Certification Problem
Input (TPDB TRS_Standard/SK90/4.37)
The rewrite relation of the following TRS is considered.
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
1.1 Bounds
The given TRS is
match-(raise)-bounded by 2.
This is shown by the following automaton.
-
final states:
{0, 1}
-
transitions:
|
a0(0) |
→ |
0 |
|
a0(1) |
→ |
0 |
|
b0(0) |
→ |
1 |
|
b0(1) |
→ |
1 |
|
b1(0) |
→ |
2 |
|
a1(2) |
→ |
0 |
|
b1(1) |
→ |
2 |
|
b1(2) |
→ |
2 |
|
b2(2) |
→ |
3 |
|
a2(3) |
→ |
0 |
|
b1(3) |
→ |
2 |
|
b2(3) |
→ |
3 |