Certification Problem
Input (TPDB TRS_Relative/Relative_05/rt2-8)
The relative rewrite relation R/S is considered where R is the following TRS
|
f(act,y) |
→ |
f(el(nact),y) |
(1) |
|
f(x,nact) |
→ |
f(x,act) |
(2) |
| act |
→ |
el(nact) |
(3) |
|
l(el(x)) |
→ |
el(l(x)) |
(4) |
|
el(r(x)) |
→ |
r(el(x)) |
(5) |
and S is the following TRS.
| nact |
→ |
l(nact) |
(6) |
| nact |
→ |
r(nact) |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves that R/S is not relative terminating.
| t0
|
= |
el(nact) |
|
→S
|
el(r(nact)) |
|
→R
|
r(el(nact)) |
|
= |
t2
|
where t2 =
C[t0]
and
C = r(☐)