Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex25_Luc06_L)
The rewrite relation of the following TRS is considered.
|
f(f(X)) |
→ |
c |
(1) |
| c |
→ |
d |
(2) |
|
h(X) |
→ |
c |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Rule Removal
Using the
Weighted Path Order with the following precedence and status
| prec(h) |
= |
0 |
|
status(h) |
= |
[1] |
|
list-extension(h) |
= |
Lex |
| prec(d) |
= |
0 |
|
status(d) |
= |
[] |
|
list-extension(d) |
= |
Lex |
| prec(c) |
= |
2 |
|
status(c) |
= |
[] |
|
list-extension(c) |
= |
Lex |
| prec(f) |
= |
0 |
|
status(f) |
= |
[1] |
|
list-extension(f) |
= |
Lex |
and the following
Max-polynomial interpretation
| [h(x1)] |
=
|
max(1, 3 + 1 · x1) |
| [d] |
=
|
max(2) |
| [c] |
=
|
max(2) |
| [f(x1)] |
=
|
2 + 1 · x1
|
all of the following rules can be deleted.
|
f(f(X)) |
→ |
c |
(1) |
| c |
→ |
d |
(2) |
|
h(X) |
→ |
c |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.