Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z049)
The rewrite relation of the following TRS is considered.
|
a(b(a(a(b(b(x1)))))) |
→ |
a(a(b(a(b(b(a(x1))))))) |
(1) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 String Reversal
Since only unary symbols occur, one can reverse all terms and obtains the TRS
|
b(b(a(a(b(a(x1)))))) |
→ |
a(b(b(a(b(a(a(x1))))))) |
(2) |
1.1 Bounds
The given TRS is
match-(raise)-bounded by 1.
This is shown by the following automaton.
-
final states:
{0, 1}
-
transitions:
|
b0(0) |
→ |
0 |
|
b0(1) |
→ |
0 |
|
a0(0) |
→ |
1 |
|
a0(1) |
→ |
1 |
|
a1(0) |
→ |
7 |
|
a1(7) |
→ |
6 |
|
b1(6) |
→ |
5 |
|
a1(5) |
→ |
4 |
|
b1(4) |
→ |
3 |
|
b1(3) |
→ |
2 |
|
a1(2) |
→ |
0 |
|
a1(1) |
→ |
7 |
| 7 |
→ |
6 |