Certification Problem

Input (TPDB TRS_Standard/SK90/2.50)

The rewrite relation of the following TRS is considered.

a(b(x)) → b(b(a(x))) (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(a(x)) → a(b(b(x))) (2)

1.1 Rule Removal

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

1.1.1 R is empty

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