Certification Problem

Input (TPDB TRS_Standard/Endrullis_06/quadruple2)

The rewrite relation of the following TRS is considered.

p(p(b(a(x0)),x1),p(x2,x3)) → p(p(b(x2),a(a(b(x1)))),p(x3,x0)) (1)

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
[b(x1)] =
1 0 0
0 0 0
0 0 1
· x1 +
0 0 0
0 0 0
1 0 0
[a(x1)] =
1 0 0
0 0 0
1 1 1
· x1 +
0 0 0
0 0 0
1 0 0
[p(x1, x2)] =
1 0 1
0 0 0
0 0 0
· x1 +
1 1 0
0 0 1
0 0 0
· x2 +
0 0 0
0 0 0
0 0 0
all of the following rules can be deleted.
p(p(b(a(x0)),x1),p(x2,x3)) → p(p(b(x2),a(a(b(x1)))),p(x3,x0)) (1)

1.1 R is empty

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