Certification Problem

Input (TPDB TRS_Standard/Rubio_04/koen)

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 2 components.

• The 1^st component contains the pair

  f#(X,c(X))

  →

  f#(s(X),X)

  (5)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [a(x1)]	=	0
  [s(x1)]	=	1
  [c(x1)]	=	2
  [f(x1, x2)]	=	0
  [f#(x1, x2)]	=	x1 + x2 + 0

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

  f#(X,c(X))

  →

  f#(s(X),X)

  (5)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.

• The 2^nd component contains the pair

  f#(s(X),X)

  →

  f#(X,a(X))

  (4)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [a(x1)]	=	1
  [s(x1)]	=	2
  [c(x1)]	=	2
  [f(x1, x2)]	=	0
  [f#(x1, x2)]	=	x1 + x2 + 0

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

  f#(s(X),X)

  →

  f#(X,a(X))

  (4)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.