Certification Problem
Input (TPDB TRS_Standard/Rubio_04/lescanne)
The rewrite relation of the following TRS is considered.
|
div(X,e) |
→ |
i(X) |
(1) |
|
i(div(X,Y)) |
→ |
div(Y,X) |
(2) |
|
div(div(X,Y),Z) |
→ |
div(Y,div(i(X),Z)) |
(3) |
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
| [div(x1, x2)] |
= |
1 + 2 · x1 + 1 · x2
|
| [e] |
= |
2 |
| [i(x1)] |
= |
2 · x1
|
all of the following rules can be deleted.
|
div(X,e) |
→ |
i(X) |
(1) |
|
i(div(X,Y)) |
→ |
div(Y,X) |
(2) |
|
div(div(X,Y),Z) |
→ |
div(Y,div(i(X),Z)) |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.