Certification Problem
Input (TPDB TRS_Standard/Zantema_05/jw27)
The rewrite relation of the following TRS is considered.
|
f(f(a,x),a) |
→ |
f(a,f(f(x,f(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(11,9) |
→ |
10 |
|
f1(10,8) |
→ |
11 |
|
f1(8,13) |
→ |
11 |
|
f1(3,9) |
→ |
10 |
|
f1(9,9) |
→ |
12 |
|
f1(8,11) |
→ |
3 |
|
f1(8,8) |
→ |
9 |
|
f1(12,8) |
→ |
13 |
|
a0
|
→ |
3 |
|
f0(3,3) |
→ |
3 |
The automaton is closed under rewriting as it is compatible.