/**
* Returns the bounds for the given scope.
*
* @return the bounds for the given scope.
*/
public final Bounds bounds(int scope) {
assert scope > 0;
final int n = scope * 3;
final List<String> atoms = new ArrayList<String>(n);
for (int i = 0; i < scope; i++) atoms.add("Object" + i);
for (int i = 0; i < scope; i++) atoms.add("Name" + i);
for (int i = 0; i < scope; i++) atoms.add("DirEntry" + i);
final Universe u = new Universe(atoms);
final TupleFactory f = u.factory();
final Bounds b = new Bounds(u);
final int max = scope - 1;
b.bound(Obj, f.range(f.tuple("Object0"), f.tuple("Object" + max)));
b.boundExactly(Root, f.setOf("Object0"));
b.bound(Cur, b.upperBound(Obj));
b.bound(File, b.upperBound(Obj));
b.bound(Dir, b.upperBound(Obj));
b.bound(Name, f.range(f.tuple("Name0"), f.tuple("Name" + max)));
b.bound(DirEntry, f.range(f.tuple("DirEntry0"), f.tuple("DirEntry" + max)));
b.bound(entries, b.upperBound(Dir).product(b.upperBound(DirEntry)));
b.bound(parent, b.upperBound(Dir).product(b.upperBound(Dir)));
b.bound(name, b.upperBound(DirEntry).product(b.upperBound(Name)));
b.bound(contents, b.upperBound(DirEntry).product(b.upperBound(Obj)));
return b;
}
public SymmetryBreakingTest() {
this.solver = new Solver();
List<String> atoms = new ArrayList<String>(USIZE);
for (int i = 0; i < USIZE; i++) {
atoms.add("" + i);
}
final Universe universe = new Universe(atoms);
this.factory = universe.factory();
to1 = Relation.binary("to1");
ord1 = Relation.unary("ord1");
first1 = Relation.unary("first1");
last1 = Relation.unary("last1");
to2 = Relation.binary("to2");
ord2 = Relation.unary("ord2");
first2 = Relation.unary("first2");
last2 = Relation.unary("last2");
to3 = Relation.binary("to3");
ord3 = Relation.unary("ord3");
first3 = Relation.unary("first3");
last3 = Relation.unary("last3");
ac1 = Relation.binary("ac1");
ac2 = Relation.binary("ac2");
ac3 = Relation.binary("ac3");
r1 = Relation.unary("r1");
r2 = Relation.binary("r2");
}
/**
* Create a {@link TupleSet} by specifying a collection of tuples
*
* @param numTuples a collection of type-specific tuples, never <code>null</code>. Each tuple must
* not be <code>null</code> and is encoded as an array. The length of the array must be the
* arity of the type
* @return a {@link TupleSet}, never <code>null</code>
*/
public TupleSet createTupleSet(final Universe universe, final Collection<int[]> numTuples) {
if (isSingleton && numTuples.size() != 1)
throw new IllegalArgumentException("Expected singleton set for singleton");
final Collection<Tuple> result;
if (mustBeSingleton) {
final int[] numbers = numTuples.iterator().next();
result = createSingleton(universe, numbers);
} else {
result = createSet(universe, numTuples);
}
final TupleSet tupleSet;
if (result.isEmpty()) {
tupleSet = universe.factory().noneOf(arity);
} else {
tupleSet = universe.factory().setOf(result);
}
return tupleSet;
}
private Tuple createSetElement(final Universe universe, final int[] numbers) {
checkArity(numbers);
final Object[] atoms = new Object[arity];
for (int i = 0; i < arity; i++) {
final int element = numbers[i];
final SetEnabledType setType = (SetEnabledType) types[i];
atoms[i] = universe.atom(setType.encodeElement(element));
}
return universe.factory().tuple(atoms);
}
private void createTuples(
final Universe universe,
final int pos,
final int[][] atomIndeces,
final Object[] atoms,
final Collection<Tuple> tuples) {
if (pos < arity) {
final int[] current = atomIndeces[pos];
for (final int index : current) {
atoms[pos] = universe.atom(index);
createTuples(universe, pos + 1, atomIndeces, atoms, tuples);
}
} else {
tuples.add(universe.factory().tuple(atoms));
}
}
/**
* Returns the bounds for relational encoding of the problem based on the input file.
