sentences:  Refinement monoid
  
  In mathematics, a refinement monoid is a commutative monoid "M" such that for any elements "a0", "a1", "b0", "b1" of "M" such that "a0+a1=b0+b1", there are elements "c00", "c01", "c10", "c11" of "M" such that "a0=c00+c01", "a1=c10+c11", "b0=c00+c10", and "b1=c01+c11".A commutative monoid "M" is "conical", if "x"+"y"=0 implies that "x"="y"=0, for any elements "x","y" of "M".