Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/baabbaab-aabbaabaabb.srs)

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 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  b#(a(a(b(b(a(a(b(x1))))))))	→	b#(b(a(a(x1))))	(3)
  b#(a(a(b(b(a(a(b(x1))))))))	→	b#(b(a(a(b(a(a(b(b(a(a(x1)))))))))))	(4)
  b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(x1)))	(5)
  b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(b(a(a(x1)))))))	(6)
  b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(a(a(b(b(a(a(x1))))))))))	(7)

  1.1.1.1 Reduction Pair Processor with Usable Rules

  Using the matrix interpretations of dimension 2 with strict dimension 1 over the arctic semiring over the naturals

  [b(x1)]	=	0 0 -2 -2 · x1 + -∞ -∞
  [a(x1)]	=	0 0 0 0 · x1 + -∞ -∞
  [b#(x1)]	=	14 16 14 16 · x1 + -∞ -∞

  together with the usable rule

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

  →

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

  (2)

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

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

  could be deleted.

  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(b(b(a(a(b(x1))))))))	→	b#(a(a(x1)))	(5)
    b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(b(a(a(x1)))))))	(6)
    b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(a(a(b(b(a(a(x1))))))))))	(7)

    1.1.1.1.1.1 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 0 -∞ -∞ -∞ 0 -∞ -∞ -∞ -∞ 0 -∞ -∞ -∞ 0 · x1 + 3 -∞ -∞ -∞
    [a(x1)]	=	-∞ -∞ -∞ -∞ 1 -∞ -∞ -∞ -∞ -∞ -∞ 0 -∞ 0 -∞ -∞ · x1 + 2 -∞ -∞ -∞
    [b#(x1)]	=	4 -∞ 3 -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ -∞ · x1 + 6 -∞ -∞ -∞

    together with the usable rule

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

    →

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

    (2)

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

    b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(x1)))	(5)
    b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(b(a(a(x1)))))))	(6)
    b#(a(a(b(b(a(a(b(x1))))))))	→	b#(a(a(b(a(a(b(b(a(a(x1))))))))))	(7)

    could be deleted.

    1.1.1.1.1.1.1 Dependency Graph Processor

    The dependency pairs are split into 0 components.