code: def lr_op(left, right):
      """Perform a LR operation.
  
      A LR operation multiplies both left and right circuits
      with the dagger of the left circuit's rightmost gate, and
      the dagger is multiplied on the right side of both circuits.
  
      If a LR is possible, it returns the new gate rule as a
      2-tuple (LHS, RHS), where LHS is the left circuit and
      and RHS is the right circuit of the new rule.
      If a LR is not possible, None is returned.
  
      Parameters
      ==========
  
      left : Gate tuple
          The left circuit of a gate rule expression.
      right : Gate tuple
          The right circuit of a gate rule expression.
  
      Examples
      ========
  
      Generate a new gate rule using a LR operation:
  
      >>> from sympy.physics.quantum.identitysearch import lr_op
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> lr_op((x, y, z), ())
      ((X(0), Y(0)), (Z(0),))
  
      >>> lr_op((x, y), (z,))
      ((X(0),), (Z(0), Y(0)))
      """
  
      if len(left) > 0:
          lr_gate = left[len(left) - 1]
          lr_gate_is_unitary = is_scalar_matrix(
              (Dagger(lr_gate), lr_gate), _get_min_qubits(lr_gate), True
          )
  
      if len(left) > 0 and lr_gate_is_unitary:
          # Get the new left side w/o the rightmost gate
          new_left = left[0 : len(left) - 1]
          # Add the rightmost gate to the right position on the right side
          new_right = right + (Dagger(lr_gate),)
          # Return the new gate rule
          return (new_left, new_right)
  
      return None
  
imports: from collections import deque
  from sympy.core.random import randint
  from sympy.external import import_module
  from sympy.core.basic import Basic
  from sympy.core.mul import Mul
  from sympy.core.numbers import Number, equal_valued
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.physics.quantum.represent import represent
  from sympy.physics.quantum.dagger import Dagger
label_desc: Use image node_id 5 for calling a global function with example usage: lr_op(left, right) and returns: None, new_left,  new_right