Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/motivation)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by AProVE @ 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

  g#(g(x))

  →

  g#(h(g(x)))

  (4)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Knuth Bendix order with w0 = 1 and the following precedence and weight functions

  prec(g)	=	1		weight(g)	=	2
  prec(h)	=	0		weight(h)	=	1

  in combination with the following argument filter

  π(g#)	=	1
  π(g)	=	[]
  π(h)	=	[]

  together with the usable rule

  h(h(x))

  →

  h(f(h(x),x))

  (3)

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

  g#(g(x))

  →

  g#(h(g(x)))

  (4)

  could be deleted.

  1.1.1.1 P is empty

  There are no pairs anymore.