Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex4_Zan97_Z)

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

  sel#(s(X),cons(Y,Z))

  →

  sel#(X,activate(Z))

  (9)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 40652
  [activate(x1)]	=	1
  [activate#(x1)]	=	0
  [f(x1)]	=	x1 + 2
  [0]	=	1
  [sel#(x1, x2)]	=	x1 + 0
  [sel(x1, x2)]	=	0
  [n__f(x1)]	=	x1 + 3
  [f#(x1)]	=	0
  [g#(x1)]	=	0
  [cons(x1, x2)]	=	x1 + 3
  [g(x1)]	=	x1 + 40651

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

  sel#(s(X),cons(Y,Z))

  →

  sel#(X,activate(Z))

  (9)

  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

  g#(s(X))

  →

  g#(X)

  (13)

  1.1.2 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [s(x1)]	=	x1 + 41064
  [activate(x1)]	=	1
  [activate#(x1)]	=	0
  [f(x1)]	=	x1 + 2
  [0]	=	1
  [sel#(x1, x2)]	=	0
  [sel(x1, x2)]	=	0
  [n__f(x1)]	=	x1 + 3
  [f#(x1)]	=	0
  [g#(x1)]	=	x1 + 0
  [cons(x1, x2)]	=	x1 + 3
  [g(x1)]	=	x1 + 41063

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

  g#(s(X))

  →

  g#(X)

  (13)

  could be deleted.

  1.1.2.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.