Certification Problem

Input (TPDB SRS_Standard/Zantema_04/z012)

The rewrite relation of the following TRS is considered.

a(x1) b(x1) (1)
a(b(x1)) b(c(a(x1))) (2)
b(x1) c(x1) (3)
c(b(x1)) a(x1) (4)

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(c) = 3 weight(c) = 0
prec(b) = 0 weight(b) = 1
prec(a) = 1 weight(a) = 1
all of the following rules can be deleted.
a(x1) b(x1) (1)
a(b(x1)) b(c(a(x1))) (2)
b(x1) c(x1) (3)
c(b(x1)) a(x1) (4)

1.1 R is empty

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