code: def cp_cmp(c, d):
      """
      Compare two critical pairs c and d.
  
      c < d iff
          - lbp(c[0], _, Num(c[2]) < lbp(d[0], _, Num(d[2])) (this
          corresponds to um_c * f_c and um_d * f_d)
      or
          - lbp(c[0], _, Num(c[2]) >< lbp(d[0], _, Num(d[2])) and
          lbp(c[3], _, Num(c[5])) < lbp(d[3], _, Num(d[5])) (this
          corresponds to vm_c * g_c and vm_d * g_d)
  
      c > d otherwise
      """
      zero = Polyn(c[2]).ring.zero
  
      c0 = lbp(c[0], zero, Num(c[2]))
      d0 = lbp(d[0], zero, Num(d[2]))
  
      r = lbp_cmp(c0, d0)
  
      if r == -1:
          return -1
      if r == 0:
          c1 = lbp(c[3], zero, Num(c[5]))
          d1 = lbp(d[3], zero, Num(d[5]))
  
          r = lbp_cmp(c1, d1)
  
          if r == -1:
              return -1
          # if r == 0:
          #    return 0
      return 1
  
imports: from sympy.core.symbol import Dummy
  from sympy.polys.monomials import monomial_mul, monomial_lcm, monomial_divides, term_div
  from sympy.polys.orderings import lex
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.polyconfig import query
label_desc: Use image node_id 17 for calling a global function with example usage: cp_cmp(c, d) and returns: int, unknown, unknown