Does a subtype "inherit" the common interface parameterized by this particular subtype (Java)?

Question

I have

class Shape implements Comparable <Shape>

and

class Square extends Shape

I wrote a general method for finding the maximum element inside an array:

public static <S extends Comparable<S>> S findMax(S[] arr)
{
    //blablabla...
    return maxS;
}

These two calls do not give me any errors and do what they should:

Shape maxShape = findMax(new Shape[]{new Shape(1), new Shape(2), new Shape(3)});
Square maxSquare = findMax(new Square[]{new Square(1), new Square(2), new Square(3)});

Therefore, it seems reasonable that, as Shapeimplements Comparable<Shape>and Squarethe extends Shape, Squaremust also be comparable, aka Squaresomehow automatically implements Comparable<Square>through inheritance (in particular, inheriting compareTo(Shape s)).

However, according to my textbook, it is not so here, "all we know is Square implements Comparable<Shape>, therefore, Squarethe IS-A Comparable<Shape>, but-the NOT-the IS A Comparable<Square>", and instead it offers a better method signature:
public static <S extends Comparable<? super S>>.

public static <S extends Comparable<S>> ?

----------------------------- UPDATE (SOURCE CODE) ------------- -----------------

public class Shape implements Comparable<Shape>{
    protected int area;
    public Shape (int i)
    {
        this.area=i;
    }

    public String toString()
    {
        return area+"";
    }

    public static void main(String[] args)
    {

        System.out.println("Bigger shape: "+findMax(new Shape[] {new Shape(2),new Shape(3)}));
        System.out.println("Bigger square: "+findMax(new Square[] {new Square(2),new Square(3)}));

    }

    public int getValue()
    {
        return area;
    }

    @Override
    public int compareTo(Shape sh) {
        return Integer.valueOf(area).compareTo(sh.getValue());
    }

    public static <N extends Comparable<N>> N findMax(N[] arr)
    {
        int maxIdx=0;
        for (int i=1; i<arr.length; i++)
            if (arr[i].compareTo(arr[maxIdx])>0)
                maxIdx=i;
        return arr[maxIdx];
    }

}

class Square extends Shape
{
    public Square(int i)
    {
        super(i);
    }

    public int compareTo(Shape sh)
    {
        return Integer.valueOf(area%3).compareTo(sh.getValue()%3);
    }
}

Bigger shape: 3
Bigger square: 2

: - . , findMax Square[] - Shape[].

Answer 1

. Javac 1.7:

> "C:\Program Files\Java\jdk1.7.0_80\bin\javac.exe" GenericTest.java
GenericTest.java:32: error: method findMax in class GenericTest cannot be applied to given types;
                Square maxSquare = findMax(new Square[]{new Square(1), new Square(2), new Square(3)});
                                   ^
  required: S[]
  found: Square[]
  reason: inferred type does not conform to declared bound(s)
    inferred: Square
    bound(s): Comparable<Square>
  where S is a type-variable:
    S extends Comparable<S> declared in method <S>findMax(S[])
1 error

Javac 1.8:

>"C:\Program Files\Java\jdk1.8.0_40\bin\javac.exe" GenericTest.java
GenericTest.java:32: error: incompatible types: inference variable S has incompatible bounds
                Square maxSquare = findMax(new Square[]{new Square(1), new Square(2), new Square(3)});
                                          ^
    equality constraints: Shape
    upper bounds: Square,Comparable<S>
  where S is a type-variable:
    S extends Comparable<S> declared in method <S>findMax(S[])
1 error

ECJ 3.10.2:

>java -jar org.eclipse.jdt.core_3.10.2.v20150120-1634.jar -source 1.7 GenericTest.java
----------
1. ERROR in C:\projects\Test\src\GenericTest.java (at line 32)
        Square maxSquare = findMax(new Square[]{new Square(1), new Square(2), new Square(3)});
                           ^^^^^^^
Bound mismatch: The generic method findMax(S[]) of type GenericTest is not applicable for the arguments (GenericTest.Square[]). 
The inferred type GenericTest.Square is not a valid substitute for the bounded parameter <S extends Comparable<S>>
----------
1 problem (1 error)

, . findMax public static <S extends Comparable<? super S>> S findMax(S[] arr), .

, , . , findMax :

System.out.println("Bigger shape: "+findMax(new Shape[] {new Shape(1),new Shape(3)}));
System.out.println("Bigger square: "+findMax(new Square[] {new Square(3),new Square(2)}));

, <S> Shape Square[] IS-A Shape[].