(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[g2, a] > [f1, h2]
Status:
f1: multiset
g2: [2,1]
a: multiset
h2: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(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) TRUE