Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex3_2_Luc97_L)
The rewrite relation of the following TRS is considered.
|
sel(0,cons) |
→ |
X |
(1) |
|
sel(s,cons) |
→ |
sel(X,Z) |
(2) |
|
dbl(0) |
→ |
0 |
(3) |
|
dbl(s) |
→ |
s |
(4) |
|
dbls(nil) |
→ |
nil |
(5) |
|
dbls(cons) |
→ |
cons |
(6) |
|
indx(nil) |
→ |
nil |
(7) |
|
indx(cons) |
→ |
cons |
(8) |
| from |
→ |
cons |
(9) |
The evaluation strategy is outermostProperty / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
sel(0,cons) |
|
→
|
sel(0,cons) |
|
= |
t1
|
where t1 =
t0