REMIS: Termination of Term Rewrite System

Termination of Term Rewrite System. Originally by Lankford 1979, Huet, and Oppen 1980.

Description of the problem on p.325: This problem decides whether we should orient the equation $(xy)^{-1}=y^{-1}x^{-1}$ into $(xy)^{-1} \to y^{-1}x^{-1}$ in order to get a terminating rewrite system for group theory. It uses a polynomial interpretation: $xy \Rightarrow x+2xy$, $x^{-1} \Rightarrow x^2$, and $1 \Rightarrow 2$.

load redlog$
rlset ofsf$

ter := ex(r,all({x,y},x>r and y>r impl x**2*(1+2*y)**2>y**2*(1+2*x**2)));

rlqe ter;

end;  % of file