*
* @return the bounds for relational encoding of the problem based on the input file.
*/
public Bounds bounds() {
try {
final BufferedReader reader = new BufferedReader(new FileReader(new File(file)));
final Pattern np = Pattern.compile("num\\((\\d+)\\)\\.");
final Pattern bp = Pattern.compile("block\\((\\d+),\\s*(\\d+)\\)\\.");
String line = "";
final Matcher m = np.matcher(line);
int n = 0;
for (line = reader.readLine();
line != null && m.reset(line).matches();
line = reader.readLine()) {
n++;
if (Integer.parseInt(m.group(1)) != n) throw new IOException();
}
if (n == 0) throw new IOException();
final List<Object> atoms = new ArrayList<Object>(n * 2);
for (int i = 0; i < n; i++) {
atoms.add("Q" + i);
}
for (int i = 0; i < n; i++) {
atoms.add(Integer.valueOf(i));
}
final Universe u = new Universe(atoms);
final Bounds b = new Bounds(u);
final TupleFactory f = u.factory();
final TupleSet qbound = f.range(f.tuple("Q0"), f.tuple("Q" + (n - 1)));
final TupleSet nbound = f.range(f.tuple(Integer.valueOf(0)), f.tuple(Integer.valueOf(n - 1)));
b.boundExactly(queen, qbound);
b.boundExactly(num, nbound);
b.bound(x, qbound.product(nbound));
b.bound(y, qbound.product(nbound));
final TupleSet obound = f.noneOf(2);
for (int i = 1; i < n; i++) {
obound.add(f.tuple((Object) Integer.valueOf(i - 1), Integer.valueOf(i)));
}
b.boundExactly(ord, obound);
for (int i = 0; i < n; i++) {
b.boundExactly(i, f.setOf(Integer.valueOf(i)));
}
// extract the partial instance for the grid
final TupleSet blocks = f.noneOf(2);
for (m.usePattern(bp); line != null && m.reset(line).matches(); line = reader.readLine()) {
Integer i = Integer.parseInt(m.group(1)) - 1;
Integer j = Integer.parseInt(m.group(2)) - 1;
if (i < 0 || i >= n || j < 0 || j >= n) throw new IOException();
blocks.add(f.tuple((Object) i, j));
}
if (line != null) throw new IOException();
b.boundExactly(blocked, blocks);
return b;
} catch (FileNotFoundException e) {
System.out.println("Could not find " + file);
usage();
} catch (IOException e) {
System.out.println("Badly formatted file: " + file);
usage();
} catch (NumberFormatException e) {
System.out.println("Badly formatted file: " + file);
usage();
}
return null;
}
public static void main(String[] args) throws Exception {
Relation x0 = Relation.unary("Int/min");
Relation x1 = Relation.unary("Int/zero");
Relation x2 = Relation.unary("Int/max");
Relation x3 = Relation.nary("Int/next", 2);
Relation x4 = Relation.unary("seq/Int");
Relation x5 = Relation.unary("String");
Relation x6 = Relation.unary("this/A");
Relation x7 = Relation.unary("this/Relation");
Relation x8 = Relation.nary("this/Relation.r", 4);
List<String> atomlist =
Arrays.asList(
"-1",
"-2",
"-3",
"-4",
"-5",
"-6",
"-7",
"-8",
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"A$0",
"A$1",
"A$2",
"Relation$0",
"unused0",
"unused1");
Universe universe = new Universe(atomlist);
TupleFactory factory = universe.factory();
Bounds bounds = new Bounds(universe);
TupleSet x0_upper = factory.noneOf(1);
x0_upper.add(factory.tuple("-8"));
bounds.boundExactly(x0, x0_upper);
TupleSet x1_upper = factory.noneOf(1);
x1_upper.add(factory.tuple("0"));
bounds.boundExactly(x1, x1_upper);
TupleSet x2_upper = factory.noneOf(1);
x2_upper.add(factory.tuple("7"));
bounds.boundExactly(x2, x2_upper);
TupleSet x3_upper = factory.noneOf(2);
x3_upper.add(factory.tuple("-8").product(factory.tuple("-7")));
x3_upper.add(factory.tuple("-7").product(factory.tuple("-6")));
x3_upper.add(factory.tuple("-6").product(factory.tuple("-5")));
