YES Termination w.r.t. Q proof of Zantema_05_jw47.ari

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(f(a, f(x, a)), a) → f(a, f(f(x, a), a))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Knuth-Bendix order [KBO] with precedence:
a > f2

and weight map:

a=1
f_2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

f(f(a, f(x, a)), a) → f(a, f(f(x, a), a))


(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) YES