Certification Problem

Input (TPDB TRS_Standard/SK90/4.38)

The rewrite relation of the following TRS is considered.

g(f(x,y),z) f(x,g(y,z)) (1)
g(h(x,y),z) g(x,f(y,z)) (2)
g(x,h(y,z)) h(g(x,y),z) (3)

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(h) = 2 weight(h) = 0
prec(g) = 3 weight(g) = 0
prec(f) = 0 weight(f) = 0
all of the following rules can be deleted.
g(f(x,y),z) f(x,g(y,z)) (1)
g(h(x,y),z) g(x,f(y,z)) (2)
g(x,h(y,z)) h(g(x,y),z) (3)

1.1 R is empty

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