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 ttt2 @ 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)

  (2)

  1.1.1 Size-Change Termination

  Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.

  app#(app(F,app(app(F,f),x)),x)	→	app#(f,x)	(2)
  2	≥	2
  1	>	2
  1	>	1

  As there is no critical graph in the transitive closure, there are no infinite chains.