Certification Problem
Input (TPDB SRS_Standard/Bouchare_06/09)
The rewrite relation of the following TRS is considered.
|
b(a(a(x1))) |
→ |
a(x1) |
(1) |
|
a(a(a(x1))) |
→ |
b(b(b(x1))) |
(2) |
|
b(b(x1)) |
→ |
a(b(a(x1))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by matchbox @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
a(b(a(a(a(x1))))) |
|
→
|
a(b(b(b(b(x1))))) |
|
→
|
a(b(b(a(b(a(x1)))))) |
|
→
|
a(a(b(a(a(b(a(x1))))))) |
|
→
|
a(a(a(b(a(x1))))) |
|
→
|
b(b(b(b(a(x1))))) |
|
→
|
b(b(a(b(a(a(x1)))))) |
|
→
|
b(b(a(a(x1)))) |
|
→
|
a(b(a(a(a(x1))))) |
|
= |
t8
|
where t8 =
t0σ
and
σ =
{x1/x1}