(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y) → h(x, y)
f(x, y) → h(y, x)
h(x, x) → x
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
f2 > h2
Status:
f2: multiset
h2: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(x, y) → h(x, y)
f(x, y) → h(y, x)
h(x, x) → x
(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