% 4.  A group where all commutators lie in the center satisfies the
% equation h(x,y*z) = h(x,y)*h(x,z). This example illustrates the
% lex command and the pick_given_ratio parameter.
%
% Contributed by John Kalman (kalman@math.auckland.ac.nz)

  set(knuth_bendix).
  clear(print_kept).  clear(print_new_demod). 
  clear(print_back_demod).  clear(print_back_sub).
  op(350,xf,^).
  assign(pick_given_ratio,8).
  assign(stats_level,1).
  lex([a,b,c,e,_^ ,h(_,_),_*_]).

  list(usable).
    x=x.
    (x*y)*z=x*y*z.
    e*x=x.
    x^ *x=e.
  end_of_list.

  list(sos).
    h(x,y)= x*y*x^ *y^.
    h(x,y)*z = z*h(x,y).
    h(a,b*c)!=h(a,b)*h(a,c).
  end_of_list.