Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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

app(id, x) → x
app(plus, 0) → id
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

[app₂, s] > plus
[id, 0]

Status:

plus: multiset
app₂: [1,2]
s: multiset
0: multiset
id: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

app(id, x) → x
app(plus, 0) → id
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))

(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE