample(LIST,A):-
legal_address_for(LIST,A),
A\=address([],0),
not(less(address([],0),A)).
%Ifthereisapairofaddressesthatisnotproperlyordered,this
predicatefinds
%them.
ordering_counterexample(LIST,A1,A2):-
legal_address_for(LIST,A1),
legal_address_for(LIST,A2),
A1\=A2,
not(less(A1,A2)),
not(less(A2,A1)).
ordering_counterexample(LIST,A1,A2):-
proper_address_for(LIST,A1),
proper_address_for(LIST,A2),
A1\=A2,
not(less(A1,A2)),
not(less(A2,A1)).
%Thispredicatechecksifachangesetisconflicted.
conflicted(LIST):-
member(X,LIST),
member(A,LIST),
X\=A,
dest(X,Y),
dest(A,B),
Y=B.
%Isaregionoftheaddressspacedeletedbyanychangeinthechange
setS?
deleted(A1,A2,S):-
member(X,S),
operation(X,delete(B,E)),
less_eq(B,A1),
%doesprovidethoroughcheckingforsmallexamples.(Giventhe
combinatorics,large
%examplesareoutofthequestion.
well_defined_for(LIST):-
not(ordering_counterexample(LIST,A1,A2)),
not(nil_minimal_counterexample(LIST,A)).
%Ifthereisanelementnotgreaterthannil,thispredicate
determinesitsidentity.
nil_minimal_counterexample(LIST,A):-
legal_address_for(LIST,A),
A\=address([],0),
not(less(address([],0),A)).
%Ifthereisapairofaddressesthatisnotproperlyordered,this
predicatefinds
%them.
ordering_counterexample(LIST,A1,A2):-
legal_address_for(LIST,A1),
legal_address_for(LIST,A2),
A1\=A2,
not(less(A1,A2)),
not(less(A2,A1)).
ordering_counterexample(LIST,A1,A2):-
proper_address_for(LIST,A1),
proper_address_for(LIST,A2),
A1\=A2,
not(less(A1,A2)),
not(less(A2,A1)).
%Thispredicatechecksifachangesetisconflicted.
conflicted(LIST):-
member(X,LIST),
member(A,LIST),
X\=A,
dest(X,Y),
dest(A,B),
Y=B.
%Isaregionoftheaddressspacedeletedbyanychangeinthechange
setS?
deleted(A1,A2,S):-
member(X,S),
operation(X,delete(B,E)),
less_eq(B,A1),