Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_AG01/#4.3)
The rewrite relation of the following TRS is considered.
f
(
g
(
x
,
y
),
x
,
z
)
→
f
(
z
,
z
,
z
)
(1)
g
(
x
,
y
)
→
x
(2)
g
(
x
,
y
)
→
y
(3)
Property / Task
Prove or disprove termination.
Answer / Result
No.
Proof (by AProVE @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
f
#
(
g
(
x
,
y
),
x
,
z
)
→
f
#
(
z
,
z
,
z
)
(4)
It remains to prove infiniteness of the resulting DP problem.
1.1 Loop
The following loop proves infiniteness of the DP problem.
t
0
=
f
#
(
g
(
x'
,
y
),
g
(
x'
,
y
),
g
(
x'
,
y
))
→
R
f
#
(
g
(
x'
,
y
),
x'
,
g
(
x'
,
y
))
→
P
f
#
(
g
(
x'
,
y
),
g
(
x'
,
y
),
g
(
x'
,
y
))
=
t
2
where t
2
= t
0