YES
Termination Proof
Termination Proof
by ttt2 (version ttt2 1.15)
Input
The rewrite relation of the following TRS is considered.
Proof
1 Rule Removal
Using the
linear polynomial interpretation over (3 x 3)-matrices with strict dimension 1
over the arctic semiring over the integers
| [b(x1)] |
= |
| 0 |
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
·
x1 +
|
-∞
|
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
|
| [a(x1)] |
= |
·
x1 +
|
-∞
|
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
|
-∞
|
-∞
|
-∞
|
|
all rules could be removed.
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.