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(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic path order with status [LPO].
Precedence:

0 > app₂
s > app₂
add > plus > app₂
add > curry > app₂

Status:

app₂: [1,2]
plus: []
0: []
s: []
curry: []
add: []

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

app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) → app(app(f, x), y)
add → app(curry, plus)

(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