Certification Problem

Input (TPDB TRS_Standard/AG01/#3.15)

The rewrite relation of the following TRS is considered.

average(s(x),y) average(x,s(y)) (1)
average(x,s(s(s(y)))) s(average(s(x),y)) (2)
average(0,0) 0 (3)
average(0,s(0)) 0 (4)
average(0,s(s(0))) s(0) (5)

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(0) = 1 weight(0) = 1
prec(average) = 2 weight(average) = 0
prec(s) = 0 weight(s) = 4
all of the following rules can be deleted.
average(s(x),y) average(x,s(y)) (1)
average(x,s(s(s(y)))) s(average(s(x),y)) (2)
average(0,0) 0 (3)
average(0,s(0)) 0 (4)
average(0,s(s(0))) s(0) (5)

1.1 R is empty

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