class_docstr: Properties
  ==========
  
  [1] `0 \in \Omega` and `\tau(1) = \epsilon`
  [2] `\alpha^x = \beta \Leftrightarrow \beta^{x^{-1}} = \alpha`
  [3] If `\alpha^x = \beta`, then `H \tau(\alpha)x = H \tau(\beta)`
  [4] `\forall \alpha \in \Omega, 1^{\tau(\alpha)} = \alpha`
  
  References
  ==========
  
  .. [1] Holt, D., Eick, B., O'Brien, E.
         "Handbook of Computational Group Theory"
  
  .. [2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson
         Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490.
         "Implementation and Analysis of the Todd-Coxeter Algorithm"
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docstr: 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
docstr_tok: ["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"]
code: def process_deductions(self, R_c_x, R_c_x_inv):
      """
      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
  
      """
      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[:]
              continue
          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
  
imports: from sympy.combinatorics.free_groups import free_group
  from sympy.printing.defaults import DefaultPrinting
  from itertools import chain, product
  from bisect import bisect_left
label_desc: Use image node_id 19 for calling the CosetTable obj's underlying member method code with example usage: obj.process_deductions(R_c_x, R_c_x_inv) without return types