Certification Problem

Input (TPDB TRS_Standard/SK90/4.13)

The rewrite relation of the following TRS is considered.

Property / Task

Answer / Result

Proof (by ttt2 @ 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,s(y))

  →

  -#(x,p(s(y)))

  (7)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the linear polynomial interpretation over (4 x 4)-matrices with strict dimension 1 over the naturals

  [p(x1)]	=	0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 · x1 + 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0
  [-#(x1, x2)]	=	0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 · x1 + 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 · x2 + 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  [s(x1)]	=	1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 · x1 + 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

  together with the usable rule

  p(s(x))

  →

  x

  (5)

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

  -#(x,s(y))

  →

  -#(x,p(s(y)))

  (7)

  could be deleted.

  1.1.1.1 P is empty

  There are no pairs anymore.