Certification Problem

Input (TPDB TRS_Standard/SK90/4.08)

The rewrite relation of the following TRS is considered.

*(x,*(y,z)) → *(*(x,y),z) (1)
*(x,x) → x (2)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Rule Removal

Using the linear polynomial interpretation over (3 x 3)-matrices with strict dimension 1 over the naturals
[*(x1, x2)] =
1 0 0
0 1 0
0 0 1
· x1 +
1 1 1
0 1 0
1 1 0
· x2 +
0 0 0
1 0 0
1 0 0
all of the following rules can be deleted.
*(x,*(y,z)) → *(*(x,y),z) (1)

1.1 Rule Removal

Using the Weighted Path Order with the following precedence and status
prec(*) = 0 status(*) = [2, 1] list-extension(*) = Lex
and the following Max-polynomial interpretation
[*(x1, x2)] = max(0, 0 + 1 · x1, 0 + 1 · x2)
all of the following rules can be deleted.
*(x,x) → x (2)

1.1.1 R is empty

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