Certification Problem

Input (TPDB TRS_Standard/Der95/03)

The rewrite relation of the following TRS is considered.

f(f(x)) → g(f(x)) (1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 Rule Removal

Using the Knuth Bendix order with w0 = 1 and the following precedence and weight functions
prec(g) = 0 weight(g) = 2
prec(f) = 1 weight(f) = 2
all of the following rules can be deleted.
f(f(x)) → g(f(x)) (1)

1.1 R is empty

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