Certification Problem
Input (TPDB TRS_Standard/Der95/04)
The rewrite relation of the following TRS is considered.
|
f(f(x)) |
→ |
g(f(x)) |
(1) |
|
g(g(x)) |
→ |
f(x) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [f(x1)] |
= |
1 · x1 + 3 |
| [g(x1)] |
= |
1 · x1 + 2 |
all of the following rules can be deleted.
|
f(f(x)) |
→ |
g(f(x)) |
(1) |
|
g(g(x)) |
→ |
f(x) |
(2) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.