Let $M$ be an oracle TM and say that $M$ is shrinking if $M$ queries its oracle only on strings strictly shorter than M$\text{'}$s input.

Suppose that a language $A$ can be written as

$$

A$=\backslash$left$\backslash \{$x $\backslash$mid M$^\{$A$\}($x$)=1\backslash$right$\backslash \}$

$$

where $M$ is a polytime and shrinking oracle TM$.$

This is an odd situation, where the algorithm has an oracle for the problem it is trying to solve! However, on input $x$$,$ that algorithm is not allowed to ask its oracle whether $x$ is in the language $($it can only ask about strictly shorter strings$).$

Prove that such a language $A$ is in PSPACE.