x3_upper.add(factory.tuple("-5").product(factory.tuple("-4")));
x3_upper.add(factory.tuple("-4").product(factory.tuple("-3")));
x3_upper.add(factory.tuple("-3").product(factory.tuple("-2")));
x3_upper.add(factory.tuple("-2").product(factory.tuple("-1")));
x3_upper.add(factory.tuple("-1").product(factory.tuple("0")));
x3_upper.add(factory.tuple("0").product(factory.tuple("1")));
x3_upper.add(factory.tuple("1").product(factory.tuple("2")));
x3_upper.add(factory.tuple("2").product(factory.tuple("3")));
x3_upper.add(factory.tuple("3").product(factory.tuple("4")));
x3_upper.add(factory.tuple("4").product(factory.tuple("5")));
x3_upper.add(factory.tuple("5").product(factory.tuple("6")));
x3_upper.add(factory.tuple("6").product(factory.tuple("7")));
bounds.boundExactly(x3, x3_upper);
TupleSet x4_upper = factory.noneOf(1);
x4_upper.add(factory.tuple("0"));
x4_upper.add(factory.tuple("1"));
x4_upper.add(factory.tuple("2"));
bounds.boundExactly(x4, x4_upper);
TupleSet x5_upper = factory.noneOf(1);
bounds.boundExactly(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("A$0"));
x6_upper.add(factory.tuple("A$1"));
x6_upper.add(factory.tuple("A$2"));
bounds.boundExactly(x6, x6_upper);
TupleSet x7_upper = factory.noneOf(1);
x7_upper.add(factory.tuple("unused0"));
x7_upper.add(factory.tuple("unused1"));
x7_upper.add(factory.tuple("Relation$0"));
bounds.bound(x7, x7_upper);
TupleSet x8_upper = factory.noneOf(4);
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("unused1")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1"))
.product(factory.tuple("A$2")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$0")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$1")));
x8_upper.add(
factory
.tuple("Relation$0")
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2"))
.product(factory.tuple("A$2")));
bounds.bound(x8, x8_upper);
bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8")));
bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7")));
bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6")));
bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5")));
bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4")));
bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3")));
bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2")));
bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1")));
bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0")));
bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1")));
bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2")));
bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3")));
bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4")));
bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5")));
bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6")));
bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7")));
Variable x12 = Variable.unary("this");
Decls x11 = x12.oneOf(x7);
Expression x16 = x12.join(x8);
Expression x18 = x6.product(x6);
Expression x17 = x6.product(x18);
Formula x15 = x16.in(x17);
Variable x21 = Variable.unary("x21");
Decls x20 = x21.oneOf(x6);
Expression x25 = x21.join(x16);
Expression x26 = x6.product(x6);
Formula x24 = x25.in(x26);
Variable x29 = Variable.unary("x29");
Decls x28 = x29.oneOf(x6);
Expression x32 = x29.join(x25);
Formula x31 = x32.one();
Formula x33 = x32.in(x6);
Formula x30 = x31.and(x33);
Formula x27 = x30.forAll(x28);
Formula x23 = x24.and(x27);
Variable x36 = Variable.unary("x36");
