Certification Problem
Input (TPDB TRS_Outermost/Zantema_08/outermost_gr)
The rewrite relation of the following TRS is considered.
|
f(x,a) |
→ |
f(x,b) |
(1) |
| b |
→ |
a |
(2) |
|
f(a,x) |
→ |
a |
(3) |
|
f(b,x) |
→ |
a |
(4) |
|
f(f(x,y),z) |
→ |
a |
(5) |
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
|
= |
f(x,b) |
|
→
|
f(x,a) |
|
→
|
f(x,b) |
|
= |
t2
|
where t2 =
t0