Certification Problem

Input (TPDB TRS_Standard/Mixed_TRS/1)

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

  f#(a,f(a,x))

  →

  f#(a,f(x,f(f(a,a),a)))

  (4)

  1.1.1 Reduction Pair Processor with Usable Rules

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

  [a]	=	1 2
  [f(x1, x2)]	=	0 1 0 0 · x1 + 0 1 0 0 · x2 + 7629 1
  [f#(x1, x2)]	=	x2 + 0 0

  together with the usable rule

  f(a,f(a,x))

  →

  f(a,f(x,f(f(a,a),a)))

  (1)

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

  f#(a,f(a,x))

  →

  f#(a,f(x,f(f(a,a),a)))

  (4)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.