Certification Problem
Input (TPDB TRS_Innermost/Transformed_CSR_innermost_04/Ex6_Luc98_L)
The rewrite relation of the following TRS is considered.
|
first(0,X) |
→ |
nil |
(1) |
|
first(s(X),cons(Y)) |
→ |
cons(Y) |
(2) |
|
from(X) |
→ |
cons(X) |
(3) |
The evaluation strategy is innermost.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(0) |
= |
0 |
|
weight(0) |
= |
1 |
|
|
|
| prec(nil) |
= |
1 |
|
weight(nil) |
= |
2 |
|
|
|
| prec(s) |
= |
2 |
|
weight(s) |
= |
1 |
|
|
|
| prec(cons) |
= |
3 |
|
weight(cons) |
= |
1 |
|
|
|
| prec(from) |
= |
4 |
|
weight(from) |
= |
1 |
|
|
|
| prec(first) |
= |
5 |
|
weight(first) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
first(0,X) |
→ |
nil |
(1) |
|
first(s(X),cons(Y)) |
→ |
cons(Y) |
(2) |
|
from(X) |
→ |
cons(X) |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.