Certification Problem

Input (TPDB TRS_Standard/CiME_04/append)

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

  ifappend#(l1,l2,cons(x,l))	→	append#(l,l2)	(9)
  append#(l1,l2)	→	ifappend#(l1,l2,l1)	(8)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [hd(x1)]	=	0
  [append#(x1, x2)]	=	x1 + 1
  [is_empty#(x1)]	=	0
  [ifappend(x1, x2, x3)]	=	0
  [false]	=	0
  [true]	=	0
  [tl#(x1)]	=	0
  [append(x1, x2)]	=	0
  [tl(x1)]	=	0
  [nil]	=	0
  [is_empty(x1)]	=	0
  [hd#(x1)]	=	0
  [cons(x1, x2)]	=	x2 + 2
  [ifappend#(x1, x2, x3)]	=	x3 + 0

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

  ifappend#(l1,l2,cons(x,l))	→	append#(l,l2)	(9)
  append#(l1,l2)	→	ifappend#(l1,l2,l1)	(8)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.