The UNR category is concerned with the "unique normal forms with respect to reduction" property (UNR) of first-order rewrite systems.
The question to be answered is whether the rewrite system has the property that no term rewrites to different normal forms. The first line of the output must be
YES, indicating that the input system is UNR,
NO, indicating that the input system is not UNR,
any other answer (e.g.,
MAYBE) indicates that the tool could not determine the status of the input problem.
In the first two cases, the output must be followed by justification that is understandable by a human expert.
(RULES a -> h(f(a),c) a -> f(c) )The correct answer is
NOand a possible output is
NO The term a rewrites to different normal forms f(c) and h(f(f(c)),c).
(VAR x) (RULES f(a,a) -> g(f(a,a)) a -> b f(b,x) -> g(f(x,x)) f(x,b) -> g(f(x,x)) )The correct answer is
YESand a possible output is
YES The TRS is left-linear and its critical pairs are development closed, and hence it is confluent and thus also UNR.