Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/PALINDROME_nosorts-noand_FR)
The rewrite relation of the following TRS is considered.
|
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
|
__(X,nil) |
→ |
X |
(2) |
|
__(nil,X) |
→ |
X |
(3) |
|
U11(tt) |
→ |
U12(tt) |
(4) |
|
U12(tt) |
→ |
tt |
(5) |
|
isNePal(__(I,__(P,I))) |
→ |
U11(tt) |
(6) |
|
activate(X) |
→ |
X |
(7) |
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(nil) |
= |
3 |
|
weight(nil) |
= |
1 |
|
|
|
| prec(tt) |
= |
1 |
|
weight(tt) |
= |
4 |
|
|
|
| prec(U11) |
= |
0 |
|
weight(U11) |
= |
1 |
|
|
|
| prec(U12) |
= |
6 |
|
weight(U12) |
= |
0 |
|
|
|
| prec(isNePal) |
= |
4 |
|
weight(isNePal) |
= |
2 |
|
|
|
| prec(activate) |
= |
5 |
|
weight(activate) |
= |
1 |
|
|
|
| prec(__) |
= |
2 |
|
weight(__) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
|
__(X,nil) |
→ |
X |
(2) |
|
__(nil,X) |
→ |
X |
(3) |
|
U11(tt) |
→ |
U12(tt) |
(4) |
|
U12(tt) |
→ |
tt |
(5) |
|
isNePal(__(I,__(P,I))) |
→ |
U11(tt) |
(6) |
|
activate(X) |
→ |
X |
(7) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.