Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_mixed_05/test75)
The rewrite relation of the following TRS is considered.
f
(
0
,
1
,
X
)
→
f
(
g
(
X
,
X
),
X
,
X
)
(1)
g
(
X
,
Y
)
→
X
(2)
g
(
X
,
Y
)
→
Y
(3)
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
(
0
,
1
),
g
(
0
,
1
),
g
(
0
,
1
))
→
f
(
g
(
0
,
1
),
1
,
g
(
0
,
1
))
→
f
(
0
,
1
,
g
(
0
,
1
))
→
f
(
g
(
g
(
0
,
1
),
g
(
0
,
1
)),
g
(
0
,
1
),
g
(
0
,
1
))
→
f
(
g
(
0
,
1
),
g
(
0
,
1
),
g
(
0
,
1
))
=
t
4
where t
4
= t
0