Certification Problem

Input (TPDB TRS_Standard/SK90/4.13)

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

  -#(x,s(y))

  →

  -#(x,p(s(y)))

  (7)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the argument filter

  π(-#)

  =

  2

  in combination with the following Weighted Path Order with the following precedence and status

  prec(s)	=	0		status(s)	=	[1]		list-extension(s)	=	Lex
  prec(greater)	=	0		status(greater)	=	[1, 2]		list-extension(greater)	=	Lex
  prec(p#)	=	0		status(p#)	=	[]		list-extension(p#)	=	Lex
  prec(p)	=	0		status(p)	=	[]		list-extension(p)	=	Lex
  prec(0)	=	0		status(0)	=	[]		list-extension(0)	=	Lex
  prec(if)	=	0		status(if)	=	[]		list-extension(if)	=	Lex
  prec(-)	=	0		status(-)	=	[1, 2]		list-extension(-)	=	Lex

  and the following Max-polynomial interpretation

  [s(x1)]	=	x1 + 11293
  [greater(x1, x2)]	=	x1 + x2 + 1
  [p#(x1)]	=	1
  [p(x1)]	=	x1 + 0
  [0]	=	0
  [if(x1, x2, x3)]	=	x1 + 1
  [-(x1, x2)]	=	x1 + x2 + 1

  together with the usable rules

  p(0)	→	0	(4)
  p(s(x))	→	x	(5)

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

  -#(x,s(y))

  →

  -#(x,p(s(y)))

  (7)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.