Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#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)
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
(
g
(
x'
)),
g
(
g
(
x'
)),
g
(
g
(
x''
)))
→
f
(
g
(
g
(
x'
)),
g
(
x'
),
g
(
g
(
x''
)))
→
f
(
g
(
g
(
x''
)),
g
(
g
(
x''
)),
g
(
g
(
g
(
x''
))))
=
t
2
where t
2
= t
0
σ and σ = {
x'
/
x''
,
x''
/
g
(
x''
)}