Certification Problem

Input (TPDB TRS_Standard/SK90/2.58)

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

  g#(a)	→	h#(a,b,a)	(7)
  h#(x,x,y)	→	g#(x)	(6)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [h(x1, x2, x3)]	=	0
  [a]	=	3
  [b]	=	1
  [f(x1, x2)]	=	0
  [h#(x1, x2, x3)]	=	x2 + 1
  [f#(x1, x2)]	=	0
  [g#(x1)]	=	x1 + 0
  [i(x1)]	=	0
  [g(x1)]	=	0
  [i#(x1)]	=	0

  having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pairs

  g#(a)	→	h#(a,b,a)	(7)
  h#(x,x,y)	→	g#(x)	(6)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.