Certification Problem

Input (TPDB TRS_Standard/SK90/4.44)

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 2 components.

• The 1^st component contains the pair

  g#(i(x))

  →

  g#(h(x))

  (7)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [h(x1)]	=	x1 + 1
  [a]	=	28958
  [b]	=	0
  [f(x1)]	=	0
  [h#(x1)]	=	0
  [f#(x1)]	=	0
  [g#(x1)]	=	x1 + 0
  [i(x1)]	=	x1 + 2
  [g(x1)]	=	0
  [i#(x1)]	=	0

  together with the usable rule

  h(a)

  →

  b

  (3)

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

  g#(i(x))

  →

  g#(h(x))

  (7)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.

• The 2^nd component contains the pair

  f#(h(x))

  →

  f#(i(x))

  (6)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [h(x1)]	=	x1 + 40652
  [a]	=	1
  [b]	=	0
  [f(x1)]	=	0
  [h#(x1)]	=	0
  [f#(x1)]	=	x1 + 0
  [g#(x1)]	=	x1 + 0
  [i(x1)]	=	x1 + 40651
  [g(x1)]	=	0
  [i#(x1)]	=	0

  together with the usable rules

  i(a)	→	b	(4)
  h(a)	→	b	(3)

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

  f#(h(x))

  →

  f#(i(x))

  (6)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.