Termination w.r.t. Q proof of TRS/SK904.01.trs

Termination w.r.t. Q of the following Term Rewriting System could be proven:

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.

↳ QTRS

  ↳ DirectTerminationProof

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.

We use [23] with the following order to prove termination.

Lexicographic path order with status [19].
Quasi-Precedence:

minux₁ > minus₁
minux₁ > +₂

Status:

trivial