Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/abababbabab-ababbabababba.srs)

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(a(b(a(b(b(a(b(a(b(x1)))))))))))	→	a#(x1)	(2)
  a#(b(a(b(a(b(b(a(b(a(b(x1)))))))))))	→	a#(b(a(b(a(b(b(a(x1))))))))	(7)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the matrix interpretations of dimension 4 with strict dimension 1 over the arctic semiring over the naturals

  [b(x1)]	=	-∞ -∞ -∞ 1 0 -∞ 1 -∞ 0 -∞ -∞ -∞ -∞ 0 -∞ -∞ · x1 + 0 -∞ -∞ -∞
  [a(x1)]	=	-∞ -∞ 0 -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ 0 -∞ 0 -∞ -∞ · x1 + 0 -∞ -∞ -∞
  [a#(x1)]	=	-∞ 4 -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ · x1 + 4 -∞ -∞ -∞

  together with the usable rule

  a(b(a(b(a(b(b(a(b(a(b(x1)))))))))))

  →

  a(b(a(b(b(a(b(a(b(a(b(b(a(x1)))))))))))))

  (1)

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

  a#(b(a(b(a(b(b(a(b(a(b(x1)))))))))))	→	a#(x1)	(2)
  a#(b(a(b(a(b(b(a(b(a(b(x1)))))))))))	→	a#(b(a(b(a(b(b(a(x1))))))))	(7)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.