Certification Problem
Input (TPDB TRS_Standard/AProVE_04/improved_usable2)
The rewrite relation of the following TRS is considered.
|
f(a,x) |
→ |
f(g(x),x) |
(1) |
|
h(g(x)) |
→ |
h(a) |
(2) |
|
g(h(x)) |
→ |
g(x) |
(3) |
|
h(h(x)) |
→ |
x |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Bounds
The given TRS is
roof-(raise)-bounded by 2.
This is shown by the following automaton.
-
final states:
{5}
-
transitions:
| 8 |
→ |
5 |
|
a1
|
→ |
8 |
|
f1(7,5) |
→ |
5 |
|
h1(8) |
→ |
5 |
|
f0(5,5) |
→ |
5 |
|
a0
|
→ |
5 |
|
g2(8) |
→ |
5 |
|
g2(8) |
→ |
7 |
|
h0(5) |
→ |
5 |
|
g1(8) |
→ |
5 |
|
g1(5) |
→ |
7 |
|
g1(5) |
→ |
5 |
|
g0(5) |
→ |
5 |
The automaton is closed under rewriting as it is compatible.