'Processes the deductions that have been pushed onto ``deduction_stack``,
described on Pg. 166 [1] and is used in coset-table based enumeration.
See Also
deduction_stack'

def process_deductions(self, R_c_x, R_c_x_inv):

    p = self.p
    table = self.table
    while (len(self.deduction_stack) > 0):
        if (len(self.deduction_stack) >= CosetTable.max_stack_size):
            self.look_ahead()
            del self.deduction_stack[:]
        else:
            (alpha, x) = self.deduction_stack.pop()
            if (p[alpha] == alpha):
                for w in R_c_x:
                    self.scan_c(alpha, w)
                    if (p[alpha] < alpha):
                        break
        beta = table[alpha][self.A_dict[x]]
        if ((beta is not None) and (p[beta] == beta)):
            for w in R_c_x_inv:
                self.scan_c(beta, w)
                if (p[beta] < beta):
                    break
