Certification Problem

Input (TPDB SRS_Standard/Zantema_06/beans6)

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 Monotonic Reduction Pair Processor with Usable Rules

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  a#(a(x1))

  →

  a#(b(a(x1)))

  (25)

  1.1.1.1.1 Reduction Pair Processor with Usable Rules

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

  [d(x1)]	=	3 2 2 2 3 0 1 2 0 · x1 + 2 -∞ -∞
  [c(x1)]	=	0 0 2 2 3 4 1 2 3 · x1 + -∞ 6 4
  [b(x1)]	=	-∞ 0 0 -∞ -∞ 0 0 -∞ -∞ · x1 + 0 -∞ -∞
  [a(x1)]	=	-∞ 1 -∞ 2 3 1 -∞ 2 0 · x1 + 1 3 -∞
  [a#(x1)]	=	0 8 -∞ -∞ -∞ -∞ -∞ -∞ -∞ · x1 + -∞ -∞ -∞

  together with the usable rules

  a(a(b(x1)))	→	c(b(a(x1)))	(8)
  a(c(x1))	→	c(a(x1))	(9)
  b(c(x1))	→	a(b(x1))	(10)
  b(a(a(x1)))	→	a(b(d(x1)))	(11)
  d(a(x1))	→	a(d(x1))	(12)
  d(b(x1))	→	b(a(x1))	(13)
  a(a(x1))	→	a(b(a(x1)))	(7)

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

  a#(a(x1))

  →

  a#(b(a(x1)))

  (25)

  could be deleted.

  1.1.1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.