Certification Problem
Input (TPDB TRS_Standard/Mixed_TRS/5)
The rewrite relation of the following TRS is considered.
|
f(x,f(a,a)) |
→ |
f(f(x,a),x) |
(1) |
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:
{2, 1}
-
transitions:
|
a1
|
→ |
4 |
|
f1(1,4) |
→ |
10 |
|
f1(2,4) |
→ |
5 |
|
f1(10,1) |
→ |
1 |
|
f1(5,2) |
→ |
1 |
|
a0
|
→ |
2 |
|
a2
|
→ |
11 |
|
f0(1,2) |
→ |
1 |
|
f0(2,1) |
→ |
1 |
|
f0(1,1) |
→ |
1 |
|
f0(2,2) |
→ |
1 |
|
f2(10,11) |
→ |
12 |
|
f2(12,10) |
→ |
1 |
The automaton is closed under rewriting as it is compatible.