Certification Problem

Input (TPDB SRS_Standard/Secret_06_SRS/9)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by matchbox @ 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

  a#(b(b(x1)))	→	a#(x1)	(3)
  a#(b(b(x1)))	→	a#(a(x1))	(4)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the matrix interpretations of dimension 2 with strict dimension 1 over the arctic semiring over the naturals

  [b(x1)]	=	-∞ 0 1 -∞ · x1 + 0 -∞
  [a(x1)]	=	0 1 -∞ 0 · x1 + 1 -∞
  [a#(x1)]	=	-∞ 22 -∞ -∞ · x1 + 12 -∞

  together with the usable rules

  a(b(a(x1)))	→	b(b(b(b(x1))))	(1)
  a(b(b(x1)))	→	b(b(a(a(x1))))	(2)

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

  a#(b(b(x1)))	→	a#(x1)	(3)
  a#(b(b(x1)))	→	a#(a(x1))	(4)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.