YES Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

a(x0) b(x0)

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)] =
3 0 0
0 0 0
0 0 0
· x1 +
-∞ -∞ -∞
-∞ -∞ -∞
-∞ -∞ -∞
all rules could be removed.

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.