(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:
[g1, a, h3] > b > f2
i1 > f2
Status:
i1: multiset
a: multiset
f2: multiset
g1: [1]
h3: [2,1,3]
b: multiset
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(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