Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/001)
The rewrite relation of the following TRS is considered.
app
(
app
(
iterate
,
f
),
x
)
→
app
(
app
(
cons
,
x
),
app
(
app
(
iterate
,
f
),
app
(
f
,
x
)))
(1)
The evaluation strategy is outermost
Property / Task
Prove or disprove termination.
Answer / Result
No.
Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
t
0
=
app
(
app
(
iterate
,
f
),
x
)
→
app
(
app
(
cons
,
x
),
app
(
app
(
iterate
,
f
),
app
(
f
,
x
)))
=
t
1
where t
1
= C[t
0
σ] and σ = {
f
/
f
,
x
/
app
(
f
,
x
)} and C =
app
(
app
(
cons
,
x
),
☐
)