Certification Problem

Input (TPDB TRS_Standard/SK90/2.35)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  implies#(not(x),not(y))

  →

  implies#(y,and(x,y))

  (9)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [and(x1, x2)]	=	x1 + 17711
  [false]	=	17711
  [not#(x1)]	=	0
  [implies#(x1, x2)]	=	x1 + x2 + 0
  [implies(x1, x2)]	=	0
  [and#(x1, x2)]	=	0
  [not(x1)]	=	x1 + 8856

  together with the usable rules

  and(x,false)	→	false	(1)
  and(x,not(false))	→	x	(2)

  (w.r.t. the implicit argument filter of the reduction pair), the pair

  implies#(not(x),not(y))

  →

  implies#(y,and(x,y))

  (9)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.