Decls x35 = x36.oneOf(x6);
Expression x38 = x25.join(x36);
Formula x37 = x38.in(x6);
Formula x34 = x37.forAll(x35);
Formula x22 = x23.and(x34);
Formula x19 = x22.forAll(x20);
Formula x14 = x15.and(x19);
Variable x42 = Variable.unary("x42");
Decls x41 = x42.oneOf(Expression.UNIV);
Variable x45 = Variable.unary("x45");
Decls x44 = x45.oneOf(Expression.UNIV);
Decls x40 = x41.and(x44);
Expression x50 = x42.product(x45);
Expression x51 = x6.product(x6);
Formula x49 = x50.in(x51);
Variable x54 = Variable.unary("x54");
Decls x53 = x54.oneOf(x6);
Expression x57 = x54.join(x50);
Formula x56 = x57.one();
Formula x58 = x57.in(x6);
Formula x55 = x56.and(x58);
Formula x52 = x55.forAll(x53);
Formula x48 = x49.and(x52);
Variable x61 = Variable.unary("x61");
Decls x60 = x61.oneOf(x6);
Expression x63 = x50.join(x61);
Formula x62 = x63.in(x6);
Formula x59 = x62.forAll(x60);
Formula x47 = x48.and(x59);
Expression x66 = x16.join(x45);
Expression x65 = x66.join(x42);
Formula x64 = x65.in(x6);
Formula x46 = x47.implies(x64);
Formula x39 = x46.forAll(x40);
Formula x13 = x14.and(x39);
Formula x10 = x13.forAll(x11);
Expression x70 = x8.join(Expression.UNIV);
Expression x69 = x70.join(Expression.UNIV);
Expression x68 = x69.join(Expression.UNIV);
Formula x67 = x68.in(x7);
Formula x71 = x0.eq(x0);
Formula x72 = x1.eq(x1);
Formula x73 = x2.eq(x2);
Formula x74 = x3.eq(x3);
Formula x75 = x4.eq(x4);
Formula x76 = x5.eq(x5);
Formula x77 = x6.eq(x6);
Formula x78 = x7.eq(x7);
Formula x79 = x8.eq(x8);
Formula x9 =
Formula.compose(FormulaOperator.AND, x10, x67, x71, x72, x73, x74, x75, x76, x77, x78, x79);
Solver solver = new Solver();
solver.options().setSolver(SATFactory.DefaultSAT4J);
solver.options().setBitwidth(4);
solver.options().setFlatten(false);
solver.options().setIntEncoding(Options.IntEncoding.TWOSCOMPLEMENT);
solver.options().setSymmetryBreaking(20);
solver.options().setSkolemDepth(0);
System.out.println(PrettyPrinter.print(x9, 0));
System.out.println(bounds);
System.out.println("Solving...");
System.out.flush();
Solution sol = solver.solve(x9, bounds);
System.out.println(sol.toString());
Instance inst = sol.instance();
Evaluator ev = new Evaluator(inst);
System.out.println("Universe: " + ev.evaluate(Expression.UNIV));
Formula xx = x46.forAll(x40).forAll(x11);
System.out.println(PrettyPrinter.print(xx, 2));
System.out.println(ev.evaluate(xx));
System.out.println(PrettyPrinter.print(x46, 4));
// Variable r = Variable.unary("this");
// Variable u1 = Variable.unary("u1");
// Variable u2 = Variable.unary("u2");
//
// Formula ff =
// u1.product(u2).in(x6.product(x6)).forAll(u1.oneOf(Expression.UNIV).and(u2.oneOf(Expression.UNIV))).forAll(r.oneOf(x7));
// System.out.println(PrettyPrinter.print(ff, 0));
// System.out.println(ev.evaluate(ff));
}
public static void main(String[] args) throws Exception {
Relation x0 = Relation.unary("Int/min");
Relation x1 = Relation.unary("Int/zero");
Relation x2 = Relation.unary("Int/max");
Relation x3 = Relation.nary("Int/next", 2);
Relation x4 = Relation.unary("seq/Int");
Relation x5 = Relation.unary("String");
Relation x6 = Relation.unary("this/Test");
Relation x7 = Relation.nary("this/Test.weight", 2);
Relation x8 = Relation.nary("this/Test.x", 2);
Relation x9 = Relation.nary("this/Test.y", 2);
List<String> atomlist =
Arrays.asList(
"-1", "-2", "-3", "-4", "-5", "-6", "-7", "-8", "0", "1", "2", "3", "4", "5", "6", "7",
"Test$0", "Test$1", "Test$2");
Universe universe = new Universe(atomlist);
