Certification Problem

Input (TPDB TRS_Standard/Rubio_04/prov)

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

  u21#(ackout(X),Y)	→	ackin#(Y,X)	(5)
  ackin#(s(X),s(Y))	→	ackin#(s(X),Y)	(4)
  ackin#(s(X),s(Y))	→	u21#(ackin(s(X),Y),X)	(3)

  1.1.1 Reduction Pair Processor with Usable Rules

  Using the Max-polynomial interpretation

  [ackin#(x1, x2)]	=	x1 + x2 + 0
  [s(x1)]	=	x1 + 1
  [u21#(x1, x2)]	=	x1 + x2 + 0
  [ackout(x1)]	=	x1 + 1
  [u21(x1, x2)]	=	x1 + 0
  [u22(x1)]	=	x1 + 0
  [ackin(x1, x2)]	=	x2 + 1

  together with the usable rules

  ackin(s(X),s(Y))	→	u21(ackin(s(X),Y),X)	(1)
  u21(ackout(X),Y)	→	u22(ackin(Y,X))	(2)

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

  u21#(ackout(X),Y)	→	ackin#(Y,X)	(5)
  ackin#(s(X),s(Y))	→	ackin#(s(X),Y)	(4)
  ackin#(s(X),s(Y))	→	u21#(ackin(s(X),Y),X)	(3)

  could be deleted.

  1.1.1.1 Dependency Graph Processor

  The dependency pairs are split into 0 components.