Certification Problem

Input (TPDB TRS_Standard/SK90/4.08)

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

  *#(x,*(y,z))	→	*#(*(x,y),z)	(4)
  *#(x,*(y,z))	→	*#(x,y)	(3)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [*#(x1, x2)]	=	x1 + x2 + 0
  [*(x1, x2)]	=	x1 + x2 + 1

  together with the usable rules

  *(x,*(y,z))	→	*(*(x,y),z)	(1)
  *(x,x)	→	x	(2)

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

  *#(x,*(y,z))

  →

  *#(x,y)

  (3)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 1 component.

  • The 1^st component contains the pair

    *#(x,*(y,z))

    →

    *#(*(x,y),z)

    (4)

    1.1.1.1.1 Reduction Pair Processor with Usable Rules

    Using the Max-polynomial interpretation

    [*#(x1, x2)]	=	x2 + 0
    [*(x1, x2)]	=	x1 + x2 + 1

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

    *#(x,*(y,z))

    →

    *#(*(x,y),z)

    (4)

    could be deleted.

    1.1.1.1.1.1 Dependency Graph Processor

    The dependency pairs are split into 0 components.