Let $$ be an oracle TM and say that $$ is shrinking if $$ queries its oracle only on strings strictly shorter

than $$s input.

Suppose that a language $$ can be written as

$=$ f$$ j $=1$g$$

where $$ 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 $,$ that algorithm is not allowed to ask its oracle whether $$ is in the language $($it can only ask

about strictly shorter strings$).$

Prove that such a language $$ is in PSPACE