Certification Problem
Input (TPDB TRS_Standard/SK90/2.37)
The rewrite relation of the following TRS is considered.
|
and(not(not(x)),y,not(z)) |
→ |
and(y,band(x,z),x) |
(1) |
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
| [and(x1, x2, x3)] |
= |
2 · x1 + 2 · x2 + 2 · x3
|
| [not(x1)] |
= |
2 + 2 · x1
|
| [band(x1, x2)] |
= |
2 · x1 + 1 · x2
|
all of the following rules can be deleted.
|
and(not(not(x)),y,not(z)) |
→ |
and(y,band(x,z),x) |
(1) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.