Certification Problem

Input (TPDB TRS_Standard/Rubio_04/aoto)

The rewrite relation of the following TRS is considered.

f(f(X)) f(g(f(g(f(X))))) (1)
f(g(f(X))) f(g(X)) (2)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
f(f(X)) f(g(f(g(f(X))))) (1)
f(g(f(X))) g(f(X)) (3)

1.1 Bounds

The given TRS is match-(raise)-bounded by 3. This is shown by the following automaton.