This category is concerned with confluence of higher-order rewrite systems.
The input is a higher-order rewrite system, specified in the HRS format.
The question to be answered is whether the higher-order rewrite system is confluent. The first line of the output must be
YES, indicating that the input system is confluent,
NO, indicating that the input system is non-confluent,
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.
(FUN abs : (term -> term) -> term app : term -> term -> term ) (VAR x : term S : term F : term -> term ) (RULES app(abs(\x.F x),S) -> F(S), abs(\x.app(S,x)) -> S )The correct answer is
YESand a possible output is
YES The HRS is weakly orthogonal.
(FUN f : o -> o -> o s : o -> o a : o b : o mu : (o -> o) -> o ) (VAR x : o Z : o -> o ) (RULES f x x -> a, f x (s x) -> b, mu (\x. Z x) -> Z (mu (\x. Z x)) )The correct answer is
NOand a possible output is
Problems are selected among those in HRS format in COPS.