Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/4.34)
The rewrite relation of the following TRS is considered.
|
a(b(x)) |
→ |
b(b(a(a(x)))) |
(1) |
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
|
= |
a(a(b(x'))) |
|
→
|
a(b(b(a(a(x'))))) |
|
→
|
b(b(a(a(b(a(a(x'))))))) |
|
= |
t2
|
where t2 =
C[t0σ]
and
σ =
{x'/a(a(x'))}
and
C = b(b(☐))