Certification Problem

Input (TPDB SRS_Standard/Wenzel_16/babbabbaba-ababbabbabba.srs)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

1.1 Semantic Labeling

Root-labeling is applied.

1.1.1 Dependency Pair Transformation

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  ab#(ba(ab(bb(ba(ab(bb(ba(ab(bb(x1))))))))))	→	ab#(x1)	(13)
  ab#(ba(ab(bb(ba(ab(bb(ba(ab(bb(x1))))))))))	→	ab#(ba(ab(x1)))	(12)

  1.1.1.1.1 Reduction Pair Processor

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

  [ab#(x1)]	=	0 -∞ -∞ + -∞ 0 -∞ -∞ -∞ -∞ -∞ -∞ -∞ · x1
  [ba(x1)]	=	0 0 1 + 0 0 0 -∞ 0 -∞ 0 0 -∞ · x1
  [ab(x1)]	=	0 0 0 + 0 -∞ 0 0 -∞ -∞ 0 0 0 · x1
  [bb(x1)]	=	0 0 0 + -∞ 0 0 0 1 0 0 -∞ 0 · x1
  [aa(x1)]	=	-∞ -∞ -∞ + 0 -∞ 0 -∞ -∞ 0 0 -∞ 0 · x1

  the pair

  ab#(ba(ab(bb(ba(ab(bb(ba(ab(bb(x1))))))))))

  →

  ab#(x1)

  (13)

  could be deleted.

  1.1.1.1.1.1 Reduction Pair Processor

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

  [ab#(x1)]	=	-∞ -∞ -∞ + 0 0 0 -∞ -∞ -∞ -∞ -∞ -∞ · x1
  [ba(x1)]	=	0 0 0 + -∞ -∞ 0 -∞ 0 0 0 -∞ 0 · x1
  [ab(x1)]	=	0 0 0 + 0 0 0 -∞ 0 0 -∞ -∞ 0 · x1
  [bb(x1)]	=	0 0 0 + 1 0 0 0 0 0 0 0 -∞ · x1
  [aa(x1)]	=	0 0 0 + 0 -∞ -∞ -∞ -∞ -∞ 0 -∞ -∞ · x1

  the pair

  ab#(ba(ab(bb(ba(ab(bb(ba(ab(bb(x1))))))))))

  →

  ab#(ba(ab(x1)))

  (12)

  could be deleted.

  1.1.1.1.1.1.1 P is empty

  There are no pairs anymore.