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.

Recursive path order with status [2].
Quasi-Precedence:
[ackin2, u212] > [ackout1, u221] > s1

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