TupleFactory factory = universe.factory();
Bounds bounds = new Bounds(universe);
TupleSet x0_upper = factory.noneOf(1);
x0_upper.add(factory.tuple("-8"));
bounds.boundExactly(x0, x0_upper);
TupleSet x1_upper = factory.noneOf(1);
x1_upper.add(factory.tuple("0"));
bounds.boundExactly(x1, x1_upper);
TupleSet x2_upper = factory.noneOf(1);
x2_upper.add(factory.tuple("7"));
bounds.boundExactly(x2, x2_upper);
TupleSet x3_upper = factory.noneOf(2);
x3_upper.add(factory.tuple("-8").product(factory.tuple("-7")));
x3_upper.add(factory.tuple("-7").product(factory.tuple("-6")));
x3_upper.add(factory.tuple("-6").product(factory.tuple("-5")));
x3_upper.add(factory.tuple("-5").product(factory.tuple("-4")));
x3_upper.add(factory.tuple("-4").product(factory.tuple("-3")));
x3_upper.add(factory.tuple("-3").product(factory.tuple("-2")));
x3_upper.add(factory.tuple("-2").product(factory.tuple("-1")));
x3_upper.add(factory.tuple("-1").product(factory.tuple("0")));
x3_upper.add(factory.tuple("0").product(factory.tuple("1")));
x3_upper.add(factory.tuple("1").product(factory.tuple("2")));
x3_upper.add(factory.tuple("2").product(factory.tuple("3")));
x3_upper.add(factory.tuple("3").product(factory.tuple("4")));
x3_upper.add(factory.tuple("4").product(factory.tuple("5")));
x3_upper.add(factory.tuple("5").product(factory.tuple("6")));
x3_upper.add(factory.tuple("6").product(factory.tuple("7")));
bounds.boundExactly(x3, x3_upper);
TupleSet x4_upper = factory.noneOf(1);
x4_upper.add(factory.tuple("0"));
x4_upper.add(factory.tuple("1"));
x4_upper.add(factory.tuple("2"));
x4_upper.add(factory.tuple("3"));
bounds.boundExactly(x4, x4_upper);
TupleSet x5_upper = factory.noneOf(1);
bounds.boundExactly(x5, x5_upper);
TupleSet x6_upper = factory.noneOf(1);
x6_upper.add(factory.tuple("Test$0"));
x6_upper.add(factory.tuple("Test$1"));
x6_upper.add(factory.tuple("Test$2"));
bounds.boundExactly(x6, x6_upper);
TupleSet x7_upper = factory.noneOf(2);
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x7_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x7, x7_upper);
TupleSet x8_upper = factory.noneOf(2);
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x8_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x8, x8_upper);
TupleSet x9_upper = factory.noneOf(2);
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$0").product(factory.tuple("7")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$1").product(factory.tuple("7")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-8")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-7")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-6")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-5")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-4")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-3")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-2")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("-1")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("0")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("1")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("2")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("3")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("4")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("5")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("6")));
x9_upper.add(factory.tuple("Test$2").product(factory.tuple("7")));
bounds.bound(x9, x9_upper);
bounds.boundExactly(-8, factory.range(factory.tuple("-8"), factory.tuple("-8")));
