Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/ExIntrod_GM01_L)
The rewrite relation of the following TRS is considered.
|
tail(cons(X)) |
→ |
L |
(1) |
|
incr(nil) |
→ |
nil |
(2) |
|
incr(cons(X)) |
→ |
cons(s(X)) |
(3) |
|
adx(nil) |
→ |
nil |
(4) |
|
adx(cons(X)) |
→ |
incr(cons(X)) |
(5) |
| nats |
→ |
adx(zeros) |
(6) |
| zeros |
→ |
cons(0) |
(7) |
|
head(cons(X)) |
→ |
X |
(8) |
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
|
= |
tail(cons(X)) |
|
→
|
tail(cons(X)) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{X/X}