Certification Problem

Input (TPDB TRS_Standard/Rubio_04/lindau)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by NaTT @ 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(X)))	→	c#(X)	(6)
  c#(b(a(X)))	→	c#(c(X))	(7)

  1.1.1 Reduction Pair Processor with Usable Rules

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

  [a(x1)]	=	0 0 1 0 · x1 + 1 1
  [b(x1)]	=	0 1 0 1 · x1 + 1 0
  [c(x1)]	=	0 0 1 1 · x1 + 1 18524
  [c#(x1)]	=	1 0 0 0 · x1 + 0 0
  [e]	=	1 0
  [a#(x1)]	=	0 0
  [b#(x1)]	=	0 0

  together with the usable rules

  c(X)	→	e	(4)
  c(b(a(X)))	→	a(a(b(b(c(c(X))))))	(1)
  b(X)	→	e	(3)
  a(X)	→	e	(2)

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

  c#(b(a(X)))	→	c#(X)	(6)
  c#(b(a(X)))	→	c#(c(X))	(7)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.