bounds.boundExactly(-7, factory.range(factory.tuple("-7"), factory.tuple("-7")));
bounds.boundExactly(-6, factory.range(factory.tuple("-6"), factory.tuple("-6")));
bounds.boundExactly(-5, factory.range(factory.tuple("-5"), factory.tuple("-5")));
bounds.boundExactly(-4, factory.range(factory.tuple("-4"), factory.tuple("-4")));
bounds.boundExactly(-3, factory.range(factory.tuple("-3"), factory.tuple("-3")));
bounds.boundExactly(-2, factory.range(factory.tuple("-2"), factory.tuple("-2")));
bounds.boundExactly(-1, factory.range(factory.tuple("-1"), factory.tuple("-1")));
bounds.boundExactly(0, factory.range(factory.tuple("0"), factory.tuple("0")));
bounds.boundExactly(1, factory.range(factory.tuple("1"), factory.tuple("1")));
bounds.boundExactly(2, factory.range(factory.tuple("2"), factory.tuple("2")));
bounds.boundExactly(3, factory.range(factory.tuple("3"), factory.tuple("3")));
bounds.boundExactly(4, factory.range(factory.tuple("4"), factory.tuple("4")));
bounds.boundExactly(5, factory.range(factory.tuple("5"), factory.tuple("5")));
bounds.boundExactly(6, factory.range(factory.tuple("6"), factory.tuple("6")));
bounds.boundExactly(7, factory.range(factory.tuple("7"), factory.tuple("7")));
Variable x13 = Variable.unary("this");
Decls x12 = x13.oneOf(x6);
Expression x16 = x13.join(x7);
Formula x15 = x16.one();
Formula x17 = x16.in(Expression.INTS);
Formula x14 = x15.and(x17);
Formula x11 = x14.forAll(x12);
Expression x20 = x7.join(Expression.UNIV);
Formula x19 = x20.in(x6);
Variable x24 = Variable.unary("this");
Decls x23 = x24.oneOf(x6);
Expression x27 = x24.join(x8);
Formula x26 = x27.lone();
Formula x28 = x27.in(Expression.INTS);
Formula x25 = x26.and(x28);
Formula x22 = x25.forAll(x23);
Expression x30 = x8.join(Expression.UNIV);
Formula x29 = x30.in(x6);
Variable x33 = Variable.unary("this");
Decls x32 = x33.oneOf(x6);
Expression x36 = x33.join(x9);
Formula x35 = x36.one();
Formula x37 = x36.in(Expression.INTS);
Formula x34 = x35.and(x37);
Formula x31 = x34.forAll(x32);
Expression x39 = x9.join(Expression.UNIV);
Formula x38 = x39.in(x6);
Variable x42 = Variable.unary("this");
Decls x41 = x42.oneOf(x6);
Expression x44 = x42.join(x7);
Expression x48 = x42.join(x8);
IntExpression x47 = x48.sum();
Expression x50 = x42.join(x9);
IntExpression x49 = x50.sum();
IntExpression x46 = x47.plus(x49);
Expression x45 = x46.toExpression();
Formula x43 = x44.eq(x45);
Formula x40 = x43.forAll(x41);
Formula x51 = x0.eq(x0);
Formula x52 = x1.eq(x1);
Formula x53 = x2.eq(x2);
Formula x54 = x3.eq(x3);
Formula x55 = x4.eq(x4);
Formula x56 = x5.eq(x5);
Formula x57 = x6.eq(x6);
Formula x58 = x7.eq(x7);
Formula x59 = x8.eq(x8);
Formula x60 = x9.eq(x9);
IntExprReduction ier = new IntExprReduction();
Formula[] formulas =
ier.reduceIntExpressions(
x11, x19, x22, x29, x31, x38, x40, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60);
Formula newFormula = Formula.compose(FormulaOperator.AND, formulas);
ier.solve(newFormula, bounds, factory, universe, 32);
}
/**
* Create a {@link TupleSet} by specifying a range for each position of the tuple. See the
* documentation of this class.
*
* <p>Both parameters should have the same length, the arity of the relation.
*
* @return a {@link TupleSet}, never <code>null</code>
*/
public TupleSet createAllTuples(final Universe universe) {
final TupleFactory factory = universe.factory();
final Tuple lowerTuple = factory.tuple(lower);
final Tuple upperTuple = factory.tuple(upper);
return factory.area(lowerTuple, upperTuple);
}