Certification Problem
Input (TPDB TRS_Standard/Der95/20)
The rewrite relation of the following TRS is considered.
|
not(not(x)) |
→ |
x |
(1) |
|
not(or(x,y)) |
→ |
and(not(not(not(x))),not(not(not(y)))) |
(2) |
|
not(and(x,y)) |
→ |
or(not(not(not(x))),not(not(not(y)))) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(and) |
= |
0 |
|
weight(and) |
= |
5 |
|
|
|
| prec(or) |
= |
2 |
|
weight(or) |
= |
5 |
|
|
|
| prec(not) |
= |
3 |
|
weight(not) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
not(not(x)) |
→ |
x |
(1) |
|
not(or(x,y)) |
→ |
and(not(not(not(x))),not(not(not(y)))) |
(2) |
|
not(and(x,y)) |
→ |
or(not(not(not(x))),not(not(not(y)))) |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.