Certification Problem
Input (TPDB TRS_Innermost/Transformed_CSR_innermost_04/Ex25_Luc06_L)
The rewrite relation of the following TRS is considered.
|
f(f(X)) |
→ |
c |
(1) |
| c |
→ |
d |
(2) |
|
h(X) |
→ |
c |
(3) |
The evaluation strategy is innermost.Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Bounds
The given TRS is
match-(raise)-bounded by 2.
This is shown by the following automaton.
-
final states:
{0, 1, 2, 3}
-
transitions:
|
f0(0) |
→ |
0 |
|
f0(1) |
→ |
0 |
|
f0(2) |
→ |
0 |
|
f0(3) |
→ |
0 |
|
c0
|
→ |
1 |
|
d0
|
→ |
2 |
|
h0(0) |
→ |
3 |
|
h0(1) |
→ |
3 |
|
h0(2) |
→ |
3 |
|
h0(3) |
→ |
3 |
|
c1
|
→ |
0 |
|
d1
|
→ |
1 |
|
d2
|
→ |
0 |
| 0 |
→ |
3 |