Certification Problem

Input (TPDB TRS_Standard/SK90/4.51)

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

  h#(g(x))

  →

  h#(f(x))

  (7)

  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(h)	=	2		status(h)	=	[]		list-extension(h)	=	Lex
  prec(a)	=	0		status(a)	=	[]		list-extension(a)	=	Lex
  prec(k)	=	0		status(k)	=	[1, 2, 3]		list-extension(k)	=	Lex
  prec(f)	=	1		status(f)	=	[]		list-extension(f)	=	Lex
  prec(h#)	=	0		status(h#)	=	[1]		list-extension(h#)	=	Lex
  prec(k#)	=	0		status(k#)	=	[]		list-extension(k#)	=	Lex
  prec(f#)	=	0		status(f#)	=	[]		list-extension(f#)	=	Lex
  prec(g)	=	2		status(g)	=	[]		list-extension(g)	=	Lex

  and the following Max-polynomial interpretation

  [h(x1)]	=	11798
  [a]	=	11799
  [k(x1, x2, x3)]	=	x1 + x2 + x3 + 1
  [f(x1)]	=	x1 + 0
  [h#(x1)]	=	x1 + 1
  [k#(x1, x2, x3)]	=	x1 + 1
  [f#(x1)]	=	1
  [g(x1)]	=	x1 + 0

  together with the usable rules

  f(a)	→	g(h(a))	(1)
  h(g(x))	→	g(h(f(x)))	(2)

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

  h#(g(x))

  →

  h#(f(x))

  (7)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.