Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/PEANO_nosorts_FR)

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

  plus#(N,s(M))

  →

  plus#(N,M)

  (6)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 1
  [activate(x1)]	=	0
  [and(x1, x2)]	=	0
  [plus#(x1, x2)]	=	x2 + 0
  [activate#(x1)]	=	0
  [0]	=	0
  [plus(x1, x2)]	=	0
  [tt]	=	0
  [and#(x1, x2)]	=	0

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

  plus#(N,s(M))

  →

  plus#(N,M)

  (6)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.