Termination w.r.t. Q proof of TRS/Rubioprov.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:

ackin(s(X), s(Y)) → u21(ackin(s(X), Y), X)
u21(ackout(X), Y) → u22(ackin(Y, X))

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

ackin(s(X), s(Y)) → u21(ackin(s(X), Y), X)
u21(ackout(X), Y) → u22(ackin(Y, X))

Q is empty.

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

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

[ackin₂, u21_2] > s₁
[ackin₂, u21_2] > [ackout₁, u22_1]

Status:

u22₁: [1]
u21₂: [2,1]
s₁: [1]
ackout₁: [1]
ackin₂: [1,2]