Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex6_9_Luc02c_L)
The rewrite relation of the following TRS is considered.
2nd
(
cons
(
X
))
→
2nd
(
cons1
(
X
,
X1
))
(1)
2nd
(
cons1
(
X
,
cons
(
Y
)))
→
Y
(2)
from
(
X
)
→
cons
(
X
)
(3)
Property / Task
Prove or disprove termination.
Answer / Result
No.
Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
t
0
=
2nd
(
cons
(
X
))
→
2nd
(
cons1
(
X
,
2nd
(
cons
(
X
))))
=
t
1
where t
1
= C[t
0
σ] and σ = {
X1
/
2nd
(
cons
(
X
))} and C =
2nd
(
cons1
(
X
,
☐
))