Certification Problem

Input (TPDB TRS_Standard/Applicative_05/Ex4MapList)

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(fmap,app(app(fcons,f),t)),x)	→	app#(app(fmap,t),x)	(4)
  app#(app(fmap,app(app(fcons,f),t)),x)	→	app#(f,x)	(5)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the

  prec(app#)	=	0		stat(app#)	=	lex
  prec(fcons)	=	0		stat(fcons)	=	lex
  prec(app)	=	1		stat(app)	=	lex
  prec(fmap)	=	0		stat(fmap)	=	lex

  π(app#)	=	1
  π(fcons)	=	[]
  π(app)	=	[1,2]
  π(fmap)	=	[]

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

  app#(app(fmap,app(app(fcons,f),t)),x)	→	app#(app(fmap,t),x)	(4)
  app#(app(fmap,app(app(fcons,f),t)),x)	→	app#(f,x)	(5)

  could be deleted.

  1.1.1.1 P is empty

  There are no pairs anymore.