Termination w.r.t. Q proof of TRS/SK904.11.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, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(0, s(y)) → s(y)
s(+(0, y)) → s(y)

Q is empty.

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

Lexicographic Path Order [19].
Precedence:

+₂ > s₁