Certification Problem
Input (TPDB TRS_Relative/Relative_05/rt3-5)
The relative rewrite relation R/S is considered where R is the following TRS
|
f(g(f(x))) |
→ |
f(g(g(g(f(x))))) |
(1) |
and S is the following TRS.
|
f(x) |
→ |
g(g(f(g(g(x))))) |
(2) |
|
g(x) |
→ |
g(g(f(g(g(x))))) |
(3) |
|
g(x) |
→ |
g(g(x)) |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
matrix interpretations of dimension 3 with strict dimension 1 over the integers
| [f(x1)] |
= |
+ · x1
|
| [g(x1)] |
= |
+ · x1
|
all of the following rules can be deleted.
|
f(g(f(x))) |
→ |
f(g(g(g(f(x))))) |
(1) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.