Certification Problem
Input (TPDB TRS_Standard/Zantema_05/jw21)
The rewrite relation of the following TRS is considered.
|
f(a,f(x,a)) |
→ |
f(f(x,f(f(a,a),a)),a) |
(1) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Bounds
The given TRS is
match-(raise)-bounded by 1.
This is shown by the following automaton.
-
final states:
{3}
-
transitions:
|
a1
|
→ |
8 |
|
f1(9,8) |
→ |
10 |
|
f1(3,10) |
→ |
11 |
|
f1(11,8) |
→ |
3 |
|
f1(9,10) |
→ |
12 |
|
f1(8,8) |
→ |
9 |
|
f1(11,10) |
→ |
11 |
|
f1(12,8) |
→ |
11 |
|
a0
|
→ |
3 |
|
f0(3,3) |
→ |
3 |
The automaton is closed under rewriting as it is compatible.