Certification Problem
Input (TPDB TRS_Relative/Relative_05/rt1-4)
The relative rewrite relation R/S is considered where R is the following TRS
|
f(el(x),y) |
→ |
f(x,el(y)) |
(1) |
and S is the following TRS.
|
l(el(x)) |
→ |
el(l(x)) |
(2) |
|
f(x,y) |
→ |
f(l(x),y) |
(3) |
|
el(r(x)) |
→ |
r(el(x)) |
(4) |
|
f(x,y) |
→ |
f(x,r(y)) |
(5) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
| prec(f) |
= |
1 |
|
stat(f) |
= |
lex
|
| prec(el) |
= |
0 |
|
stat(el) |
= |
lex
|
| π(f) |
= |
[1,2] |
| π(el) |
= |
[1] |
| π(l) |
= |
1 |
| π(r) |
= |
1 |
all of the following rules can be deleted.
|
f(el(x),y) |
→ |
f(x,el(y)) |
(1) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.