Termination w.r.t. Q proof of TRS/SK902.17.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:

sum(0) → 0
sum(s(x)) → +(sum(x), s(x))
sum1(0) → 0
sum1(s(x)) → s(+(sum1(x), +(x, x)))

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

sum(0) → 0
sum(s(x)) → +(sum(x), s(x))
sum1(0) → 0
sum1(s(x)) → s(+(sum1(x), +(x, x)))

Q is empty.

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

Recursive path order with status [2].
Quasi-Precedence:

sum₁ > 0 > s₁
sum₁ > +₂ > s₁
sum1₁ > 0 > s₁
sum1₁ > +₂ > s₁

Status:

sum₁: multiset
+₂: multiset
0: multiset
s₁: multiset
sum1₁: [1]