Certification Problem

Input (TPDB SRS_Standard/Mixed_SRS/09)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by matchbox @ termCOMP 2023)

1 String Reversal

1.1 Dependency Pair Transformation

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  a#(b(b(b(x1))))	→	a#(x1)	(5)
  a#(b(b(b(x1))))	→	a#(a(x1))	(6)
  a#(b(b(b(x1))))	→	a#(a(a(x1)))	(7)
  a#(b(a(x1)))	→	a#(b(b(b(x1))))	(8)

  1.1.1.1 Reduction Pair Processor with Usable Rules

  Using the matrix interpretations of dimension 3 with strict dimension 1 over the arctic semiring over the naturals

  [b(x1)]	=	0 0 3 0 0 0 -3 0 0 · x1 + -∞ -∞ -∞
  [a(x1)]	=	0 0 0 0 0 0 0 0 0 · x1 + -∞ -∞ -∞
  [a#(x1)]	=	5 5 5 5 5 5 5 5 5 · x1 + -∞ -∞ -∞

  together with the usable rules

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

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

  a#(b(b(b(x1))))	→	a#(x1)	(5)
  a#(b(b(b(x1))))	→	a#(a(x1))	(6)
  a#(b(b(b(x1))))	→	a#(a(a(x1)))	(7)

  could be deleted.

  1.1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.