Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#4.18)
The rewrite relation of the following TRS is considered.
|
a(b(a(b(x)))) |
→ |
b(a(b(a(a(b(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(b(a(a(b(a(b(x'))))))) |
|
→
|
a(b(a(b(a(b(a(a(b(x'))))))))) |
|
→
|
b(a(b(a(a(b(a(b(a(a(b(x'))))))))))) |
|
= |
t2
|
where t2 =
C[t0σ]
and
σ =
{x'/a(a(b(x')))}
and
C = b(☐)