Certification Problem

Input (TPDB SRS_Standard/Waldmann_07_size11/size-11-alpha-2-num-2)

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(a(x1))))	→	a#(b(b(x1)))	(3)
  a#(b(b(a(x1))))	→	a#(b(a(b(b(x1)))))	(4)
  a#(b(b(a(x1))))	→	a#(a(b(a(b(b(x1))))))	(5)

  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)]	=	-∞ -∞ 1 0 -∞ -∞ -∞ -∞ -∞ · x1 + 1 -∞ -∞
  [a(x1)]	=	0 0 -∞ -∞ 0 0 -∞ 0 1 · x1 + -∞ 2 2
  [a#(x1)]	=	3 8 -∞ -∞ -∞ -∞ -∞ -∞ -∞ · x1 + 10 -∞ -∞

  together with the usable rules

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

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

  a#(b(b(a(x1))))	→	a#(b(b(x1)))	(3)
  a#(b(b(a(x1))))	→	a#(b(a(b(b(x1)))))	(4)
  a#(b(b(a(x1))))	→	a#(a(b(a(b(b(x1))))))	(5)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.