Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.4)
The rewrite relation of the following TRS is considered.
f
(
g
(
x
),
x
,
y
)
→
f
(
y
,
y
,
g
(
y
))
(1)
g
(
g
(
x
))
→
g
(
x
)
(2)
Property / Task
Prove or disprove termination.
Answer / Result
No.
Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
t
0
=
f
(
g
(
x
),
x
,
g
(
g
(
x61
)))
→
f
(
g
(
g
(
x61
)),
g
(
g
(
x61
)),
g
(
g
(
g
(
x61
))))
→
f
(
g
(
g
(
x61
)),
g
(
g
(
x61
)),
g
(
g
(
x61
)))
→
f
(
g
(
g
(
x61
)),
g
(
x61
),
g
(
g
(
x61
)))
=
t
3
where t
3
= t
0
σ and σ = {
x61
/
x61
,
x
/
g
(
x61
)}