NFP Category

The NFP category is concerned with the normal form property (NFP) of first-order rewrite systems.

Format

The input is a first-order rewrite system without conditions, specified in the basic TRS format or the extended TRS format.

The question to be answered is whether the rewrite system has the property that every term which convertible to a normal form rewrites to that normal form. The first line of the output must be

• YES, indicating that the input system is NFP,
• NO, indicating that the input system is not NFP,
• 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.

Examples

1. (VAR x)
   (RULES
     F(x,x) -> A
     G(x) -> F(x,G(x))
     C -> G(C)
   )
   

   The correct answer is NO and a possible output is

   NO
   
   The term G(A) and the normal form A are convertible, but G(A) does not
   rewrite to A.
   

2. (RULES
     a -> b
     a -> c
     b -> b
     c -> c
   )
   

   The correct answer is YES and a possible output is

   YES
   
   There are no non-variable normal forms. Since the rules are non-collapsing,
   NFP holds trivially.
   

Problem Selection

Problems are selected among those in COPS with the 'trs' tag. Problems that were shown confluent by at least one participating tool in the CoCo 2022 full run are not considered.