  Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{T}_{n}$ be the
semigroup of full transformations on $[n]$. Let $\mathcal{CT}_{n}=\{\alpha\in
\mathcal{T}_{n}: (for ~all~x,y\in
[n])~\left|x\alpha-y\alpha\right|\leq\left|x-y\right|\}$, then
$\mathcal{CT}_{n}$ is a subsemigroup of $\mathcal{T}_{n}$. In this paper, we
give a necessary and sufficient condition for an element to be regular and
characterize all the Green's equivalences for the semigroup $\mathcal{CT}_{n}$.
We further show that the semigroup $\mathcal{CT}_{n}$ is a left abundant
semigroup.
