Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z043)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by matchbox @ termCOMP 2023)

1 Dependency Pair Transformation

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

• The 1^st component contains the pair

  c#(b(a(a(x1))))	→	c#(x1)	(2)
  c#(b(a(a(x1))))	→	c#(b(a(c(x1))))	(3)

  1.1.1 Reduction Pair Processor with Usable Rules

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

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

  together with the usable rule

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

  →

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

  (1)

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

  c#(b(a(a(x1))))	→	c#(x1)	(2)
  c#(b(a(a(x1))))	→	c#(b(a(c(x1))))	(3)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.