Certification Problem

Input (TPDB TRS_Standard/Various_04/15)

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

  f#(s(x))

  →

  f#(p(s(x)))

  (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(s)	=	1		status(s)	=	[]		list-extension(s)	=	Lex
  prec(p#)	=	0		status(p#)	=	[]		list-extension(p#)	=	Lex
  prec(f)	=	0		status(f)	=	[]		list-extension(f)	=	Lex
  prec(p)	=	0		status(p)	=	[]		list-extension(p)	=	Lex
  prec(0)	=	0		status(0)	=	[]		list-extension(0)	=	Lex
  prec(f#)	=	0		status(f#)	=	[1]		list-extension(f#)	=	Lex

  and the following Max-polynomial interpretation

  [s(x1)]	=	x1 + 21239
  [p#(x1)]	=	1
  [f(x1)]	=	1
  [p(x1)]	=	x1 + 0
  [0]	=	0
  [f#(x1)]	=	x1 + 1

  together with the usable rule

  p(s(x))

  →

  x

  (3)

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

  f#(s(x))

  →

  f#(p(s(x)))

  (5)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.