Certification Problem

Input (TPDB SRS_Standard/Secret_06_SRS/multum5)

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

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

  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

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

  together with the usable rules

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

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

  b#(b(x1))

  →

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

  (6)

  could be deleted.

  1.1.1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 1 component.

  • The 1^st component contains the pair

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

    →

    b#(x1)

    (7)

    1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

    Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1

    [a(x1)]	=	x1 + 1
    [b#(x1)]	=	x1 + 0

    having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair

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

    →

    b#(x1)

    (7)

    and no rules could be deleted.

    1.1.1.1.1.1.1.1 Dependency Graph Processor

    The dependency pairs are split into 0 components.