Certification Problem

Input (TPDB TRS_Standard/Applicative_05/Ex6_11)

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

  app#(app(F,app(app(F,f),x)),x)

  →

  app#(f,x)

  (5)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [G]	=	0
  [F]	=	23676
  [app#(x1, x2)]	=	x1 + x2 + 0
  [app(x1, x2)]	=	x1 + x2 + 0

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

  app#(app(F,app(app(F,f),x)),x)

  →

  app#(f,x)

  (5)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.