Certification Problem
Input (TPDB TRS_Standard/SK90/2.36)
The rewrite relation of the following TRS is considered.
|
implies(not(x),y) |
→ |
or(x,y) |
(1) |
|
implies(not(x),or(y,z)) |
→ |
implies(y,or(x,z)) |
(2) |
|
implies(x,or(y,z)) |
→ |
or(y,implies(x,z)) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(not) |
= |
0 |
|
weight(not) |
= |
1 |
|
|
|
| prec(implies) |
= |
2 |
|
weight(implies) |
= |
0 |
|
|
|
| prec(or) |
= |
1 |
|
weight(or) |
= |
1 |
|
|
|
all of the following rules can be deleted.
|
implies(not(x),y) |
→ |
or(x,y) |
(1) |
|
implies(not(x),or(y,z)) |
→ |
implies(y,or(x,z)) |
(2) |
|
implies(x,or(y,z)) |
→ |
or(y,implies(x,z)) |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.