Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/PALINDROME_nosorts-noand_L)
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) |
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
| [__(x1, x2)] |
= |
2 + 1 · x1 + 1 · x2
|
| [nil] |
= |
2 |
| [U11(x1)] |
= |
2 + 2 · x1
|
| [tt] |
= |
2 |
| [U12(x1)] |
= |
2 · x1
|
| [isNePal(x1)] |
= |
2 · x1
|
all of the following rules can be deleted.
|
__(X,nil) |
→ |
X |
(2) |
|
__(nil,X) |
→ |
X |
(3) |
|
U11(tt) |
→ |
U12(tt) |
(4) |
|
U12(tt) |
→ |
tt |
(5) |
|
isNePal(__(I,__(P,I))) |
→ |
U11(tt) |
(6) |
1.1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(__) |
= |
0 |
|
weight(__) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.