Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.20a)

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#(s(0))

  →

  g#(f(s(0)))

  (4)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	2
  [f(x1)]	=	1
  [0]	=	1
  [f#(x1)]	=	0
  [g#(x1)]	=	x1 + 0
  [g(x1)]	=	0

  together with the usable rules

  f(f(x))	→	f(x)	(1)
  f(s(x))	→	f(x)	(2)

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

  g#(s(0))

  →

  g#(f(s(0)))

  (4)

  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#(s(x))

  →

  f#(x)

  (6)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 2
  [f(x1)]	=	1
  [0]	=	1
  [f#(x1)]	=	x1 + 0
  [g#(x1)]	=	x1 + 0
  [g(x1)]	=	0

  together with the usable rules

  f(f(x))	→	f(x)	(1)
  f(s(x))	→	f(x)	(2)

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

  f#(s(x))

  →

  f#(x)

  (6)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.