(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:
Recursive path order with status [RPO].
Quasi-Precedence:
0 > [app2, plus, s, curry]
add > [app2, plus, s, curry]
Status:
add: multiset
curry: multiset
plus: multiset
app2: [1,2]
s: multiset
0: multiset
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