The \(\kappa\)-word problem over \(\sf DRG\)

Let \(\kappa\) be the signature that naturally generalizes the usual signature on groups: it consists of the multiplication, and of the \((\omega-1)\)-power. We denote by \(\sf DRG\) the pseudovariety all finite semigroups whose regular \(\mathcal R\)-classes are groups. Below, you can test whether two \(\kappa\)-terms are equal over \(\sf DRG\).
The syntax is the following: multiplication of terms \(s\) and \(t\) is represented by "st", and the \((\omega-1)\)-power of a term \(t\) by "t^w-1". Thus if, for instance, one of the \(\kappa\)-terms you wish to test is \((a(b^{\omega-1}a)^{\omega-1})^{\omega-1}b\), you should insert "(a(b^w-1a)^w-1)^w-1b".