Certification Problem

Input (TPDB TRS_Standard/AG01/#3.21)

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

  times#(x,plus(y,1))

  →

  times#(x,plus(y,times(1,0)))

  (5)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the argument filter
  in combination with the following Weighted Path Order with the following precedence and status

  prec(1)	=	3		status(1)	=	[]		list-extension(1)	=	Lex
  prec(plus#)	=	0		status(plus#)	=	[1, 2]		list-extension(plus#)	=	Lex
  prec(times#)	=	0		status(times#)	=	[2]		list-extension(times#)	=	Lex
  prec(0)	=	0		status(0)	=	[]		list-extension(0)	=	Lex
  prec(times)	=	2		status(times)	=	[2]		list-extension(times)	=	Lex
  prec(plus)	=	1		status(plus)	=	[2, 1]		list-extension(plus)	=	Lex

  and the following Max-polynomial interpretation

  [1]	=	8367
  [plus#(x1, x2)]	=	max(x1 + 1, x2 + 1, 0)
  [times#(x1, x2)]	=	x2 + 0
  [0]	=	0
  [times(x1, x2)]	=	x1 + x2 + 0
  [plus(x1, x2)]	=	max(x1 + 0, x2 + 8366, 0)

  together with the usable rules

  times(x,0)	→	0	(4)
  times(x,plus(y,1))	→	plus(times(x,plus(y,times(1,0))),x)	(1)
  plus(x,0)	→	x	(3)
  times(x,1)	→	x	(2)

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

  times#(x,plus(y,1))

  →

  times#(x,plus(y,times(1,0)))

  (5)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.