Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z101)

The rewrite relation of the following TRS is considered.

a(a(x1)) → b(b(b(x1))) (1)
b(b(b(b(b(x1))))) → a(a(a(x1))) (2)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[b(x1)] = x1 +
8
[a(x1)] = x1 +
13
all of the following rules can be deleted.
a(a(x1)) → b(b(b(x1))) (1)
b(b(b(b(b(x1))))) → a(a(a(x1))) (2)

1.1 R is empty

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