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 AProVE @ termCOMP 2023)

1 Rule Removal

Using the Knuth Bendix order with w0 = 1 and the following precedence and weight functions
prec(minus) = 0 weight(minus) = 2
prec(minux) = 2 weight(minux) = 4
prec(+) = 1 weight(+) = 0
all of the following rules can be deleted.
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)

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.