I was reading the paper Mechanized Metatheory for the Masses: the PoplMark Challenge by Aydemir et al (PDF) and I found the following three questions on page 13 of the PDF a bit confusing.
Challenge 3: Testing and Animating with respect to semantics.
Given $\mathrm{F}_{\texttt{<:}}$ terms $t$ and $t'$, decide whether $t\rightarrow t'$.
Given $\mathrm{F}_{\texttt{<:}}$ terms $t$ and $t'$, decide whether $t \rightarrow^* t' \not\rightarrow$, where $\rightarrow^*$ is the reflexive-transitive closure of $\rightarrow$.
Given an $\mathrm{F}_{\texttt{<:}}$ term $t$, find a term $t'$ such that $t\rightarrow t'$.
I think question (3) is saying reduce a term $t$ to $t'$ until which is no longer can be reduced (or become a value). What about question (1), are they just saying check the result if it is equal to some term $t'$? and question (2).
Could someone explain me their differences?