Certification Problem

Input (TPDB TRS_Standard/AotoYamada_05/006)

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(mapbt,f),app(app(app(branch,x),l),r))	→	app#(f,x)	(10)
  app#(app(mapbt,f),app(leaf,x))	→	app#(f,x)	(9)
  app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),r)	(4)
  app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),l)	(6)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [mapbt]	=	1
  [app#(x1, x2)]	=	x1 + 0
  [branch]	=	1
  [leaf]	=	1
  [app(x1, x2)]	=	x2 + 1

  together with the usable rules

  app(app(mapbt,f),app(leaf,x))	→	app(leaf,app(f,x))	(1)
  app(app(mapbt,f),app(app(app(branch,x),l),r))	→	app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))	(2)

  (w.r.t. the implicit argument filter of the reduction pair), the pairs

  app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(f,x)	(10)
  app#(app(mapbt,f),app(leaf,x))	→	app#(f,x)	(9)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 1 component.

  • The 1^st component contains the pair

    app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),r)	(4)
    app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),l)	(6)

    1.1.1.1.1 Reduction Pair Processor with Usable Rules

    Using the Max-polynomial interpretation

    [mapbt]	=	0
    [app#(x1, x2)]	=	x2 + 0
    [branch]	=	0
    [leaf]	=	0
    [app(x1, x2)]	=	x1 + x2 + 7758

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

    app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),r)	(4)
    app#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app#(app(mapbt,f),l)	(6)

    could be deleted.

    1.1.1.1.1.1 Dependency Graph Processor

    The dependency pairs are split into 0 components.