Certification Problem

Input (TPDB TRS_Standard/AProVE_04/improved_usable)

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

  f#(a,h(x))

  →

  f#(g(x),h(x))

  (6)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [h(x1)]	=	x1 + 1
  [a]	=	28959
  [f(x1, x2)]	=	0
  [h#(x1)]	=	0
  [f#(x1, x2)]	=	x1 + 0
  [g#(x1)]	=	0
  [g(x1)]	=	28958

  together with the usable rule

  g(h(x))

  →

  g(x)

  (3)

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

  f#(a,h(x))

  →

  f#(g(x),h(x))

  (6)

  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

  g#(h(x))

  →

  g#(x)

  (5)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [h(x1)]	=	x1 + 1
  [a]	=	28959
  [f(x1, x2)]	=	0
  [h#(x1)]	=	0
  [f#(x1, x2)]	=	x1 + 0
  [g#(x1)]	=	x1 + 0
  [g(x1)]	=	8856

  together with the usable rule

  g(h(x))

  →

  g(x)

  (3)

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

  g#(h(x))

  →

  g#(x)

  (5)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.