Certification Problem

Input (TPDB SRS_Standard/Trafo_06/un10)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by AProVE @ 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#(b(b(b(a(b(b(a(b(b(x1))))))))))	→	b#(b(b(b(x1))))	(9)
  b#(b(b(b(a(b(b(a(b(b(x1))))))))))	→	b#(b(b(b(b(x1)))))	(8)
  b#(b(b(b(a(b(b(a(b(b(x1))))))))))	→	b#(b(b(x1)))	(10)

  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

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

  the pair

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

  →

  b#(b(b(x1)))

  (10)

  could be deleted.

  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

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

  the pair

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

  →

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

  (8)

  could be deleted.

  1.1.1.1.1.1 Reduction Pair Processor

  Using the linear polynomial interpretation over the rationals with delta = 48

  [b#(x1)]	=	0 + 1 · x1
  [b(x1)]	=	4 + 2 · x1
  [a(x1)]	=	0 + 1/4 · x1

  the pair

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

  →

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

  (9)

  could be deleted.

  1.1.1.1.1.1.1 P is empty

  There are no pairs anymore.