Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/aabaababaab-aababaababaaba.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#(a(b(a(a(b(a(b(a(a(b(x1)))))))))))	→	a#(x1)	(2)
  a#(a(b(a(a(b(a(b(a(a(b(x1)))))))))))	→	a#(a(b(a(x1))))	(8)

  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)]	=	0 0 4 4 0 0 0 0 0 0 0 0 -4 0 0 0 · x1 + -∞ -∞ -∞ -∞
  [a(x1)]	=	0 0 0 0 -4 -4 0 0 -4 -4 -4 0 -4 -4 -4 0 · x1 + -∞ -∞ -∞ -∞
  [a#(x1)]	=	11 13 13 14 11 13 13 14 11 13 13 14 11 13 13 14 · x1 + -∞ -∞ -∞ -∞

  together with the usable rule

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

  →

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

  (1)

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

  a#(a(b(a(a(b(a(b(a(a(b(x1)))))))))))	→	a#(x1)	(2)
  a#(a(b(a(a(b(a(b(a(a(b(x1)))))))))))	→	a#(a(b(a(x1))))	(8)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.