Certification Problem

Input (TPDB TRS_Standard/AG01/#3.37)

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

  evenodd#(s(x),s(0))	→	evenodd#(x,0)	(8)
  evenodd#(x,0)	→	evenodd#(x,s(0))	(7)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 1
  [evenodd#(x1, x2)]	=	x1 + 0
  [false]	=	0
  [true]	=	0
  [not#(x1)]	=	0
  [0]	=	28958
  [evenodd(x1, x2)]	=	0
  [not(x1)]	=	0

  having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair

  evenodd#(s(x),s(0))

  →

  evenodd#(x,0)

  (8)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.