Certification Problem
Input (TPDB TRS_Standard/Der95/12)
The rewrite relation of the following TRS is considered.
|
not(not(x)) |
→ |
x |
(1) |
|
not(or(x,y)) |
→ |
and(not(x),not(y)) |
(2) |
|
not(and(x,y)) |
→ |
or(not(x),not(y)) |
(3) |
|
and(x,or(y,z)) |
→ |
or(and(x,y),and(x,z)) |
(4) |
|
and(or(y,z),x) |
→ |
or(and(x,y),and(x,z)) |
(5) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
| prec(not) |
= |
2 |
|
stat(not) |
= |
mul
|
| prec(or) |
= |
0 |
|
stat(or) |
= |
mul
|
| prec(and) |
= |
1 |
|
stat(and) |
= |
mul
|
| π(not) |
= |
[1] |
| π(or) |
= |
[1,2] |
| π(and) |
= |
[1,2] |
all of the following rules can be deleted.
|
not(not(x)) |
→ |
x |
(1) |
|
not(or(x,y)) |
→ |
and(not(x),not(y)) |
(2) |
|
not(and(x,y)) |
→ |
or(not(x),not(y)) |
(3) |
|
and(x,or(y,z)) |
→ |
or(and(x,y),and(x,z)) |
(4) |
|
and(or(y,z),x) |
→ |
or(and(x,y),and(x,z)) |
(5) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.