Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

minus(minus(x)) → x
minux(+(x, y)) → +(minus(y), minus(x))
+(minus(x), +(x, y)) → y
+(+(x, y), minus(y)) → x

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Precedence:

minux₁ > +₂ > minus₁

Status:

minus₁: multiset
minux₁: multiset
+₂: [1,2]

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

minus(minus(x)) → x
minux(+(x, y)) → +(minus(y), minus(x))
+(minus(x), +(x, y)) → y
+(+(x, y), minus(y)) → x

(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE