Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z098)

The rewrite relation of the following TRS is considered.

a(a(a(b(b(b(x1)))))) b(b(b(b(a(a(a(a(x1)))))))) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
b(b(b(a(a(a(x1)))))) a(a(a(a(b(b(b(b(x1)))))))) (2)

1.1 Bounds

The given TRS is match-(raise)-bounded by 5. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.