Certification Problem

Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.37)

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#(c(x,s(y)))

  →

  g#(c(s(x),y))

  (4)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 1
  [c(x1, x2)]	=	x2 + 28958
  [f(x1)]	=	0
  [f#(x1)]	=	0
  [g#(x1)]	=	x1 + 0
  [g(x1)]	=	0

  having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair

  g#(c(x,s(y)))

  →

  g#(c(s(x),y))

  (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#(c(s(x),y))

  →

  f#(c(x,s(y)))

  (3)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 1
  [c(x1, x2)]	=	x1 + 40651
  [f(x1)]	=	0
  [f#(x1)]	=	x1 + 0
  [g#(x1)]	=	0
  [g(x1)]	=	0

  having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair

  f#(c(s(x),y))

  →

  f#(c(x,s(y)))

  (3)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.