Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/PEANO_nosorts_FR)
The rewrite relation of the following TRS is considered.
|
and(tt,X) |
→ |
activate(X) |
(1) |
|
plus(N,0) |
→ |
N |
(2) |
|
plus(N,s(M)) |
→ |
s(plus(N,M)) |
(3) |
|
activate(X) |
→ |
X |
(4) |
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(tt) |
= |
0 |
|
weight(tt) |
= |
1 |
|
|
|
| prec(0) |
= |
3 |
|
weight(0) |
= |
1 |
|
|
|
| prec(activate) |
= |
1 |
|
weight(activate) |
= |
1 |
|
|
|
| prec(s) |
= |
4 |
|
weight(s) |
= |
1 |
|
|
|
| prec(and) |
= |
2 |
|
weight(and) |
= |
0 |
|
|
|
| prec(plus) |
= |
5 |
|
weight(plus) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
and(tt,X) |
→ |
activate(X) |
(1) |
|
plus(N,0) |
→ |
N |
(2) |
|
plus(N,s(M)) |
→ |
s(plus(N,M)) |
(3) |
|
activate(X) |
→ |
X |
(4) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.