(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(a, f(f(a, x), a)) → f(f(a, f(a, x)), a)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Precedence:
a > f2
Status:
a: multiset
f2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(a, f(f(a, x), a)) → f(f(a, f(a, x)), 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