Certification Problem

Input (TPDB TRS_Standard/SK90/4.01)

The rewrite relation of the following TRS is considered.

minus(minus(x))	→	x	(1)
minux(+(x,y))	→	+(minus(y),minus(x))	(2)
+(minus(x),+(x,y))	→	y	(3)
+(+(x,y),minus(y))	→	x	(4)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

minux^#(+(x,y))	→	minus^#(y)	(5)
minux^#(+(x,y))	→	minus^#(x)	(6)
minux^#(+(x,y))	→	+^#(minus(y),minus(x))	(7)

1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.