Certification Problem
Input (TPDB TRS_Standard/Various_04/07)
The rewrite relation of the following TRS is considered.
|
f(x,y) |
→ |
h(x,y) |
(1) |
|
f(x,y) |
→ |
h(y,x) |
(2) |
|
h(x,x) |
→ |
x |
(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) |
= |
[2, 1] |
|
list-extension(h) |
= |
Lex |
| prec(f) |
= |
1 |
|
status(f) |
= |
[2, 1] |
|
list-extension(f) |
= |
Lex |
and the following
Max-polynomial interpretation
| [h(x1, x2)] |
=
|
max(1, 1 + 1 · x1, 1 + 1 · x2) |
| [f(x1, x2)] |
=
|
max(0, 1 + 1 · x1, 1 + 1 · x2) |
all of the following rules can be deleted.
|
f(x,y) |
→ |
h(x,y) |
(1) |
|
f(x,y) |
→ |
h(y,x) |
(2) |
|
h(x,x) |
→ |
x |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.