Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#4.2)
The rewrite relation of the following TRS is considered.
f
(
g
(
x
),
s
(
0
),
y
)
→
f
(
y
,
y
,
g
(
x
))
(1)
g
(
s
(
x
))
→
s
(
g
(
x
))
(2)
g
(
0
)
→
0
(3)
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
=
f
(
g
(
s
(
0
)),
g
(
s
(
0
)),
g
(
s
(
0
)))
→
f
(
g
(
s
(
0
)),
s
(
g
(
0
)),
g
(
s
(
0
)))
→
f
(
g
(
s
(
0
)),
s
(
0
),
g
(
s
(
0
)))
→
f
(
g
(
s
(
0
)),
g
(
s
(
0
)),
g
(
s
(
0
)))
=
t
3
where t
3
= t
0