Certification Problem
Input (TPDB TRS_Standard/SK90/2.59)
The rewrite relation of the following TRS is considered.
|
f(g(x),y,y) |
→ |
g(f(x,x,y)) |
(1) |
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(f) |
= |
1 |
|
status(f) |
= |
[1, 2, 3] |
|
list-extension(f) |
= |
Lex |
| prec(g) |
= |
0 |
|
status(g) |
= |
[1] |
|
list-extension(g) |
= |
Lex |
and the following
Max-polynomial interpretation
| [f(x1, x2, x3)] |
=
|
max(0, 2 + 1 · x1, 1 + 1 · x2, 0 + 1 · x3) |
| [g(x1)] |
=
|
1 + 1 · x1
|
all of the following rules can be deleted.
|
f(g(x),y,y) |
→ |
g(f(x,x,y)) |
(1) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.