Termination w.r.t. Q proof of TRS/SK904.05.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:

*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, 1) → x
*(1, y) → y

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

*(x, +(y, z)) → +(*(x, y), *(x, z))
*(+(x, y), z) → +(*(x, z), *(y, z))
*(x, 1) → x
*(1, y) → y

Q is empty.

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

Lexicographic Path Order [19].
Precedence:

*₂ > +₂
1 > +₂