Certification Problem
Input (TPDB TRS_Standard/AG01/#3.53a)
The rewrite relation of the following TRS is considered.
|
g(x,y) |
→ |
x |
(1) |
|
g(x,y) |
→ |
y |
(2) |
|
f(s(x),y,y) |
→ |
f(y,x,s(x)) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [g(x1, x2)] |
= |
1 · x1 + 1 · x2
|
| [f(x1, x2, x3)] |
= |
2 · x1 + 1 · x2 + 1 · x3
|
| [s(x1)] |
= |
2 + 2 · x1
|
all of the following rules can be deleted.
|
f(s(x),y,y) |
→ |
f(y,x,s(x)) |
(3) |
1.1 Rule Removal
Using the
linear polynomial interpretation over the naturals
| [g(x1, x2)] |
= |
1 + 1 · x1 + 1 · x2
|
all of the following rules can be deleted.
|
g(x,y) |
→ |
x |
(1) |
|
g(x,y) |
→ |
y |
(2) |
1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.